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The Singapore Savings Bonds (SSB) is a unique investment program offered by the Singapore government whereby retail investors can earn risk-free tax-free step-up interest closely matched to Treasury bond rates for up to 10 years and can redeem on any business day prior to maturity without any early redemption penalty. This study analyses the unique design of the SSB and provides a valuation of the Bermudan option for early redemption that is embedded in the SSB. The Black–Derman–Toy model is used to build the interest rate tree, and an iterative method is employed to avoid arbitrary specification of the pre-determined short rate volatility function. This bespoke Bermudan option can have changing strike prices over time. It also has a novel characteristic whereby the value of exercise to a buyer need not equal to the cost of being exercised to a seller. Better understanding of embedded options within government savings bonds leads to innovative designs that may encourage effective citizens’ savings.

This study addresses interest rate sensitivity of emerging market corporate debt. Previous research suggests that interest rate sensitivity of corporate bonds depends on residual maturity of issues, creditworthiness of issuers, embedded options and other idiosyncratic factors. However, the dependence of interest rate sensitivity on phases of the business cycle has not received an appropriate academic attention. This paper provides empirical evidence and theoretical interpretation of a dichotomy of interest rate sensitivity across the phases of the cycle, and sheds light on how credit spreads respond to interest rates. The historical span of the research covers the period of 2004–2016. The fndings imply that hedging interest rate risk ought to be a dynamic process and take into consideration where the economy is positioned in the current business cycle. This research provides important insights on the nature of interest rate sensitivity, capable of enhancing fnancial stability and improving efciency of fnancial system. info:eu-repo/semantics/publishedVersion

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then - unlike the case of asset portfolios - take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.

In recent years, with the rapid increase of the business volume of housing mortgage loans of commercial banks, the risk of prepayment is increasingly exposed. Prepayment will have a great impact on the duration and convexity of housing mortgage loans of commercial banks and then bring difficulties to the asset liability management of banks. Therefore, empirical research on the changes of duration and convexity of housing mortgage loans caused by prepayment when the market interest rate changes is of great significance for commercial banks to manage interest rate risk exposure. Based on the analysis of the option characteristics of prepayable housing mortgage loan, the CIR model with GARCH(1, 1) is selected to describe the interest rate change path, and the computer simulation method is used to calculate OAS and then calculate the effective duration and effective convexity of housing mortgage loan under different prepayment rates, so as to understand the interest rate risk of housing mortgage loan in the presence of embedded option.

This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. We use the Ho and Lee (HL) and Black, Derman, and Toy (BDT) consistent interest rate models. In addition, specific interest rate measures that consider the contingent cash-flow structure of these coupon-bearing bonds must be computed. In our empirical analysis, we obtained evidence that effective duration and effective convexity depend primarily on the level of the forward interest rate and volatility. In addition, the higher the interest rate change and the lower the volatility, the greater the differences in pricing of these bonds when using the HL or BDT models.

Standard treatments of the impact of interest rate changes on bond prices include duration and convexity. These concepts derive from the first and second derivatives of a Taylor series expansion of an option-free bond price as a function of interest rates. Does the third derivative matter? This paper derives the formula for the third derivative- based term, which we call tilt, and explores its properties. Tilt tells how quickly the convexity changes. Similar to the properties of duration, a higher yield reduces tilt, a longer maturity increases tilt, and a higher coupon reduces tilt, ceteris paribus. Tilt adds little to the accuracy of the impact of small interest rate changes for default-free option-free bonds. Tilt becomes interesting for bonds with embedded options such as callable bonds and mortgage-backed securities. Such bonds can experience rapidly changing convexity and price under certain interest rate regimes.

Under the condition of continuous innovation of financial derivatives and marketization of interest rate, interest rates fluctuate more frequently and fiercely, and the measurement of interest rate risk also attracts more attention. Under the premise that the fluctuation of interest rate follows fuzzy stochastic process, based on the option characteristics of financial instruments with embedded option, this paper takes effective duration and effective convexity as tools to measure interest rate risk when embedded options exist, tries to choose CIR extended model as term structure model, and uses the Monte Carlo method for hybrid low deviation sequences (HPL-MC) to analyze the prepayment characteristics of MBS, a representative financial instrument with embedded options, when interest rates fluctuate; on this basis, the effectiveness of effective duration management of interest rate risk is demonstrated with asset liability management cases of commercial banks.

Purpose of the study : How to best structure an IP licensing agreement taking account of embedded optionalities and other terms negotiated between licensor and licensee via a case study involving a prototypical options-based business model (biotech industry). Methodology : Binomial lattice simulation. Findings : It shows how IP management practices would change depending on who pays for the development costs, controls the continuation/development or abandonment option and thereby appropriates most of the embedded option’s value. It presents alternative (iso-value) menu licensing term choices (different combinations of royalty vs. fixed upfront fee or milestone payments) that are fair and optimal in properly accounting for the optionality embedded in RD (b) consider licensor and licensee perspectives in negotiating the terms of the IP licensing agreement, providing guidelines on how to determine its optimal remuneration structure reflecting a fair sharing of project value and embedded optionality among the parties; (c) offer a tool for IP portfolio management that helps a licensor prioritize internal R&D projects accounting for managerial flexibility and optimal licensing design under uncertainty.

The correlations between financial variables are always nonlinear and the financial instruments with several influence factors are therefore characteristized with complicated risk-return. Thus, this paper attempts to decompose the mezzanine financing into three parts to conveniently value them respectively. In order to dispose complicated relationship between variables during valuation, the support vector machine is introduced to give a nonparametric estimation of the equity embedded in the mezzanine financing. Therefore, a quantitative analysis framework for the valuation of the mezzanine financing is constructed to deal with the dual risk-return nature of both equity and debt of mezzanine financing. Experimental results display the proposed methodology can efficiently address sophisticated risk-return nature of mezzanine financing and deal with nonlinear dynamics embedded in sample data, which provides investors, issuers and regulators with constructive decision-making basis.

This paper is concerned with the valuation of equity-linked annuities with mortality risk under a double regime-switching model, which provides a way to endogenously determine the regime-switching risk. The model parameters and the reference investment fund price level are modulated by a continuous-time, finite-time, observable Markov chain. In particular, the risk-free interest rate, the appreciation rate, the volatility and the martingale describing the jump component of the reference investment fund are related to the modulating Markov chain. Two approaches, namely, the regime-switching Esscher transform and the minimal martingale measure, are used to select pricing kernels for the fair valuation. Analytical pricing formulas for the embedded options underlying these products are derived using the inverse Fourier transform. The fast Fourier transform approach is then used to numerically evaluate the embedded options. Numerical examples are provided to illustrate our approach.

This study applies the contingent claim approach to evaluate retirement benefits with the options of choosing the maximum defined benefit and defined contribution pension plans. A least-squares Monte Carlo simulation values complex retirement benefits that feature the properties of multiple variables, early exercise, stochastic interest rates, and several embedded options. Furthermore, this study examines the impacts of different forms of early decrements of the value of retirement benefits with options.

Cut-off Grade Strategy (COGS) is a concept that directly influences the financial, technical, economic, environmental, and legal issues in relation to exploitation of a mineral resource. A decision making system is proposed to select the best technically feasible COGS under price uncertainty. In the proposed system both the conventional discounted cash flow and modern simulation based real option valuations are used to evaluate the alternative strategies. Then the conventional expected value criterion and a multiple criteria ranking system were used to rank the strategies based on the two valuation methods. In the multiple criteria ranking system besides the expected value other stochastic orders expressing abilities of strategies in producing extra profits, minimizing losses and achieving the predefined goals of the exploitation strategy are considered. Finally, the best strategy is selected based on the overall average rank of strategies through all ranking systems. The proposed system was examined using the data of Sungun Copper Mine. To assess the merits of the alternatives better, ranking process was done at both high (prevailing economic condition) and low price conditions. Ranking results revealed that at different price conditions and valuation methods, different results would be obtained. It is concluded that these differences are due to the different behavior of the embedded option to close the mine early, which is more likely to be exercised under low price condition rather than high price condition. The proposed system would enhance the quality of decision making process by providing a more informative and certain platform for project evaluation.

In addition to an interest rate guarantee and annual surplus participation, life insurance contracts typically embed the right to stop premium payments during the term of the contract (paid-up option), to resume payments later (resumption option), or to terminate the contract early (surrender option). Terminal guarantees are on benefits payable upon death, survival and surrender. The latter are adapted after exercising the options. A model framework including these features and an algorithm to jointly value the premium payment and surrender options is presented. In a first step, the standard principles of risk-neutral evaluation are applied and the policyholder is assumed to use an economically rational exercise strategy. In a second step, option value sensitivity on different contract parameters, benefit adaptation mechanisms, and exercise behavior is analyzed numerically. The two latter are the main drivers for the option value.

This study proposes a Dynamic Option Simulation (DOS) approach to evaluate natural resource investment projects that contain several embedded options and limited reserves. To construct a practical pricing model, DOS combines simulation and dynamic programming techniques that can value natural resource investments with multi-variable, early exercise, various embedded options and finite reserve properties. A copper mine project offers a demonstration; the mine holder may temporarily close, reopen and abandon the mine at specific times before the expiration date. The mine holder may also accelerate mining speed to be optimal, referred to as the acceleration option. Numerical analyses of the copper price and interest rate effects on the copper mine value suggest that DOS can efficiently assess complex, multiple-variable, American-style real options problems.

Banks and other financial institutions issue hybrid capital as part of their risk capital. Hybrid capital has no maturity, but, similarly to most corporate debt, includes an embedded issuer’s call option. To obtain acceptance as risk capital, the first possible exercise date of the embedded call is contractually deferred by several years, generating a protection period . We value the call feature as a European option on perpetual defaultable debt. We do this by first modifying the underlying asset process to incorporate a time-dependent bankruptcy level before the expiration of the embedded option. We identify a call option on debt as a fixed number of put options on a modified asset, which is lognormally distributed, as opposed to the market value of debt. To include the possibility of default before the expiration of the option we apply barrier options results. The formulas are quite general and may be used for valuing both embedded and third-party options. All formulas are developed in the seminal and standard Black–Scholes–Merton model and, thus, standard analytical tools such as ‘the greeks’, are immediately available.

This paper investigates the decision of an automaker concerning the alternative promotion of a hybrid vehicle (HV) and a full electric vehicle (EV). We evaluate the HV project by considering the option to change promotion from the HV to the EV in the future. The results not only extend previous findings concerning American options on multiple assets, but also include several new implications. One notable observation is that the increased market demand for EVs can accelerate the promotion of the HV because of the embedded option.

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.

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.

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.

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

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.

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.

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.

This paper alters the traditional model of valuation by introducing trinomial trees, and determines the difference between the traditional plain‐vanilla, adjustable‐rate mortgages and cash rebate mortgages. By presenting an economic model for studying the combined effects of mortgage value by prepayment, delinquency, default, and cure speed, the model builds a simulation program to generate different cash flow scenarios. The results indicate that the value of cash rebate mortgages is higher than that of standard mortgages, although they are more sensitive to embedded options. If the probability of exercising an option is higher, then the value of cash rebate mortgages will drop at a faster rate than that of standard mortgages.

We use a contingent claims framework for valuing the the default and prepayment embedded options in certain British fixed-rate endowment mortgages, with a (capped) mortgage indemnity guarantee (MIG). This methodology provides a template for the borrower, lender, and insurer to compare mortgage terms, including the fairness of contract rates, arrangement fees, prepayment penalties, any MIG premiums required, and co-insurance exposure. With empirical inputs, this model may eventually be useful as a “mark-to-value” proxy for all parties, as expected parameters change (especially interest rate and house price levels, and expected future volatilities), for purposes of determining “valued added accounting”, appropriate reserves, and indeed for setting premiums and business drivers. Fixed-rate endowment mortgages differ from fixed-rate repayment mortgages primarily because, in the event of early termination, the amount owed by the borrower is a function of the evolution of the term structure of interest rates, whereas for a repayment mortgage it is pre-determined. We compare endownment and repayment mortgages for different levels of loan-to-value ratios, interest rate and house price volatilities.

Convertible bonds are commonplace securities, but valuing them properly is tricky. In addition to being exposed to interest rate risk like any bond in a stochastic interest rate environment, they contain both an option to convert them into shares of the issuing firm, and also exposure to the risk of default. In this article, Hung and Wang present a lattice technique that allows relatively straightforward valuation, even in the presence of these three sources of risk. After describing their technique in general, they put it to use to evaluate a convertible bond issued by Lucent.

In this paper, we provide descriptive evidence of primary market activity in the Eurobond market for the period 1980-2000. This study explores the Bondware Database that contains 33,024 publicly issued Eurobonds. We analyse some characteristics of the issuers (nationality, industry and credit quality), the intermediary parties (bookrunners, lead managers, ...) and the structures used for the bonds (currencies, size, years to maturity, interest and repayment structure, embedded options).

This paper provides an in-depth analysis into the structuring and the pricing of an innovative financial market product. This instrument is called contingent conversion convertible bond or "CoCoCo". This hybrid bond is itself a combination of two other hybrid instruments: a contingent convertible ("CoCo") and a convertible bond. This combination introduces more complexity in the structure but it now allows investors to profit from strong share price performances. This upside potential is added on top of the normal contingent convertible mechanics whereas CoCos only expose the investors to downside risk. This sets up a new avenue for the banks to create new capital. First, we explain how the features of the contingent convertible bonds on one side and the features of the standard convertible bonds on the other side are combined. Thereafter, we propose a pricing approach which moves away from the standard Black & Scholes setting. The CoCoCos are evaluated using the Heston process to which a Hull-White interest rate process has been added. We demonstrate the importance of using a stochastic interest rate when modeling this instrument. Finally we quantify the loss absorbing capacity of this instrument.

The focus of this paper is to analyze the effect that ambiguity will have on the buyer’s reservation price and the value of the option to purchase the durable good with an embedded option to resell it. The agent is assumed to be risk neutral and ambiguity averse. The problem is formulated as an optimal stopping problem with multiple priors in continuous time with infinite horizon. Uncertainty comes from prices, which is summarized in a state variable that follows a Brownian motion. Preferences have a multiple-prior utility representation where the set of priors consist of a family of Brownian motions with unknown drift and common variance. We show that the direction of the change in the buyer’s reservation price depends on the parametrization of the model and that the value of the embedded option is decreasing in the perceived level of ambiguity.

There is an extensive literature on ways of valuing bonds with embedded options and measuring their interest rate risk exposure. Price sensitivity measures-effective duration and effective convexity-are found by shocking rates up and down by the same number of basis points and determining the impact on the value of the security. Yet, despite the critical importance of the measures that are derived from a valuation model-option-adjusted spread, effective duration, and effective convexity-there appears to be no empirical study that examines whether interest rate models produce any significant differences for these measures. The authors examine a callable bond, a putable bond, a callable range note, and a putable range note using several popular interest rate models. The substantial differences in the measures estimated are attributed to characteristics of the interest rate model.

Term-structure models are widely used to price interest rate derivatives, such as swap options and bonds with embedded options. We describe how a general one-factor model of the short rate can be implemented as a recombining trinomial tree and calibrated to market prices of actively traded instruments. The general model encompasses most popular one-factor Markov models as special cases. The implementation and the calibration procedures are sufficiently general that they can select the functional form of the model that best fits the market prices. This characteristic allows the model to fit the prices of in- and out-of-the-money options when there is a volatility skew. It also allows the model to work well with economies characterized by very low interest rates, such as Japan, for which other models often fail.

Publisher Summary The realization that investment opportunities also carry embedded options has revolutionized the theory of capital investment analysis. Unfortunately, it has also complicated project evaluation to the point where optimal investment decisions invariably depend on a series of intractable valuation expressions. In such cases, custom dictates that numerical evaluation is the most practical (and often the only) way of determining optimal investment expenditures. However, it is often possible to use power series expansions to obtain analytic expressions for the value of a firm's investment opportunities. These permit a somewhat deeper investigation of the criteria leading to the optimal investment decisions made by firms. Furthermore, they can often identify the specialized circumstances under which it will be possible to obtain closed-form expressions for the value of a firm's investment opportunities. Another stochastic process is the scaled distribution of Praetz and Blattberg and Gonedes. This process is based on the assumption that expected changes in operating cash flows are always towards a long-run mean, are potentially negative and have a variance, which depends on the difference between the ‘current’ and long-run operating cash flows. Hence, the uncertainty associated with future cash flows depends on the current level of the operating cash flow—something that intuition suggests ought to be the case.

We begin by considering how to model market rents using random walk and autoregressive models. We then show how to value rental income on properties subject to upward only rent reviews where market rents are described by these two models. The values are obtained using three valuation methodologies. Two of the valuation techniques take account of the embedded upward only rent review option whereas one of the techniques takes the traditional approach, effectively ignoring the option value. The resulting values depend both on the model of the behaviour of rents and on the valuation method.

A callable bond will be paid off before maturity if the issuer finds the interest rate environment favors that strategy. But a putable bond may experience the same fate, at the option of the bondholder. Combining both call and put features in a single bond creates enough contingencies that quite different-seeming instruments may actually be essentially the same. This article examines such a structure and shows both how it behaves and why the ability to take it apart and effectively sell off some of the components as stand-alone options can make it particularly attractive to an issuer.

During the recent market turmoil, one of the financial instruments most often discussed was that of interest rate swaps, especially those with embedded options. In this article, one approach to understanding these products is suggested and examples given the interest rate sensitivity of a wide range of various interest rate products.

Th arbitrage-free binomial model has been applied to value bonds with embedded options. This article extends the binomial model to incorporate the risk of payment default. The basic solution procedure is modified by adjusting the expected cash flows for the likelihood of a payment default and the expected cash recovery when a payment default occurs. The default probabilities can be estimated from the historical default experience of similarly rated bonds. The expected cash recoveries can be estimated by calibrating to the yield curve for par value bonds with the same rating. The author applies the model to value payment-in-kind debentures, which are rich in embedded options.

The embedded options found in some securities are known to have significant impact on product pricing, secondary market valuation, and risk measurement and management. The option to withdraw commonly found in bank deposits is one of the least studied of these. We help to fill this gap by examining the level and interest rate sensitivity of early withdrawals of retail time deposits using panel data from the Thrift Financial Report. We find that longer-maturity time deposit portfolios commonly experience early withdrawals at economically significant levels. Further, we find that depositors respond positively, with increased levels of early withdrawal, to the reinvestment incentive they face when new deposit rates rise. These findings increase our understanding of consumer behavior with regard to financial products and have significant implications for the competitive pricing of deposit products and the management of bank interest rate risk.

The case for accounting separately for the debt and equity features of a convertible bond is based on two main assumptions: convertible debt can be decomposed into two, or more, fundamental financial instruments, and a convertible bond has the same economic substance as a bond with a detachable warrant. These assumptions are re-examined in this paper where it is shown that it is generally not possible to decompose a convertible bond into fundamental financial instruments, nor is it possible to form a package of a bond and a detachable warrant that replicates the character of the convertible bond.

This paper provides an example of the valuation of a “real option” in a large-scale infrastructure project. The Transurban City Link project in Melbourne, Australia is a major project involving the financing, construction, operation and maintenance of 22 kilometers of toll-roads. Two interacting embedded options are identified in the project. In the past it has often been considered too difficult to explicitly value interacting embedded options. This paper presents a straight-forward methodology for valuing the options and their “interaction effect.“ To the author's knowledge, this is the first paper that has attempted to value complex interacting real options. The procedure involves simulating the key underlying risk factors using Monte Carlo methods. The results indicate that at least one of the options, which allows Transurban to defer payment of the concession fee to the Government, has a very significant value. In fact the option value could account for more than half of the market value of Transurban securities. This significant value is attributed to the fact that the option preserves investor returns for (approximately) the first 15 years of the project's life.

A depository institution's interest rate risk (IRR) exposure is the sensitivity of its earnings or market value of equity to changes in interest rates. Since the mid-1980's, bank regulators have developed broadly applied, centralized IRR models which are used to help assess individual institutions' capital adequacy. This paper tests the effectiveness of the earliest of these regulatory IRR models: the incomegap estimates calculated by the Federal Home Loan Bank Board (FHLBB) during the latter 1980's. Despite the many problems caused by the broad application of generic assumptions and the presence of embedded options, we find that the FHLBB gap estimates provided a significant measure of IRR exposure. We believe that these results bode well for the success of ongoing, more sophisticated regulatory modeling efforts.

The last two decades have witnessed a tremendous growth in the volume of assets and liabilities whose cash flows depend, in a variety of ways, on the path of interest rates. Some of these, including floating-rate notes and swap agreements, contractually base cash flows on current and past interest rates and contain caps, floors, and other, more complex features. Others, including mortgages, many corporate bonds, and time deposits, are fixed-rate instruments that contain embedded options, such as those to prepay, call, or withdrawal. The irregular exercise of these options causes cash flows to vary as time proceeds and interest rates rise or fall. This paper develops a state-contingent claims technique for valuing such securities. It is derived from the option-based model of Breeden and Litzenberger (1978) using the transition matrix approach of Banz and Miller (1978). Particular attention is paid to valuing so-called path-dependent securities whose contemporaneous cash flows depend on the historical path of interest rates as well as their current level. A detailed example is provided in which an adjustable-rate mortgage is valued under a variety of economic and security specific assumptions.

The guaranteed minimum withdrawal benefit (GMWB) rider, as an add on to a variable annuity (VA), guarantees the return of premiums in the form of peri- odic withdrawals while allowing policyholders to participate fully in any market gains. GMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We consider fair pricing of the GMWB rider from a financial economic perspective. Particular focus is placed on the distinct perspectives of the insurer and policyholder and the unifying relationship. We extend a decomposition of the VA contract into components that reflect term-certain payments and embedded derivatives to the case where the policyholder has the option to surrender, or lapse, the contract early., Comment: 18 pages, proof of Lemma A.1 expanded for clarity

The valuing (or pricing) of a bond without an embedded option (that is, an option-free bond) is straightforward. The value is equal to the present value of the expected cash flows. Ignoring defaults, for an option-free bond the cash flows are known and consist of the periodic interest payments and principal at the maturity date. The interest or discount rates for computing the present value of the cash flows begin with the spot rates for a benchmark security and to those rates an appropriate spread is added. Moving from valuing option-free bonds to corporate bonds and agency debentures with embedded options is not simple. The interest rate–sensitive options that can be embedded into these bonds are call options, put options, accelerated sinking provisions, and, for floating-rate securities, caps on the interest rate. The reason valuation is complicated is that the embedded options must be taken into account and the theoretical option-free value of the bond must be adjusted accordingly. The technique typically used for valuing corporate bonds and agency debentures with embedded options is the lattice method. Mortgage-backed securities also have embedded options: the right of the borrowers in a loan pool to prepay their mortgage loan. However, because future cash flows for a loan pool are sensitive to not only the current interest rate but the history of rates since the loans were originated, the lattice method which is solved using backward induction cannot be employed. Instead, the most common methodology used for valuing mortgage-backed securities and mortgage-related asset-backed securities is the Monte Carlo simulation model. Other types of asset-backed securities are straightforward to value. In addition to the complications in valuing mortgage-backed securities and mortgage-related asset-backed securities, there is the difficulty in estimating their price sensitivity to changes in interest rates (that is, duration and convexity). The Monte Carlo simulation model can be used to compute the effective duration of these securities. This duration measure takes into consideration how a change in interest rates can impact a security's cash flow. Keywords: asset-backed securities (ABS); mortgage-backed securities (MBS); Monte Carlo simulation model; cash-flow yield; reinvestment risk; interest rate risk; modeling risk; nominal spread; zero-volatility spread (Z-spread); option-adjusted spread (OAS); theoretical value; option cost; effective duration; option-adjusted duration; effective convexity; positive convexity; negative convexity

In principle, the valuation of a financial instrument is straightforward: It is the present value of the expected cash flow. For fixed income securities, the expected cash flow, ignoring the possibility of default, is the periodic interest payments and the maturity value. The interest rates used to discount the expected cash flows are obtained from an appropriate benchmark spot rate curve. When a fixed-rate or floating-rate bond has an interest-sensitive embedded option such as a call option, put option, or a cap in the case of a floater, the expected cash flow will be dependent on future interest rates. To value fixed income securities with embedded options, the lattice framework is the standard tool in practice. The same lattice-based framework is also used to value interest-sensitive derivatives such as options, caps, and floors and mortgage-backed securities. Keywords: lattice model; recursive valuation process; option-free bond; callable bond; binomial interest rate tree; putable bond; capped floater; callable capped floater; interest rate cap; interest rate floor; step-up callable notes; range floater; option on a bond; option-adjusted spread; effective duration; effective convexity

In the previous chapter I have introduced the subject of embedded options and guarantees. Now I will specify the terms embedded option and guarantee and present a systematisation of common examples thereof. Subsequently there will be a literature survey to outline to the reader the actual state of scientific knowledge that is of relevance for the purpose of this thesis.

Universal life insurance contracts, which usually have the so-called cliquet syle interest rate guarantees, are quite popular in China. These contracts often include other options such as the surrender option. This paper attempts to valuate these policies using the risk-neutral pricing method of financial mathematics. The framework in which the fair value of these policies is priced in a stochastic interest rate environment is presented. We analyze the guaranteed interest rate option and the surrender option separately. The values of embedded options are derived using the Least Square Monte Carlo approach. Using the calibrated parameters, we find out that the stochastic interest rate assumption affects the valuation considerably in comparison to the constant interest rate. Additionally, the volatility of assets and the smoothing mechanism are important for valuing the policyholder s' claim.

In Chap. 17 it was outlined how the Basel II risk parameters can be used for the risk management of loans. It was shown in detail how to apply a risk-adjusted pricing formula for the calculation of a loan’s terms and of general loss provisions. In the framework of Chap. 17 a loan was characterized by a pre-defined structure of future interest rate and amortization payments only. In reality, loans are in general much more complex products.