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After the replacement of Libor with alternative reference rates across the world, market participants must now adjust to a variety of changes to both contract terms and market rate dynamics. Focusing mostly on the new SOFR rate in the US, this paper considers the interaction of two important characteristics of SOFR derivatives: the backward-looking settlement style of SOFR floating rate payments; and the historically ‘jagged’ nature of SOFR time series. We introduce mechanisms that allow us to modify existing term structure models to incorporate rich dynamics for both ‘surprising’ and anticipated spikes and hikes in overnight rates. Numerical tests on SOFR-style caplets show that such model enhancements can produce significant effects on implied caplet volatility levels and skews. Besides establishing a practitioner-friendly framework for derivatives pricing, our paper is broadly applicable to scenario generation and risk management in any market with discontinuous rates dynamics. [ABSTRACT FROM AUTHOR]

In current financial markets negative interest rates have become rather persistent, while in theory it is often common practice to discard such rates as incredible and irrelevant. However, from a risk management perspective, it is crucially important to financial institutions to properly account for this phenomenon in their Asset Liability Management (ALM) studies. In this paper, we develop a coherent framework on how to best incorporate negative interest rates in these studies through a single curve stochastic term structure model and compare it to its multiple curve analogue. It turns out that, from the wide range of available single curve models, especially the Lévy Forward Price model (LFPM) of Eberlein and Özkan [The Lévy LIBOR model. Financ. Stoch., 2005, 9, 327–348] seems appropriate for ALM purposes. This paper describes an optimisation routine for calibrating this LFPM under the risk-neutral measure in both the single and multiple curve framework to the market prices of interest rate caplets with different strike rates, maturities and tenors. In addition, an empirical performance analysis is made of the single and multiple curve LFPM, where we include four deterministic volatility specifications and provide an explicit parametrisation of a piecewise homogeneity restriction with both deterministic and random breakpoints. This comparative analysis indicates that both the single and multiple curve LFPM is best adopted with the Linear-Exponential Volatility (LEV) specification and that deterministic breakpoints should be included, rather than random breakpoints. [ABSTRACT FROM AUTHOR]

The contributions of this paper are twofold: we define and investigate the properties of a short rate model driven by a general Gaussian Volterra process and, after defining precisely a notion of convexity adjustment, derive explicit formulae for it. [ABSTRACT FROM AUTHOR]

Fourier transforms provide versatile techniques for pricing financial derivative securities. In applying such techniques, a typical derivative valuation expression is often written as an inner product of the Fourier transform of payoff and the characteristic function of the underlying asset dynamics. Some modelling specifications imply that it might be challenging to find a closed-form expression for the characteristic function. In such situations, numerical approximations have to be employed. This paper utilises the power series approximation technique in finding explicit expressions of the characteristic function for the underlying stochastic variables. We analyse the convergence and accuracy of this technique in the context of valuing European style options written on underlying securities whose dynamics evolve under the influence of multiple Heston-type stochastic volatilities [Heston, S., A closed-form solution for options with Stochastic volatility with applications to Bond and currency options. Rev. Financ. Stud., 1993, 6, 327–343] and Cox–Ingersoll–Ross stochastic interest rates [Cox, J., Ingerson, J. and Ross, S., A theory of the term structure of interest rates. Econometrica, 1985, 53, 385–407]. This paper contributes to the existing literature four-fold by: (i) adapting the valuation technique to long-dated instruments; (ii) providing an adjustment to a series of points around which the power series expansion is performed; (iii) analysing the performance of different strategies for hedging European call options; (iv) applying the power series approach to the valuation of guaranteed minimum accumulation benefit riders embedded in variable annuity contracts. Our results demonstrate a high computational efficiency of the power series approximation method for evaluation of derivative prices and hedge ratios. [ABSTRACT FROM AUTHOR]

In this paper, we examine how the relationship between the US stock index and the US Treasury market has changed after the start of the Covid-19 crisis. For that purpose, we compute upside and downside correlations between the index and interest rates of different maturities. Our main findings are as follows: first, we document the correlation asymmetry. The downside correlation is higher than the upside correlation before the crisis but the opposite is true after the start of the crisis for all maturities. The magnitude of the change is large for short-term maturities but small for long-term maturities. It indicates that the benefit of holding the short-term government bonds as a diversifier for stock investors is weakened after the start of the Covid-19 crisis. We also study the economic impact of ignoring the correlation asymmetry and report that the cost increased after the start of the crisis in general. [ABSTRACT FROM AUTHOR]

This paper analyzes an interest rate model with self-exciting jumps, in which a jump in the interest rate model increases the intensity of jumps in the same model. This self-exciting property leads to clustering effects in the interest rate model. We obtain a closed-form expression for the conditional moment-generating function when the model coefficients have affine structures. Based on the Girsanov-type measure transformation for general jump-diffusion processes, we derive the evolution of the interest rate under the equivalent martingale measure and an explicit expression of the zero-coupon bond pricing formula. Furthermore, we give a pricing formula for the European call option written on zero-coupon bonds. Finally, we provide an interpretation for the clustering effects in the interest rate model within a simple framework of general equilibrium. Indeed, we construct an interest rate model, the equilibrium state of which coincides with the interest rate model with clustering effects proposed in this paper. [ABSTRACT FROM AUTHOR]

Pricing of interest rate derivatives, such as CMS spread or mid-curve options, depends on the modelling of the underlying single rates. For flexibility and realism, these rates are often described in the framework of stochastic volatility models. In this paper we allow rates to be modelled within a class of general stochastic volatility models, which includes the SABR, ZABR, free SABR and Heston models. We provide a versatile technique called Effective Markovian Projection, which allows a tractable model to be found that mimics the distribution of the more complex models used to price multi-rate derivatives. Three different numerical approaches are outlined and applied to relevant examples from practice. Finally, a new method that involves moment-matching of Johnson distributions is applied to facilitate closed-form pricing formulas. [ABSTRACT FROM AUTHOR]

We introduce a first theory of price impact in the presence of an interest rate term structure. We explain how one can formulate instantaneous and transient price impact on zero-coupon bonds with different maturities, including a cross price impact that is endogenous to the term structure. We connect the introduced impact to classic no-arbitrage theory for interest rate markets, showing that impact can be embedded in the pricing measure and that no arbitrage can be preserved. We extend the price impact setup to coupon-bearing bonds and further show how to implement price impact in an HJM framework. We present pricing examples in the presence of price impact and numerical examples of how impact changes the shape of the term structure. Finally, we show that our approach is applicable by solving an optimal execution problem in interest rate markets with the type of price impact we developed in the paper. [ABSTRACT FROM AUTHOR]

Writing non-negative equity guarantees (NNEGs) is the main method used to deal with the risks of equity release products in the United Kingdom. The existing empirical literature indicates the potential for contagion of interregional and international house prices, but no studies have modeled these contagion effects. This paper applies a Merton-jump-diffusion model to propose a general model to investigate the impacts of house price contagion on the valuation of NNEGs. We derive a closed-form solution for the price of NNEGs and use an analytic formula to investigate contagion effects on NNEGs efficiently. This research establishes that ignoring the contagion effects of house prices can lead to underestimating of the value of NNEGs. Treating the contagion effect is critical for valuing NNEGs, in light of the development of equity release products. [ABSTRACT FROM AUTHOR]

This paper provides extensions to existing procedures for representing one-factor no-arbitrage models of the short rate in the form of a tree. It allows a wide range of drift functions for the short rate to be used in conjunction with a wide range of volatility assumptions. It shows that, if the market price of risk is a function only of the short rate and time, a single tree with two sets of probabilities on branches can be used to represent rate moves in both the real-world and risk-neutral world. Examples are given to illustrate how the extensions can provide modelling flexibility when interest rates are negative. [ABSTRACT FROM AUTHOR]

This paper addresses a gap in the literature concerning robust portfolio analysis for commodity markets in the presence of stochastic interest rates. For generality, we study an ambiguity-averse investor with a Cramér-Lundberg surplus to be allocated into a mean-reverting asset representing a commodity and a bond with a Vasicek interest rate model. Our framework allows for closed-form solutions for the optimal strategy, worst case measure, terminal wealth and value functions. We provide necessary conditions for a well-behaved solution. A full estimation is conducted on two commodity representatives: WTI oil prices and gold prices. We find strong evidence that optimal exposures to commodity risk and interest rate risk, as well as the performance of the portfolio, are significantly affected by the level of ambiguity aversion. Our analyses demonstrate that investors who ignore uncertainty incur drastic equivalent welfare losses, in particular ignoring commodity uncertainty is more costly than neglecting interest rate uncertainty. In a comparison between stocks and commodities, ignoring uncertainty on the latter is also more damaging. We also confirm the importance of working in a complete market (investing in Bonds) for commodity investors, otherwise welfare losses could easily reach 45%. In terms of parameter mis-specifications, we find that incorrect large correlation, smaller variance or simply the wrong market price of commodity risk, can lead to drastically large wealth-equivalent losses. [ABSTRACT FROM AUTHOR]

In this paper, first we study a stochastic volatility market model for which an explicit candidate solution to the problem of maximizing the utility function of terminal wealth is obtained. Applying this result, we present a complete solution for the Heston model, which is a particular case of the general model. A verification result and a martingale representation of the solution are provided for the Heston model. Finally, the same techniques are used to study a stochastic interest rate model and a necessary and sufficient condition for exploding growth is presented. [ABSTRACT FROM PUBLISHER]

The Chinese convertible bond market has been developing rapidly in the last 10 years. However, some special characteristics of the Chinese convertible bond, such as the soft call/put provision, cause huge difficulty in the valuation. In this paper, we establish a new valuation model for the Chinese convertible bond, based on the available Chinese market data, through a hybrid willow tree approach with consideration of the underlying stock price, stochastic interest rate, and credit risk of the issuer. We employ the Brownian bridge to handle the special characteristics. Finally, we examine our model prices for the daily market closing prices for 20 Chinese convertible bonds traded from 2007 to 2017. The empirical results show the effectiveness of our valuation model under the historical and implied volatilities of the underlying stock price. [ABSTRACT FROM AUTHOR]

Based on the multi-currency LIBOR Market Model, this paper constructs a hybrid commodity interest rate market model with a stochastic local volatility function allowing the model to simultaneously fit the implied volatility surfaces of commodity and interest rate options. Since liquid market prices are only available for options on commodity futures, rather than forwards, a convexity correction formula for the model is derived to account for the difference between forward and futures prices. A procedure for efficiently calibrating the model to interest rate and commodity volatility smiles is constructed. Finally, the model is fitted to an exogenously given correlation structure between forward interest rates and commodity prices (cross-correlation). When calibrating to options on forwards (rather than futures), the fitting of cross-correlation preserves the (separate) calibration in the two markets (interest rate and commodity options), while in the case of futures a (rapidly converging) iterative fitting procedure is presented. The fitting of cross-correlation is reduced to finding an optimal rotation of volatility vectors, which is shown to be an appropriately modified version of the ‘orthonormal Procrustes’ problem in linear algebra. The calibration approach is demonstrated in an application to market data for oil futures. [ABSTRACT FROM AUTHOR]

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper. [ABSTRACT FROM AUTHOR]

The paper introduces a Black–Cox-type structural model for credit default swaps (CDS). The existing literature on structural CDS pricing is extended by allowing a general functional form for the default barrier specified without reference to asset volatilities, dividend yields or interest rates. We develop a fast and robust algorithm to compute survival probabilities numerically. An empirical application suggests that the market-implied barrier is stable over time, with a possibly hump-shaped term structure. The implied barrier can be used for computing survival probabilities consistent with objective expectations of asset evolution, for pricing under counterparty risk, and for determining optimal corporate bond covenants. [ABSTRACT FROM AUTHOR]

A number of mortgage prepayment models require a specification of the mortgage rate process. Usually, ad-hoc models are used (e.g., a Treasury yield plus some constant). Recently, a number of papers have appeared where the authors have utilized a mortgage rate implied by the current yield curve (the so-called endogenous mortgage rate). However, the existing computational algorithms suffer from the curse of dimensionality and, consequently, are problematic to use for full-scale problems. A computational algorithm, proposed in this paper, is tractable in the sense that its complexity is equivalent to the problem of mortgage valuation. Moreover, the algorithm does not require iterations. The numerical example is based on a PDE computation. An implementation of a Monte Carlo method is also discussed. [ABSTRACT FROM AUTHOR]

It has been claimed that, for dynamic investment strategies, the simple act of rebalancing a portfolio can be a source of additional performance, sometimes referred to as the volatility pumping effect or the diversification bonus because volatility and diversification turn out to be key drivers of the portfolio performance. Stochastic portfolio theory suggests that the portfolio excess growth rate, defined as the difference between the portfolio expected growth rate and the weighted-average expected growth rate of the assets in the portfolio, is an important component of this additional performance (see Fernholz [Stochastic Portfolio Theory, 2002 (Springer)]). In this context, one might wonder whether maximizing a portfolio excess growth rate would lead to an improvement in the portfolio performance or risk-adjusted performance. This paper provides a thorough empirical analysis of the maximization of an equity portfolio excess growth rate in a portfolio construction context for individual stocks. In out-of-sample empirical tests conducted on individual stocks from 4 different regions (US, UK, Eurozone and Japan), we find that portfolios that maximize the excess growth rate are characterized by a strong negative exposure to the low volatility factor and a higher than 1 exposure to the market factor, implying that such portfolios are attractive alternatives to competing smart portfolios in markets where the low volatility anomaly does not hold (e.g. in the UK, or in rising interest rate scenarios) or in bull market environments. [ABSTRACT FROM AUTHOR]

Value at Risk (VaR) and stressed value at Risk (SVaR) or expected shortfall are important risk measures widely used in the financial services industry for risk management and market risk capital computation. Fundamental to any (S)VaR model is the choice of the return type model for each risk factor. Because the resulting SVaR numbers are highly sensitive to the chosen return type model it is important to make a prudent choice on the return type modelling. We propose to estimate the return type model from historic data without making an a priori model assumption on the return model. We explain the fundamentals of return type modelling and how it impacts the magnitude of SVaR. We further show how to obtain a global return type model from a set of similar return type models by using geometric calculus. Numerical simulations and illustrations are provided. In this paper, we consider interest rate data, but the proposed methodology is general and can be applied to any other asset class such as inflation, credit spread, equity or fx. [ABSTRACT FROM AUTHOR]

This paper values guaranteed minimum withdrawal benefit (GMWB) riders embedded in variable annuities assuming that the underlying fund dynamics evolve under the influence of stochastic interest rates, stochastic volatility, stochastic mortality and equity risk. The valuation problem is formulated as a partial differential equation (PDE) which is solved numerically by employing the operator splitting method. Sensitivity analysis of the fair guarantee fee is performed with respect to various model parameters. We find that (i) the fair insurance fee charged by the product provider is an increasing function of the withdrawal rate; (ii) the GMWB price is higher when stochastic interest rates and volatility are incorporated in the model, compared to the case of static interest rates and volatility; (iii) the GMWB price behaves non-monotonically with changing volatility of variance parameter; (iv) the fair fee increases with increasing volatility of interest rates parameter, and increasing correlation between the underlying fund and the interest rates; (v) the fair fee increases when the speed of mean-reversion of stochastic volatility or the average long-term volatility increases; (vi) the GMWB fee decreases when the speed of mean-reversion of stochastic interest rates or the average long-term interest rates increase. We investigate both static and dynamic (optimal) policyholder's withdrawal behaviours; we present the optimal withdrawal schedule as a function of the withdrawal account and the investment account for varying volatility and interest rates. When incorporating stochastic mortality, we find that its impact on the fair guarantee fee is rather small. Our results demonstrate the importance of correct quantification of risks embedded in GMWBs and provide guidance to product providers on optimal hedging of various risks associated with the contract. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a regime switching Lucas economy in continuous time, with multiple dividend streams and labour income. We determine the asset prices in equilibrium in the economy with regime switching, and derive a system of partial differential equations for the asset prices and the short interest rate. The solutions for the endogenous short interest rate, the bond price and the yield of the bond are obtained. We also consider applications of the equilibrium model and show that the model implies a rich framework for the term structure of interest rates. We demonstrate how the regime switching economy helps to improve the model-implied annual excess rate of return. This assists in explaining the famous equity premium puzzle. [ABSTRACT FROM AUTHOR]

The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of paths for nested Monte Carlo simulations, resulting in large variances of estimators in practice. We propose a novel approach based on Kolmogorov forward and backward PDEs, where we counter the high dimensionality by a generalization of anchored-ANOVA decompositions. By computing only the most significant terms in the decomposition, the dimensionality is reduced effectively, such that a significant computational speed-up arises from the high accuracy of PDE schemes in low dimensions compared to Monte Carlo estimation. Moreover, we show how this truncated decomposition can be used as control variate for the full high-dimensional model, such that any approximation errors can be corrected while a substantial variance reduction is achieved compared to the standard simulation approach. We investigate the accuracy for a realistic portfolio of exchange options, interest rate and cross-currency swaps under a fully calibrated 10-factor model. [ABSTRACT FROM AUTHOR]

In this paper, we show how we can deploy machine learning techniques in the context of traditional quant problems. We illustrate that for many classical problems, we can arrive at speed-ups of several orders of magnitude by deploying machine learning techniques based on Gaussian process regression. The price we have to pay for this extra speed is some loss of accuracy. However, we show that this reduced accuracy is often well within reasonable limits and hence very acceptable from a practical point of view. The concrete examples concern fitting and estimation. In the fitting context, we fit sophisticated Greek profiles and summarize implied volatility surfaces. In the estimation context, we reduce computation times for the calculation of vanilla option values under advanced models, the pricing of American options and the pricing of exotic options under models beyond the Black-Scholes setting. [ABSTRACT FROM AUTHOR]

The stochastic-alpha-beta-rho (SABR) model is widely used by practitioners in interest rate and foreign exchange markets. The probability of hitting zero sheds light on the arbitrage-free small strike implied volatility of the SABR model (see, e.g. De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709-737], Gulisashvili [Int. J. Theor. Appl. Financ., 2015, 18, 1550013], Gulisashvili et al. [Mass at zero in the uncorrelated SABR modeland implied volatility asymptotics, 2016b]), and the survival probability is also closely related to binary knock-out options. Besides, the study of the survival probability is mathematically challenging. This paper provides novel asymptotic formulas for the survival probability of the SABR model as well as error estimates. The formulas give the probability that the forward price does not hit a nonnegative lower boundary before a fixed time horizon. [ABSTRACT FROM AUTHOR]

We study the mass at the origin in the uncorrelated stochastic alpha, beta, rho stochastic volatility model and derive several tractable expressions, in particular when time becomes small or large. As an application—in fact the original motivation for this paper—we derive small-strike expansions for the implied volatility when the maturity becomes short or large. These formulae, by definition arbitrage free, allow us to quantify the impact of the mass at zero on existing implied volatility approximations, and in particular how correct/erroneous these approximations become. [ABSTRACT FROM AUTHOR]

This paper uses an extensive set of market data of forward swap rates and swaptions covering 3 July 2002 to 21 May 2009 to identify a two-dimensional stochastic volatility process for the level of rates. The process is identified step by step by increasing the requirement of the model and introducing appropriate adjustments. The first part of the paper investigates the smile dynamics of forward swap rates at their setting dates. Comparing the SABR (with different) and Heston stochastic volatility models informs us what different specifications of the driving SDEs have to offer in terms of reflecting the dynamics of the smile across dates. The outcome of the analysis is that a normal SABR model () satisfactorily passes all tests and seems to provide a good match to the market. In contrast, we find that the Heston model does not. The next step is to seek a model of the forward swap rates (in their own swaption measure) based on only two Brownian motions that enables a specification with common parameters. It turns out that this can be done by extending the SABR model with a time-dependent volatility function and a mean-reverting volatility process. The performance of the extended (SABR with mean-reversion) model is analysed over several historical dates and is shown to be a stable and flexible choice that allows for good calibration across expiries and strikes. Finally, a time-homogeneous candidate stochastic volatility process that can be used as a driver for all swap rates is identified. This candidate process may in future work be used as a building block for a separable stochastic volatility LIBOR market model or a stochastic volatility Markov-functional model. [ABSTRACT FROM PUBLISHER]

In this paper, a full Bayesian procedure is developed and implemented for the market consistent valuation of a fairly general class of equity-linked savings contracts. The developed procedure allows several combinations of contract properties. For example, the contract returns may include a guaranteed interest rate and a bonus depending on the yield of a total return equity index. Especially, the contract may include an American-style path-dependent surrender option. The underlying asset and interest rate processes are estimated using the Markov chain Monte Carlo method, and their simulation is based on their posterior predictive distribution, which is, however, adjusted to give risk-neutral dynamics. Financial guarantees and equity-linked components are common in many life insurance products. From the insurance company’s viewpoint, this paper provides a realistic and flexible modelling tool for product design and risk analysis. The focus is on a novel application of advanced theoretical and computational methods, which enable us to deal with a fairly realistic valuation framework and to address model and parameter error issues. Our empirical results support the use of elaborated instead of stylized models for asset dynamics in practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we introduce tractable dynamic models for financial variables (such as interest rates, foreign exchange rates, commodity prices, etc.) with capturing both jump risk and boundedness of the price fluctuation in a regulated market. For the jump risk, we use a compound Poisson process with double exponential jump amplitude to describe the jumps. As for the boundedness of the fluctuation, we introduce two regulators to regulate (or control) the price dynamics. Based on such a dynamics, we then study the default events under the structural framework for credit risk. The explicit expression for the Laplace transform of the default time is derived. For exploring the effect of the jump risk and the regulation, we perform some numerical simulation. As a practical application, an analytic valuation of defaultable zero-coupon bonds is presented. It turns out that our model can produce a variety of strictly positive credit spread term structures, including downward, humped and upward styles. [ABSTRACT FROM AUTHOR]

This paper tries to link the uncovered interest rate parity condition to the discussion about interest rate convergence in currency unions. Techniques of fractional cointegration analysis are used to examine the relationship between German and Spanish government bond yields with maturities of two, five, seven and ten years in the period 05 January 2001 to 29 December 2006. Back then (in the good times of the currency union) financial markets did not have to fear exchange rate risk and sovereign credit risk. Thus, the risk premia to be observed were small and driven by liquidity risk. Economic theory suggests that a cointegration vector of between the interest rates can only exist when markets do not expect exchange rate movements and the risk premium is not interest rate sensitive (or practically speaking the sensitivity is low). Given the data set examined here, it is probably no surprise that the interest rates of the two countries are cointegrated and that the cointegration vector of German and Spanish government bond yields with maturities of two, five and seven years seems to be . We then have also examined the degree of interest rate sensitivity of the yield spread between Spain and Germany. The differential between the yields of the two countries in all maturity brackets do not react to the level of interest rates in the currency union. This fits perfectly to our results with regard to the cointegration vector. [ABSTRACT FROM AUTHOR]

In this paper, we focus on backward simulation of the CIR process. The purpose is to solve the memory requirement issue of the Least Squares Monte Carlo method when pricing American options by simulation. The concept of backward simulation is presented and it is classified into two types. Under the framework of the second type backward simulation, we seek the solutions for the existing CIR schemes. Specifically, we propose forward–backward simulation approaches for Alfonsi’s two implicit schemes, the fixed Euler schemes and the exact scheme. The proposed schemes are numerically tested and compared in pricing American options under the Heston model and the stochastic interest rate model. Some numerical properties such as the convergence order of the explicit–implicit Euler schemes, the storage requirement estimation of the forward–backward exact scheme and its computing time comparison with the squared Bessel bridge are also tested. Finally, the pros and cons of the related backward simulation schemes are summarized. [ABSTRACT FROM PUBLISHER]

Foreign exchange options are studied in the Heston stochastic volatility model for the exchange rate combined with the Coxet al. dynamics for the domestic and foreign stochastic interest rates. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate. The main result furnishes a semi-analytical formula for the price of the foreign exchange European call option. The FX options pricing formula is derived using the probabilistic approach, which leads to explicit expressions for conditional characteristic functions. Stylized numerical examples show that the dynamics of interest rates are important for the valuation of foreign exchange options. We argue that the model examined in this paper is the only analytically tractable version of the foreign exchange market model that combines the Heston stochastic volatility model for the exchange rate with the CIR dynamics for interest rates. [ABSTRACT FROM AUTHOR]

Studies of the term structure of interest rates try to explain the relationship between the yield to maturity on zero-coupon bonds and their time to maturity. Over the years, many theoretical models have been developed to explain the stylized facts of U.S. Treasury yields; however, model comparison, parameter estimation and hypothesis testing remain thorny issues. The purpose of this paper is to show that Bayesian methods and Markov Chain Monte Carlo (MCMC) methods, in particular, may help resolve a number of these problems, especially those related to model comparison. We use MCMC to compare the seminal models of Vasicek and Cox, Ingersoll and Ross (CIR). The most surprising result of our analysis is that one of these two models is almost 50 000 times more likely than the other. In contrast, results in the previous literature have been much more ambiguous because they are based on a variety of goodness-of-fit measures. A Monte Carlo study shows that these results are not spurious: the MCMC method is able to select the correct data generation model, whereas goodness-of-fit measures are virtually indistinguishable regardless of whether the data were generated from Vasicek or CIR. [ABSTRACT FROM AUTHOR]

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds. [ABSTRACT FROM PUBLISHER]

This paper presents new approximation formulae for European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models [Int. J. Theor. Appl. Finance, 2010, 13(4), 603–634] for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of stochastic dividends or stochastic convenience yields. We finally provide numerical results to illustrate the accuracy with real market data. [ABSTRACT FROM AUTHOR]

In a series of papers during the last ten years an interest rate theory with models which are driven by Lévy or more general processes has been developed. In this paper we derive explicit formulas for the correlations of interest rates as well as zero coupon bonds with different maturities. The models considered in this general setting are the forward rate (HJM), the forward process and the LIBOR model as well as the multicurrency extension of the latter. Specific subclasses of the class of generalized hyperbolic Lévy motions are studied as driving processes. Based on a data set of parametrized yield curves derived from German government bond prices we estimate correlations. In a second step the empirical correlations are used to calibrate the Lévy forward rate model. The superior performance of the Lévy driven models becomes obvious from the graphs. [ABSTRACT FROM AUTHOR]

This paper examines an alternative approach to interest rate modeling, in which the nonlinear and random behavior of interest rates is captured by a stochastic differential equation evolving on a curved state space. We consider as candidate state spaces the matrix Lie groups; these offer not only a rich geometric structure, but-unlike general Riemannian manifolds-also allow for diffusion processes to be constructed easily without invoking the machinery of stochastic calculus on manifolds. After formulating bilinear stochastic differential equations on general matrix Lie groups, we then consider interest rate models in which the short rate is defined as linear or quadratic functions of the state. Stochastic volatility is also augmented to these models in a way that respects the Riemannian manifold structure of symmetric positive-definite matrices. Methods for numerical integration, parameter identification, pricing, and other practical issues are addressed through examples. [ABSTRACT FROM AUTHOR]

In this paper, we estimate the term structure of interest rate volatilities. It is well known that volatility is the main input for option and other fixed income derivatives valuation models. However, we find that volatility estimates depend significantly on the model used to estimate the zero coupon yield curve (Nelson and Siegel; Vasicek and Fong) and the assumption concerning the heteroskedasticity structure of errors (OLS or GLS weighted by duration). We conclude in our empirical analysis that there are significant differences between these volatility estimates in the short term (less than one year) and in the long term (more than 10 years). [ABSTRACT FROM AUTHOR]

In this paper we present a Markov-Functional hybrid interest rate/foreign exchange model that allows calibration to given market volatility surfaces in both dimensions simultaneously. This is achieved by extending the approach introduced by Fries and Rott by a functional for the foreign exchange rate (FX), which allows a fast, yet accurate calibration to a given market FX volatility surface. This calibration procedure comes as an additional step to the known calibration of the LIBOR functional, resulting in an efficient implementation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to demonstrate the powerful and flexible applicability of the Gram-Charlier expansion to pricing of a wide variety of interest rate related products involving interest rate risk and credit risk. In this paper, we develop easily implemented approximations of the prices of several derivatives; swaptions, CMS, CMS options, and vulnerable options. Associated with the default risk, a survival contingent forward measure is constructed. [ABSTRACT FROM AUTHOR]

This paper derives analytical solutions for arbitrage-free bond yields when the short-term interest rate follows an autoregressive process with the intercept switching endogenously. This process from the SETAR family is especially suited to capture the near-unit-root behaviour typically observed in the evolution of short-term interest rates. The derived yield functions, mapping the one-month rate into n-period yields, exhibit a convex/concave shape to the left and right of the threshold value, respectively, a pattern which is also found in US bond yield data. The longer the time to maturity, the more distinct the nonlinearity of the yield function becomes. [ABSTRACT FROM AUTHOR]

When equity default swap (EDS) contracts were first included in a rated collateralized debt obligation (CDO) deal, some critics doubted the originality of the product. In fact, EDSs are equivalent to already existing binary barrier options on equity, except the premium is not paid upfront, but over time, and conditional on the trigger event not having occurred. Therefore, as opposed to existing options, the buyer of an EDS: (1) postpones payment for protection, and (2) purchases not only protection against a sharp drop in the price of equity, but also the right to cease payments in case the barrier is hit. This paper derives the closed-form pricing formula for equity default swap spreads under the Black–Scholes assumptions, and then quantifies the fraction of the EDS spread actually due to the ‘swap’ feature of the contract for plausible parameter values. It is found that the extra spread due to the swap nature of EDSs is economically significant only for high volatility, high trigger levels, and long time-to-maturity. The impact of interest rates on the value of the ‘swap’ feature is almost exclusively due to the postponement of payments. [ABSTRACT FROM AUTHOR]

A broad class of exotic interest rate derivatives can be valued simply by adjusting the forward interest rate. This adjustment is known in the market as convexity correction . Various ad hoc rules are used to calculate the convexity correction for different products, many of them mutually inconsistent. In this research paper we put convexity correction on a firm mathematical basis by showing that it can be interpreted as the side-effect of a change of probability measure. This provides us with a theoretically consistent framework to calculate convexity corrections. Using this framework we review various expressions for LIBOR in arrears and diff swaps that have been derived in the literature. Furthermore, we propose a simple method to calculate analytical approximations for general instances of convexity correction. [ABSTRACT FROM AUTHOR]

This paper proposes a jump-diffusion model, in closed form, to price corporate debt securities, senior and junior, with the same maturity and violation of the absolute priority rule. We take the structural approach that the firm's asset value follows a jump-diffusion process in a stochastic interest rate economy. Default occurs only if the firm value at the maturity of the corporate debts is less than the sum of the prespecified face values. Unlike previous models in the structural approach, our model is consistent with the current term structures of credit spreads for both senior and junior debts. In particular, it captures realistic short maturity credit spreads observed in the market. The key idea is to allow the jump intensity to be a time-dependent function. As an application, valuation of credit spread options is presented. [ABSTRACT FROM AUTHOR]

Short-term interest rate derivatives present a few unresolved problems. It is not obvious which pricing model to use, and the usual Heath-Jarrow-Morton type models seem insufficient to describe the risk they entail. Moreover, the hedging process is fairly delicate as the liquidity of short-term products cannot always be relied upon. In this paper, we justify the use of a market model with jumps to price these products. The main advantage of this approach is two fold. First, we will show how realistic such a model proves to be. Then, using justified approximations, the market model with jumps is made very tractable. Finally, the hedging issue is resolved by describing a dynamic delta-hedging strategy provided by the model in addition to a static vega-hedging strategy designed to use the relevant liquid products at the trader's disposal. [ABSTRACT FROM AUTHOR]

The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. This paper investigates whether the use of models which allow for negative interest rates can improve option pricing and implied volatility forecasting. This is done with special attention to foreign exchange and index options. To this end, we carried out an empirical analysis on the prices of call and put options on the US S&P 500 index and Eurodollar futures using a generalization of the Heston model in the stochastic interest rate framework. Specifically, the dynamics of the option’s underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. Explicit formulas for the transition probability density function and moments are derived. These formulas are used to estimate the model parameters efficiently. Three empirical analyses are illustrated. The first two show that the use of models which allow for negative interest rates can efficiently reproduce implied volatility and forecast option prices (i.e. S&P index and foreign exchange options). The last studies how the US three-month government bond yield affects the US S&P 500 index. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce an extension to the LIBOR Market Model (LMM) that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LMM by a regime-switching jump diffusion. We demonstrate that the new Markov-switching jump diffusion (MSJD) LMM can be embedded into a generalized regime-switching Heath–Jarrow–Morton model and prove that the considered market is arbitrage-free. We derive pricing formulas for caps, floors and swaptions using Fourier pricing techniques and show how the model can be calibrated to real market data. [ABSTRACT FROM AUTHOR]

One-factor no-arbitrage models of the short rate are important tools for valuing interest rate derivatives. Trees are often used to implement the models and fit them to the initial term structure. This paper generalizes existing tree building procedures so that a very wide range of interest rate models can be accommodated. It shows how a piecewise linear volatility function can be calibrated to market data and, using market data from days during the period 2004–2013, finds a best fit to cap prices. [ABSTRACT FROM AUTHOR]

This paper proposes an integrated pricing framework for convertible bonds, which comprises firm value evolving as an exponential jump diffusion, correlated stochastic interest rates movements and an efficient numerical pricing scheme. By construction, the proposed stochastic model fits in the framework of affine jump diffusion processes of Duffieet al.[Econometrica, 2000,68, 1343–1376] with tractable behaviour. We define the firm’s optimal call policy and investigate its impact on the computed convertible bond prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps, stochastic interest rates and a non-zero correlation structure between firm value and interest rates. [ABSTRACT FROM AUTHOR]

The paper considers a test for structural breaks based on quantile regressions instead of OLS estimates. Besides granting robustness, this allows us to verify the impact of a break in more than one point of the conditional distribution. The quantile regression test is then repeatedly implemented as a diagnostic tool to uncover partial or spurious breaks. The test is also implemented to measure the contribution of each explanatory variable to the instability of the regression coefficients, thus finding which one of the different possible sources of breaks linked to the nature of the explanatory variables is the most effective. A real data example of exchange rates shows the presence of a time-driven break, but only at the lower quartile, while the analysis of the explanatory variable excludes its involvement in the break. Since the asymptotic distribution of the OLS test for structural change depends on i.i.d. normal errors and on the exogeneity of the explanatory variables, a Monte Carlo study analyses the behavior of OLS and quantile regression tests for structural changes with lagged endogenous variables, non-normal errors, spurious or partial breaks, and misspecification. [ABSTRACT FROM AUTHOR]

This paper investigates how interest rates affect the probability of default (PD) in a general equilibrium incomplete markets economy. We show that the PD depends positively on the loan interest rate and negatively on the economy base interest rate. Empirically, this finding is confirmed by estimation of the Cox proportional hazard model with time-varying covariates using a sample of 445 889 individual contracts from a large Brazilian bank. Among the controls are macroeconomic variables and specific characteristics of the contracts and borrowers. A lower base interest rate, implied by easing monetary policy, leads banks to lend more money for riskier borrowers, increasing the PD. [ABSTRACT FROM AUTHOR]