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This paper revisits the notion of a convenience yield in the context of modern option pricing theory. We show that, with a proper specification of the cash flows to holding a commodity, a convenience yield as a separate concept does not exist. Rather, a convenience yield is best viewed as a label given to certain cash flows generated from storing a commodity. In particular, it represents the payoffs from two embedded options which we call the scarcity and usage options. This characterization of a convenience yield is new to the literature, although consistent with its existing interpretations and uses.

The Treasury bond futures contract has known embedded options, namely the quality option that permits the short side to deliver the cheapest bond and the three timing options that permit the short side to deliver at the most favorable time. In this article, the authors use a two-factor Cox–Ingersoll–Ross term structure model calibrated to the Treasury yield curve to compute the futures price with the forward pricing methodology. Using weekly futures prices from January 1992 through December 2000, they discover a substantial difference between the risk-neutral expectation used in the literature and the forward expectation that requires a recursive algorithm. The authors find that the correctly estimated futures price with the quality option is 1% lower on average than the futures price estimated in the literature. They also estimate the end-of-month timing option to be 23 basis points on average. This indicates that the end-of-month timing option value has been overestimated in the literature because of a wrongly estimated quality option value.

The dramatically growing disproportion between the value of corporate assets and market valuation has resulted in a well-researched schism between strategic management and financial theory. Options theory provides a potent tool to resolve this issue. We propose a model which is consistent with both the Resource- and Contractual-Based Theories of the Firm and which demonstrates that corporate strategy can be perceived as a portfolio of embedded and real options. We further argue that embedded options typically serve as hedging instruments for real options which enhances their value and should be a major consideration when assessing the structure and form of contracts. Special emphasis is granted to human capital and the contractual arrangements through which firms purchase its product. Human capital is the key resource for the processes of real-options discovery and strategy-setting, both of which constitute the essential part of a modern firm's value.

Life insurance products have profit sharing features in combination with guarantees. These so-called embedded options are often dependent on or approximated by forward swap rates. In practice, these kinds of options are mostly valued by Monte Carlo simulations. However, for risk management calculations and reporting processes, lots of valuations are needed. Therefore, a more efficient method to value these options would be helpful. In this paper analytical approximations are derived for these kinds of options, based on an underlying multi-factor Gaussian interest rate model. The analytical approximation for options with direct payment is almost exact while the approximation for compounding options is also satisfactory. In addition, the proposed analytical approximation can be used as a control variate in Monte Carlo valuation of options for which no analytical approximation is available, such as similar options with management actions. Furthermore, it’s also possible to construct analytical approximations when returns on additional assets (such as equities) are part of the profit sharing rate.

Over the last years the valuation of life insurance contracts using concepts from financial mathematics has become a popular research area for actuaries as well as financial economists. In particular, several methods have been proposed of how to model and price participating policies, which are characterized by an annual interest rate guarantee and some bonus distribution rules. However, despite the long terms of life insurance products, most valuation models allowing for sophisticated bonus distribution rules and the inclusion of frequently offered options assume a simple Black-Scholes setup and, in particular, deterministic or even constant interest rates. We present a framework in which participating life insurance contracts including predominant kinds of guarantees and options can be valuated and analyzed in a stochastic interest rate environment. In particular, the different option elements can be priced and analyzed separately. We use Monte Carlo and discretization methods to derive the respective values. The sensitivity of the contract and guarantee values with respect to multiple parameters is studied using the bonus distribution schemes as introduced in Bauer et al. (2006). Surprisingly, even though the value of the contract as a whole is only moderately affected by the stochasticity of the short rate of interest, the value of the different embedded options is altered considerably in comparison to the value under constant interest rates. Furthermore, using a simplified asset portfolio and empirical parameter estimations, we show that the proportion of stock within the insurer’s asset portfolio substantially affects the value of the contract.

In the flrst part of the paper, we consider the wide range of extrapolative stochastic mortality models that have been proposed over the last 15 to 20 years. A number of models that we consider are framed in discrete time and place emphasis on the statistical aspects of modelling and forecasting. We discuss how these models can be evaluated, compared and contrasted. We also discuss a discrete-time market model that facilitates valuation of mortality-linked contracts with embedded options. We then review several approaches to modelling mortality in continuous time. These models tend to be simpler in nature, but make it possible to examine the potential for dynamic hedging of mortality risk. Finally, we review a range of flnancial instruments (traded and over-the-counter) that could be used to hedge mortality and risk. Some of these, such as mortality swaps, already exist, while others anticipate future developments in the market.

This paper proposes new measures that provide us with the level of sequential arbitrage in bond markets. All the measures vanish in an arbitrage-free market and all of them are positive otherwise. Each measure is generated by a dual pair of optimization problems. Primal problems permit us to compute optimal sequential arbitrage strategies, if available. Each dual problem generates a concrete proxy for the term structure of interest rates. The set of proxies allows us to obtain the exact market price of any bond and may measure several effects. For instance, the credit risk spread of nondefault free bonds, or the embedded option price of callable or extendible bonds. The developed theory has been tested empirically. Research partially supported by Welzia Management SGIIC, RD_Sistemas, Comunidad Autónoma de Madrid (Spain), Grant s-0505/tic/000230, and MEyC (Spain), Grant SEJ2006-15401-C04-03 Publicado

The analysis of network effects in technology-based networks continues to be of significant managerial importance in e-commerce and traditional IS operations. Competitive strategy, economics and IS researchers share this interest, and have been exploring technology adoption, development and product launch contexts where understanding the issues is critical. This article examines settings involving countervailing and complementary network effects, which act as drivers of business value at several levels of analysis: the industry or market level, the firm or process level, the individual or product level, and the technology level. It leverages real options analysis for managerial decision-making under uncertainty across these contexts. We also identify a set of real options--compatibility, sponsorship and ownership option--which are unique to these settings, and which provide a template for managerial thinking and analysis when it is possible to delay an investment decision. We employ a hybrid jump-diffusion process to model countervailing and complementary network effects from the perspective of a user or a firm joining a network. We also do this from the perspective of a network developer. Our analysis shows that when countervailing and complementary network effects occur in the same network technology context, they give rise to real option value effects that may be used to control or modify the valuation trajectory of a network technology. The option value of waiting in these contexts jumps when the related business environment experiences shocks. Further, we find that the functional relationship between network value and the option value is not linear, and that taking into account a risk premium may not always result in a risk-neural investment. We also provide a managerial decision-making template through the different kinds of deferral options that we identify for this IT analysis context.

A new prepayment model is developed, which improves the modeling of the borrowers decision process by incorporating an occupation-time derivative in the valuation framework of a fixed-rate mortgage. This option-theoretic mortgage valuation model is based on stochastic house-price and interest-rate models, and requires a particularly subtle technique to incorporate a new type of occupation-time derivative, where the barrier (which activates the derivative) is in the value process and not the underlying process (as it is in standard occupation-time derivatives). This new model simulates a delay in prepayment by the borrower (beyond the time simple ruthless prepayment dictates), thus increasing the value of the mortgage to the lender, compared to the value gained using more basic models. This allows for a more advanced borrower decision process, where a rational exercise structure is retained in a modified form. Empirical evidence supports this theory, which should be beneficial for accurate mortgage-backed security pricing. The results in this paper explore thoroughly the effect on the mortgage value of a delay in prepayment by the borrower on the embedded options held and on the insurance component.

This paper applies contingent claim analysis to value pension contracts for real-life collective pension plans with intergenerational risk sharing and offering db-like benefits. We rewrite the balance sheet of such a pension fund as an aggregate of embedded generational options. This implies that a pension fund is a zero-sum game in value terms, so any policy change inevitably leads to value transfers between generations. We explore intergenerational value transfers that may arise from a plan redesign or from changes in funding policy and risk sharing rules. We develop a stochastic framework which accounts for time-varying investment opportunities and computes the embedded generational options. Changes in the values of the generational options enable us to evaluate the impact of policy modifications in the pension contract with respect to intergenerational transfers and redistribution. We find that a switch to a less risky asset mix is beneficial to elderly members at the expense of younger members who lose value. A reallocation of risk bearing from a plan with flexible contributions and fixed benefits to a plan with fixed contributions and flexible benefits leads to value redistribution from older plan members to younger ones.

Interest rate contingent claims such as swaptions, caps and floors, callable bonds, mortgage-backed securities and many balance sheet items are subject to vega risk. Vega risk is defined as the interest rate volatility risk of an interest rate contingent claim, the uncertain change in volatility affecting the embedded option value. Since these contingent claims9 values are affected by the interest rate volatilities and these volatilities are stochastic, any hedging strategies, or more generally risk management, of these interest rate contingent claims should take the vega risk into account. However, based on market conventions, the interest rate volatilities are represented by a set of approximately 120 implied volatilities of the at-the-money swaptions over a range of tenors and expiration dates, called the volatility surface. And this volatility surface is stochastic. Controlling for these vega risks poses a significant practical challenge to managing these large number of risk sources. Thus far, there is a lack of solutions. This article introduces the key rate vega measures to manage the vega risks. Furthermore, the article shows how the key rate vega measures can depict the option risks embedded in an interest rate contingent claim and how they can be used for hedging a mortgage interest-only strip using key rate vega measures and key rate duration measures together, as an illustration of broader applications of the key rate vega measures.

In this paper we propose a discrete-time model with fixed maximum time to maturity of traded bonds. At each trading time, a bond matures and a new bond is introduced in the market, such that the number of traded bonds is constant. The entry price of the newly issued bond depends on the prices of the bonds already traded and a stochastic term independent of the existing bond prices. Hence, we obtain a bond market model for the reinvestment risk, which is present in practice, when hedging long term contracts. In order to determine optimal hedging strategies we consider the criteria of super-replication and risk-minimization.

Most bank deposits contain an embedded option which permits the depositor to withdraw funds at will. Demand deposits generally allow costless withdrawal, while time deposits often require payment of an early withdrawal penalty. Managing the risk that depositors will exercise their withdrawal option is an important aspect of input pricing. This paper acknowledges the threat of deposit withdrawal and then solves for the optimal structure of bank deposit rates.

Under the common assumption of constant interest rates, we show that penalties for early termination of a lease are often structured in such a way that the cancellation option embedded in consumer automotive leases has little value. Furthermore, our estimates drawn from a sample of three popular car models over 1990 to 2000 indicate that the stand-alone value of the lease-end purchase option is, on average, about 16% of the market value of underlying used vehicles, or about $1,462 per contract. Finally, we examine the sensitivity of our option value estimates to model parameters and default risk. RECENT YEARS HAVE WITNESSED A DRAMATIC GROWTH in the leasing of automobiles. For instance, overall industry sales data indicate that about a third of the new vehicles and trucks sold in the United States are leased (Hendel and Lizzeri (2002), and Miller (1995)), and the Federal Reserve Board survey of family finances reports that the use of leased vehicles by individuals (nonbusiness consumers) has risen from 2.9% to 5.8% over the 1992 to 2001 period (Azicorbe, Kennickell, and Moore (2003)). Consumer automobile lease contracts for new cars often include two embedded options that are not associated with a typical debt contract. The first is a cancellation option that allows the lessee to terminate the lease early. The second is a European call option, which gives the lessee the right, but not the obligation, to purchase the leased (used) vehicle at the scheduled termination of the lease at a predetermined exercise price. Both of these options are simple examples of real options because the asset underlying these options is a used car, that is, a real asset; however, these options constitute a special case of real options since they are embedded in the lease contract, which is a financial (credit) instrument. Theoretical analyses of lease contracts show that the cancellation option is quite valuable (Schallheim and McConnell (1985)). With respect to the purchase option, Hendel and Lizzeri (2002) argue that they can play an important role in

This article describes how entrepreneurs can use external uncertainty, ambiguity, and turmoil to advantage by reframing them as hidden opportunities. A three-step process discusses how and why. First, future uncertainties need to be analyzed and then synthesized into a limited number of possible scenarios that are beyond the control of the company. Second, the current strategy should be stress-tested against these scenarios and adjusted in case it results in misfortune in one or more of the scenarios. The basic idea is to separate parts of the strategy that are robust across scenarios (meaning they work well in each scenario) from those strategy components that are fragile (meaning they work well in just one or two scenarios but not all of them). Third, investments in the fragile elements need to be approached from an options perspective in as far as possible. Rather than bet fully on fragile elements of the plan, entrepreneurs need to retain enough flexibility to adjust the plan if and when necessary. This means carefully monitoring and scanning those external events that could affect the strategy, either to exercise the embedded options in the strategy or to pull the plug on losing investments. The key is to manage these three-step process as a dynamic compass for navigating the future. Keywords: scenario planning; flexible strategies; real options; dynamic monitoring; scanning; robustness tests; uncertainty; ambiguity; strategic compass; key success factors; biases

The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. For DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio of assets and we develop a discrete model that optimally selects the reference portfolio to minimise the cost of a guarantee. While the relation DB-DC is typically viewed as a binary one, the model can be used to price a wide range of guarantees creating a continuum between DB and DC. Integrating guarantee pricing with asset allocation decision is useful to both pension fund managers and regulators. The former are given a yardstick to assess if a given asset portfolio is fit-for-purpose; the latter can assess differences of specific reference funds with respect to the optimal one, signalling possible cases of moral hazard. We develop the model and report numerical results to illustrate its uses.

In this chapter we present a discussion on convertible bonds, which have become popular hybrid financial instruments. Convertible bonds are financial instruments that give the bondholders the right, without imposing an obligation, to convert the bond into underlying security, usually common stocks, under conditions illustrate in the indenture at the time of issue. The hybrid characteristic defines the traditional valuation approach as the sum of two components: the option-free bond and an embedded option (call option). The option element makes the valuation not easy, above all in pricing term sheets with specific contract clauses as the inclusion of soft calls, put options and reset features. The chapter shows practical examples of valuation in which financial advisors and investment banks adopts in different contexts.

Under the background of “Internet +”, strategic emerging enterprises must make themselves embedded in the enterprise value network to gain sustainable and healthy development, but it is difficult for decision maker to make the embedded choice effective. From the perspective of “cognitive dissonance” and “non-economics”, this article analyzed the reasons why the value network embedded option induced the loss of business performance in strategic emerging enterprises and the countermeasures to reduce loss, so as to provide theoretical support and method guidance for reducing the loss.

German Abstract: Die Integration von Migranten, die Qualifizierung von Kindern mit Lernschwachen oder die Resozialisierung wiederholt straffallig gewordener Jugendlicher sind Beispiele von immer neuen gesellschaftlichen Herausforderungen. In vielen Landern fehlen hierzu "staatliche Auffangnetze". Aber auch in Deutschland, einem der letzten verbliebenen Sozialstaaten in der Welt, tut man sich immer schwerer, hier die passenden Leistungen anzubieten. Kreativitat und Innovation werden in diesem System aber kaum finanziert. Hier soll der Social Impact Bond Abhilfe schaffen. Kurz gesagt, zahlt der staatliche Trager von Sozialmasnahmen an private Geldgeber das von ihnen uberlassene Kapital nebst Zinsen, sofern ein bestimmter vorher festgelegter Mindesterfolg mit den finanzierten Sozialleistungen vom Kapitalnehmer nachgewiesen wird. Wird das Ziel nicht erreicht, mussen die Anleger mit Ertragseinbusen rechnen oder vollig auf eine Rendite verzichten. Das Prinzip soll die Effizienz in der Umsetzung von Sozialleistungen erhohen und zu innovativen Leistungsangeboten anregen.Social Impact Bonds haben mit einer herkommlichen Anleihe wie beispielsweise einer Bundesanleihe nichts gemeinsam. Es handelt sich vielmehr um eine offentlich-private Partnerschaft und ist fur Anleger nicht auf den ersten Blick zu durchschauen. Es sind komplexe Vertragsgebilde mit vielen darin eingebundenen Parteien, die unterschiedliche Aufgaben ubernehmen. Chancen und Risiken von Social Impact Bonds haben daruber hinaus hohe Ahnlichkeiten mit Derivaten, vor allem Optionen. Dies ist das Ergebnis einer Analyse von 14 in den USA und Grosbritannien eingefuhrten Social Impact Bonds. Ans Tageslicht gefordert wurden vielversprechende neue, unterschiedliche Ansatze um vor allem die Wirksamkeit von Sozialleistungen bei den adressierten Zielgruppen zu erhohen. Trotz aller Vielfalt gelang es, zwei Obergruppen von Social Impact Bonds auszumachen, worunter verschiedene am Finanzmarkt vorfindbare Bonds eingeordnet werden konnten. Im nachsten Schritt wurde erhoben, auf welche Chancen und Risiken sich Anleger beim Erwerb solcher Bonds einlassen. Die Analyse forderte etliche versteckte Eigenschaften zu Tage, die exotischen Derivaten aus dem Optionsbereich ahneln. Vor allem wurden Strukturen entdeckt, die auf eine enge Verwandtschaft von Social Impact Bonds zu sog. Digitaloptionen schliesen lassen. Bei solchen Optionen gewinnt der Anleger entweder einen bestimmten Geldbetrag oder verliert seinen Einsatz (zumindest teilweise). Ferner wurde deutlich, dass Social Impact Bonds ganz spezielle Risikoquellen haben, wenn die unter dem Dach des Bonds arbeitenden Partner wie die offentliche Hand einzelne Sozialdienstleister, Datenmanager etc. nicht optimal miteinander zusammenar-beiten. English Abstract: Social Impact Bonds have emerged out of nowhere when some years ago in Great Britain a prototype, the Peterborough prison bond, was constructed and attracted a lot of awareness in financial markets as well as in many public authorities of other countries. Currently the number of new Social Impact Bonds around the world has increased in only a few years to more than 60 and their growth rates are above average. Thus the financing of social services in several countries is experiencing new perspectives by the issuance of such bonds. Beside the very general attributes of such bonds as financial instruments that pay a return to investors depending on the success of the financed social enterprise or project, little is known about their conventional parameters of a capital market theoretical based valuation, i.e. return and risks.The working paper tackles some of these aspects and is organized two folded: In the first part the very nature of Social Impact Bonds as representatives of impact investing related financial contracts is clarified and serves as a basis for a following systematic categorization. On a sample of 14 in the US and the UK issued Social Impact Bonds two general categories are derived, that can serve as frames for differently modified prototypes. The analysis uncovers that Social Impact Bonds represent a very complex nexus of contracts between very different parties like public authorities, social services providers, investors and enablers. The different individual goals of each of these parties, special information sets available for each of them and intransparencies among them can create very special behavioral risks. This part of the analysis demonstrates that Social Impact Bonds have nothing in common with bonds in the manner of straight bonds or related types, which usually can be found in capital markets. Social Impact Bonds stand much closer to public private partnerships than to traditional lender-borrower relationships. As Social Impact Bonds pay due to the success of the financed social activity they at first glance seem to incorporate contingent claim related components. If the financed project works well with respect to the predetermined impact parameters and quantitative targets, the investor can expect a payment of earnings. If the project fails to achieve the targets, the investor bears in parts the loss as his earnings out of the bond will be cut or in extreme completely omitted. Such a construction in many of the analyzed bonds in practice inspires assumptions of a derivative related structure of such bonds. The second part of the paper picks up the idea of a contingent claim related financial instrument. It is analyzed how Social Impact Bonds can be understood as financial instruments with embedded options. The analysis uncovered option related structures inside a Social Impact Bonds consisting of very special features. Contrary to the plain vanilla world of financial options Social Impact Bonds differ in two aspects:1. Social Impact Bonds operate in a setting of cash flow streams that are generated by a real project and not by a financial instrument. That brings such bonds closer to real options as they also operate with non-financial underlyings as they refer to future cash flow streams of real investment projects. Each single Social Impact Bond requires a careful individual analysis of its option structures and their classification compared to financial options.2. A first classification by analyzing the UK Peterborough Prison Bonds unveiled structures of exotic options and among them predominantly digital options. Referring to the before clarified contractual relationships among the parties of a Social Impact Bond and the embodied informational and behavioral uncertainties, the different nature of stochastic compared to plain vanilla financial options is demonstrated. As it is explained in the paper, the stochastic processes of the generated cash flow in a Social Impact Bond and yet one of the most important value driver of an option is dominated by behavioral uncertainty and only to a very minor part influenced by the usual stochastic processes of financial market based prices. The normal distribution function of stochastic processes therefore seems to be inadequate to determine the risky part of a Social Impact Bond's value. The results of the working paper should to be understood as a kick off of following analysis that attempt to evaluate single Social Impact Bonds according to their special nature as contingent claims in a real project and related cash flow setting. A growing body of politicians, social service providers and representatives of the civil society favor Social Impact Bonds as innovative instruments to overcome financial shortages in public budgets or to gain more efficiency in the supply of social services. In some countries like the US and the UK the issuance of Social Impact Bonds gains momentum and identifies many new fields for their operations. Investors are often foundations that are willing to cover first losses of financed social ventures. At the moment they are not demanding a rational based evaluation of such bonds according to the standard principles of capital market theory based modeling. But time seems to be ripe to formulate adequate valuation methods to make risk and return inside a Social Impact Bonds transparent and to calculate the fair values of such bonds. As could be observed in the past in other segments of financial markets such a progress stimulates the evolution of new financial instruments and make markets more liquid.

This manuscript is program documentation for a model to create a trinomial stock price tree with mean reversion to price convertible bonds and convertible preferred stock.

The finance literature has long recognized the existence of embedded put options within mortgage contracts, such as a prepayment option and a walk-away default option. This Article identifies a previously unrecognized option embedded in residential mortgages: a mortgagor’s unilateral option to increase total leverage on the collateral property through junior liens irrespective of existing mortgagees’ wishes. We term this the “leverage option.” We show how the leverage option was created as an unintended consequence of a federal law enacted to deal with seller financing arrangements that prevailed during the inflationary economy of the 1970s. The leverage option was of little importance until the housing bubble in the 2000s, as homeowners massively increased their leverage using second-lien mortgages. We demonstrate the problems that the leverage option causes for lenders, for homeowners (who pay for it, regardless of whether they want it), for regulators, and for the economy at large. We propose a discrete legal change that will convert the leverage option from being a mandatory embedded option to a bargained-for, unembedded option that will enable efficient pricing and force the information about total mortgage market leverage that is necessary for both effective market oversight.

This chapter is an analytical review of callable and putable bonds, which like convertible securities have an embedded option. Bonds with embedded options are debt instruments that give the right to redeem the bond before maturity. As we know, the yield to maturity represents the key measure of bond’s return. The calculation of the return is particularly easy for conventional bonds because the redemption date is known with certainty, as their value. In contrast, for callable bonds, but also for other bonds as putable and sinking fund bonds, the redemption date is not known with certainty because the bonds can be redeemed before maturity. In this chapter, we illustrate the pricing of bonds with embedded options adopting the binomial tree model, recalling the concepts of interest-rate structure provided in Chapters 3 and 4. The analysis of callable bond yield using the option-adjusted spread (OAS) technique is also provided, with an illustration of OAS calculation for a hypothetical callable bond and treasury bond.

The search for derivative contracts with complex features can also be explained as the market’s attempt to elude the restrictions imposed by the law on money loans. This is an undesirable effect of anti-usury rules. It can be added to the one mentioned by Montesquieu and Adam Smith, who pointed out that usury increases with the severity of the prohibition, since the lender indemnifies himself for the risk he runs of suffering the penalty.In this paper we look at some of the ways in which derivative contracts can be used to circumvent anti-usury provisions and conceal money loans made at exorbitant rates.After examining the simplest cases, we will consider more complex contracts, such as swaps with embedded options, which are often used in dealings between banks and municipalities. Our thesis is that, in all these cases, in order to detect usury, we have to calculate the contracts’ option-adjusted yields.

In this chapter, we discuss how financial engineering and option pricing principles can be used to value equity and equity-linked products. We first review the structural models of default and show how they can be used to link bond, CDS, and equity markets. We discuss the different uses of the basic Merton (1974) model to calculate the value of equity, to back out implied credit spreads, or to back out an implied equity volatility. We show how the Merton model is applied in practice to inform capital structure arbitrage strategies. Next, we introduce another class of bonds with embedded options in the form of convertible bonds. Convertible bonds can be decomposed into a straight debt component and a call option and we show how the decomposition can be used for so-called convertible bond arbitrage strategies. We discuss the sources of profits in capital structure and convertible bond arbitrage strategies and contract the role implied volatility and draw conclusions about the relative riskiness of the two classes of strategies. Finally we discuss warrants and uses of convertible bonds in practice.

The risk management of non-maturing account positions in a bank's balance like savings deposits or certain types of loans is complicated by the embedded options that clients may exercise. In addition to the usual interest rate risk, there is also uncertainty in the timing and amount of future cash flows. Since the corresponding volume risk cannot directly be hedged, the account must be replicated by a portfolio of instruments with explicit maturities. This paper introduces a multistage stochastic programming model that determines an optimal replicating portfolio from scenarios for future outcomes of the relevant risk factors: Market rates, client rates and volume of the non-maturing account. The weights for the allocation of new tranches are frequently adjusted to latest observations of the latter. A case study based on data of a real deposit position demonstrates that the resulting dynamic portfolio provides a significantly higher margin at lower risk compared to a static benchmark.

PurposeThis paper aims to identify the imbedded option value in price of auctioned land in Hong Kong, and to propose a more accurate valuation method in predicting land price.Design/methodology/approachBased on records of land auctions and property transactions during two periods of very different market conditions, land prices are estimated using the traditional hedonic pricing method as well as the option model modified from Quigg. The results are compared to deduce whether there is any imbedded option value, thus concluding whether the option model facilitates a more accurate valuation of land prices.FindingsThis study concludes that land auction prices have embedded option value in waiting to develop land. Option premiums increase with implied volatilities, which go up during market downturns, suggesting that developers place higher value on the option to develop during recessions.Research limitations/implicationsThe accuracy of the analysis may have been compromised by the limited number of land auctions conducted and the difficulties in inferring the value of multi‐ownership residential buildings from sample transactions of their constituent individual units. Future research will benefit from a larger sample of transactions.Practical implicationsThis paper illustrates that real option models provide the property industry with a valuation tool that addresses the concern arising from the irreversibility of investment decisions.Originality/valueThe study finds out the option premiums of vacant land in Hong Kong, lending empirical support to the application of option‐based models for more accurate land valuation under different market conditions.

Mortgage backed securities (MBS) have embedded options that are dependent on the primary mortgage rate, since this is what homeowners use to make their exercise decision. In valuing MBS in uncertain rate environments, practitioners have traditionally assumed that the primary mortgage rate has a fixed spread to a benchmark interest rate (such as the 10-year Treasury). This naive method is actually inconsistent with the OAS methodology used to price MBS and has performed poorly. In this article the authors present the Citigroup Mortgage Option-Adjusted Term Structure (MOATS) model to derive the mortgage rate in any interest rate scenario. MOATS assumes that the OAS of the current-coupon mortgage is constant and thus projects mortgage rates by taking into account the optionality embedded in the mortgage rate itself. This article gives a detailed description of the MOATS methodology and examines the underlying assumptions. Empirical studies show that the assumptions embedded in MOATS are reasonable and that MOATS outperforms traditional mortgage rate models.

Long-term contracts may contain valuable embedded options. I develop an alternative approach to traditional discounted cash flow (DCF) analysis for valuing the profits that are lost when a long-term contract is breached, resulting in the loss of potentially valuable options. One recent example concerns the much publicized supervisory goodwill contracts, some of which were scheduled to expire more than 30 years from the time the US government breached them. I illustrate the contingent-claims approach using this example. I develop a contingent-claims damages model and use it to measure the lost profits damages that two thrifts - California Federal Bank and Glendale Federal Bank - suffered when the US government extinguished supervisory goodwill and prematurely terminated their long-dated goodwill options. The same analytical approach can be adapted to value other opportunities lost due to moral hazard risk.

In this paper we propose a valuation and hedging strategy for a guaranteed minimal rate of return on a mix fund, which participates in both bonds and stocks. For the case where a fixed amount of money is invested, we show that a European put option on the mix fund replicates the cash flows of this guarantee at all times and using the arbitrage-free pricing methodology, the market value of the guarantee can be obtained explicitly. Using historical data, we show that modeling the correlation between equity and bond returns is of fundamental importance when the stochastic nature of the term structure of interest rates is taken into account. For this model we define a hedging strategy which shows how the dependency of the option on the changing yield of the bond fund can be hedged away using mix fund contracts. We also show how Monte Carlo methods can be used to analyze the case where the guarantee is given on periodically invested fixed amounts of money instead of one single payment.

This paper analyzes some features of non-callable convertible bonds with reset clauses via both analytic and Monte Carlo simulation approaches. Assume that the underlying stock receives no dividends and that it has credit risk of the issuer. We mean by reset that the conversion price is adjusted downwards if the underlying stock price does not exceed pre-specified prices. Reset convertibles are usually issued when the outlook for the issuer is unfavorable. The price of any convertible bonds can be approximately viewed as a sum of values of an otherwise identical non-convertible bond plus an embedded option to convert the bond into the underlying stock. In this paper, we first develop an exact formula for the conversion option value of the European riskless convertible in the classical Black–Scholes–Merton framework. It is shown by Monte Carlo simulation that conversion option value estimates of the American risky convertible are located in a certain region defined by this formula. From estimates of the conversion probability, it is also shown that there exists an optimal reset time in the latter half of the trading interval.

This article presents a contingent claim valuation of a callable convertible bond with the issuer's credit risk. The optimal call, voluntary conversion, and bankruptcy strategies are jointly determined by shareholders and bondholders to maximize the equity value and the bond value, respectively. This model not only incorporates tax benefits, bankruptcy costs, refunding costs, and a call notice period, but also takes account of the issuer's debt size and structure. The numerical results show that the predicted optimal call policies are generally consistent with recent empirical findings; therefore, calling convertible bonds too late or too early can be rational. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:895–922, 2006

Newly introduced government-subsidized pension products in Germany are required to contain a promise by the seller to provide a “money-back guarantee” at the end of the term. The client is also given the right to stop paying premiums at any time (paid-up option). In this case, the amount of all premiums paid must also be guaranteed by the seller at maturity, no matter when the client stopped paying the premiums. Previous analyses of guarantees in such government-subsidized pension products have ignored this additional option. Within a generalized Black/Scholes framework, we analyze the value of the paid-up option for different products, market scenarios, and client behavior. Our results indicate that the paid-up option significantly increases the value of the money-back guarantee. Furthermore, we find that reducing volatility by shifting the client's assets from stocks to bonds as maturity approaches is a suitable means of reducing the risk arising from the “pure” money-back guarantee but much less effective in reducing the risk arising from the paid-up option. The Geneva Risk and Insurance Review (2006) 31, 43–60. doi:10.1007/s10713-006-9467-9

A firm issues a convertible bond. At each subsequent time, the bondholder must decide whether to continue to hold the bond, thereby collecting coupons, or to convert it to stock. The bondholder wishes to choose a conversion strategy to maximize the bond value. Subject to some restrictions, the bond can be called by the issuing firm, which presumably acts to maximize the equity value of the firm by minimizing the bond value. This creates a two-person game. We show that if the coupon rate is below the interest rate times the call price, then conversion should precede call. On the other hand, if the dividend rate times the call price is below the coupon rate, call should precede conversion. In either case, the game reduces to a problem of optimal stopping.

We analyze the effect various delivery options embedded in commodity futures contracts have on the futures price. The two embedded options considered are the timing and location options. We show that early delivery is always optimal when only a timing option is present, but not so when joint options are present. The estimates of the combined options are much smaller than the comparable estimates for the timing option alone. The average value of the joint option is about 5% of the average basis on the first day of the maturity month. This suggests that joint options can increase deliverable supplies while potentially having only a small effect on basis behavior.

This paper reviews the developments in reporting of traditional embedded value and summarises some of the reasons why this is now undergoing change. It considers the purpose of an embedded value calculation and the effect of differing attitudes to risk. It comments on the recently developed European Embedded Value Principles and sets out the main areas where scope remains to apply judgement.The paper proposes the market-consistent embedded value framework as a way forward to help provide guidance in some of these areas, in particular on the choice of discount rate and on calibration of stochastic techniques used to value embedded options and guarantees. The paper recognises that market-consistent embedded values are in relative infancy and sets out areas for possible future development.

The credit derivatives market, widely regarded as the fastest growing sector of the derivatives industry, is estimated at over $5 trillion in average outstanding notional principal worldwide. Credit default swaps account for approximately 73% of the market. Options on credit default swaps—known as CDS swaptions—have recently become popular among end users. CDS swaptions come in two general varieties: calls and puts written on CDS, and cancelable CDS. A cancelable CDS includes an embedded option to terminate a CDS contract (an embedded CDS swaption). The authors describe credit default swaptions and their uses in creating synthetic collateralized debt obligations, and illustrate accessible valuation models.

The asset allocation is a crucial decision for pension funds, and this paper analyses the economic factors which determine this choice. The analysis proceeds on the basis that, in the absence of taxation, risk sharing and default insurance, the asset allocation between equities and bonds is indeterminate and governed by the risk/return preferences of the trustees and the employer. If the employing company and its shareholders are subject to taxation, there is a tax advantage in a largely bond allocation. Risk sharing between the employer and the employees often means that one group favours a high equity allocation, while the other favours a low equity allocation. Underpriced default insurance creates an incentive for a high equity allocation. When taxation, risk sharing and underpriced default insurance are all present, it is concluded that the appropriate asset allocation varies with the circumstances of the scheme; but that a high equity allocation is probably inappropriate for many private sector pension schemes.

This paper examines the methodology and assumptions of Ashton, D., Cooke, T., Tippett, M., Wang, P. (2004) employing recursion value η as an explanatory single-variable in a model of the firm, first introduced by Ashton, D., Cooke, T., Tippett, M., in (2003). A qualitative analysis of all of their numerical findings is given together with an indication of how more useful is the tool of special function theory, here requiring confluent hyper-geometric functions associated with the Merton-style valuation equation A justification and a wider interpretation of their model and findings is offered: these come from inclusion of strictly convex dissipating frictions arising either as insurance costs, replacement costs of funds paid out, or of debt service, and from the inclusion of alternative adaptation options embedded in the equity value of a firm; these predict not only a J-shaped equity curve, but also, under the richer modelling assumption, a snake-like curve that may result from financial frictions like insurance. These ‘smirks’ in the equity curve may be empirically tested. It is shown that the inclusion of frictions in dividend selection (e.g. the signalling costs of Bhattacharya, 1979) leads to an optimal dividend payout of αη that is a constant coupon for an interval of η values preceded by an interval in which α = r; this is at variance with the ACTW model where the exogeneous assumption of a constant a is made.

Contingent claims theory has shown that because of limited liability in bankruptcy, there are embedded options in the plain vanilla stock, bonds, and other securities issued by a firm that affect their values. When a firm issues claims that are themselves options on some underlying asset, the various sources of optionality interact with one another. For example, if the written option gets too deep in the money, the firm will have to default on its obligation. This places an effective cap on the potential payoff to the option holder. The impact on the value of subordinated debt becomes particularly complex. In this article, Episcopos clarifies how the values of corporate securities are affected when a firm’s capital structure includes a significant short option position.

Danish mortgage loans have several features that make them interesting: Short-term revolving adjustable-rate mortgages are available, as well as fixed-rate, 10-, 20- or 30-year annuities that contain embedded options (call and delivery options). The decisions faced by a mortgagor are therefore non-trivial, both in terms of deciding on an initial mortgage, and in terms of managing (rebalancing) it optimally. We propose a two-factor, arbitrage-free interest-rate model, calibrated to observable security prices, and implement on top of it a multi-stage, stochastic optimization program with the purpose of optimally composing and managing a typical mortgage loan. We model accurately both fixed and proportional transaction costs as well as tax effects. Risk attitudes are addressed through utility functions and through worst-case (min–max) optimization. The model is solved in up to 9 stages, having 19,683 scenarios. Numerical results, which were obtained using standard soft- and hardware, indicate that the primary determinant in choosing between adjustable-rate and fixed-rate loans is the short–long interest rate differential (i.e., term structure steepness), but volatility also matters. Refinancing activity is influenced by volatility and, of course, transaction costs.

This paper considers a class of leases with indexed rents subject to a floor. Such leases have an upward-only flavour to them, although not in exactly the same sense as in the traditional upward-only institutional lease. After deriving a general result, three empirically important cases are considered: a modified upward-only lease, the Swedish standard contract for commercial leases and the percentage lease. Analytical results and numerical examples are used to illustrate how the leases relate to other contract types.

A firm issues a convertible bond. At each subsequent time, the bondholder must decide whether to continue to hold the bond, thereby collecting coupons, or to convert it to stock. The firm may at any time call the bond. Because calls and conversions often occur far from maturity, it is not unreasonable to model this situation with a perpetual convertible bond, i.e., a convertible coupon-paying bond without maturity. This model admits a relatively simple solution, under which the value of the perpetual convertible bond, as a function of the value of the underlying firm, is determined by a nonlinear ordinary differential equation.

Several earlier theoretical studies on the optimal issuer's calling policy of a convertible bond suggest that the issuer should call the bond as soon as the conversion value exceeds the call price. However, empirical studies on actual cases of calling by convertible bond issuers reveal that firms “delayed” calling their convertible bonds until the conversion value well exceeded the call price. In this paper, we construct valuation algorithms that price risky convertible bonds with embedded option features. In particular, we examine the impact of the soft call and hard call constraints, notice period requirement and other factors on the optimal issuer's calling policy. Our results show that the critical stock price at which the issuer should optimally call the convertible bond depends quite sensibly on these constraints and requirements. The so-called “delayed call phenomena” may be largely attributed to the underestimation of the critical call price due to inaccurate modeling of the contractual provisions. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:513–532, 2004

This examination of the pricing performance of a reduced-form convertible bond valuation model uses a recent sample of monthly U.S. convertible bond prices observed over January 2001–September 2002. Recent U.S. data help us understand the particular market. The model produces prices that are consistently lower than observed market prices when the embedded conversion option is in the money and higher than observed market prices when the conversion option is out of the money. Evidence from the sample suggests that the deep out-of-the-money bias is not related to the theoretical model9s performance but rather the result of the fact that convertible bonds with low conversion value seem to be generally underpriced so much that their prices often imply negative embedded option values.

Fair valuation of insurance contracts, and of options embedded in them, is an important, incompletely understood issue. With the coming IAS insurance contract standard, the valuation of liabilities in life insurance is due to a drastic change. We present a computationally tractable model for fair valuation of participating life insurance contracts with given, almost arbitrary bonus policies. Unlike traditional valuation methods, our model captures several essential features of participating life insurance contracts, such as fair values of interest rate guarantees and of various bonus policies. In the model, fair value of life insurance contracts is understood as the arbitrage free price in the presence of liquid markets for liabilities. In addition to numerical results, the model gives solutions in closed form.

In the framework of the structural approach of bond pricing, we extend the Fujita–Ishizaka model by considering more realistic payoffs. The payoff to the bondholder at time of default, provided that default occurs prior to maturity, depends on the firm value at time of default. We also find the new measure with the advantage to calculate the value of bond and its financial interpretation. In addition, we present some numerical exmaples.

Traditional and standard discounted cash flow valuation techniques are unable to deal with a variety of options contained in lease contracts. In the United Kingdom the most important embedded option is the upward-only rent review. This becomes more valuable to the landlord in an era of low demand and low inflation, as nominal market rents are more likely to fall. Lease contracts are freely negotiated between landlord and tenant, and alternative forms of rent review clause would fundamentally change the investment characteristics of property. Many other less common options also exist in lease contracts and these create further valuation difficulties. It is essential that property valuation techniques be developed that explicitly value the options in lease contracts.