Download or read book American Options in Levy Models With Stochastic Interest Rate of CIR Type written by Svetlana Boyarchenko and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of interest rate driven by the square root process with embedded jumps is derived. Numerical examples show that fairly accurate results can be obtained in reasonable time. It is shown that the shape of the early exercise boundary strongly depends on the sign of the leverage parameter.

Download or read book American Options in the Heston Model With Stochastic Interest Rate written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the Heston model with the stochastic interest rate of the CIR type and more general models with stochastic volatility and interest rates depending on two CIR - factors. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options arising in the time - discretization of a Markov - modulated Levy model. Options in this sequence are solved using an iteration method based on the Wiener - Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff - Schwartz method and Medvedev - Scaillet asymptotic method is demonstrated.

Download or read book American Options in Levy Models with Stochastic Volatility written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in the sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of a Levy process with the intensity coefficient driven by the square root process with embedded jumps is derived. Numerical examples corroborate the general result about a gap between strike and early exercise boundary at expiry, in a neighborhood of r=0, in the presence of jumps.

Download or read book American Options in L vy Models with Stochastic Interest Rates written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. An explicit algorithm for the case of positive stochastic interest rates driven by a process of the Ornstein-Uhlenbeck type is derived. Efficiency of the method is illustrated with numerical examples.

Download or read book American Options in Regime Switching L vy Models With Non Semibounded Stochastic Interest Rates written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. Contrary to the earlier version of the method, the interest rate may assume non-positive values. As applications, explicit algorithms for Vasicek and Black's models with jumps are derived. Numerical examples show that the option prices in these two models are very close.

Download or read book American Options in Regime Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2007 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper, we solve the pricing problem for American options in Markov-modulated Levy models. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization for regime-switching models. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modelled as finite-state Markov chains.

Download or read book Perpetual American Options in Regime Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2007 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper, we solve the pricing problem for perpetual American options in Markov-modulated Levy models. The early exercise boundaries and prices are calculated using an iteration procedure. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modelled as finite-state Markov chains.

Download or read book Essays on American Options Pricing Under Levy Models with Stochastic Volatility and Jumps written by Ye Chen and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In ``A Multi-demensional Transform for Pricing American Options Under Stochastic Volatility Models", we present a new transform-based approach for pricing American options under low-dimensional stochastic volatility models which can be used to construct multi-dimensional path-independent lattices for all low-dimensional stochastic volatility models given in the literature, including SV, SV2, SVJ, SV2J, and SVJ2 models. We demonstrate that the prices of European options obtained using the path-independent lattices converge rapidly to their true prices obtained using quasi-analytical solutions. Our transform-based approach is computationally more efficient than all other methods given in the literature for a large class of low-dimensional stochastic volatility models. In ``A Multi-demensional Transform for Pricing American Options Under Levy Models", We extend the multi-dimensional transform to Levy models with stochastic volatility and jumps in the underlying stock price process. Efficient path-independent tree can be constructed for both European and American options. Our path-independent lattice method can be applied to almost all Levy models in the literature, such as Merton (1976), Bates (1996, 2000, 2006), Pan (2002), the NIG model, the VG model and the CGMY model. The numerical results show that our method is extemly accurate and fast. In ``Empirical performance of Levy models for American Options", we investigate in-sample fitting and out-of-sample pricing performance on American call options under Levy models. The drawback of the BS model has been well documented in the literatures, such as negative skewness with excess kurtosis, fat tail, and non-normality. Therefore, many models have been proposed to resolve known issues associated the BS model. For example, to resolve volatility smile, local volatility, stochastic volatility, and diffusion with jumps have been considered in the literatures; to resolve non-normality, non-Markov processes have been considered, e.g., Poisson process, variance gamma process, and other type of Levy processes. One would ask: what is the gain from each of the generalized models? Or, which model is the best for option pricing? We address these problems by examining which model results in the lowest pricing error for American style contracts. For in-sample analysis, the rank (from best to worst) is Pan, CGMYsv, VGsv, Heston, CGMY, VG and BS. And for out-of-sample pricing performance, the rank (from best to worst) is CGMYsv, VGsv, Pan, Heston, BS, VG, and CGMY. Adding stochastic volatility and jump into a model improves American options pricing performance, but pure jump models are worse than the BS model in American options pricing. Our empirical results show that pure jump model are over-fitting, but not improve American options pricing when they are applied to out-of-sample data.

Download or read book Interest Rate Option Models written by Riccardo Rebonato and published by . This book was released on 1996-09-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible, first-rate overview of interest rate dependent options for traders and institutional investors Until now market professionals seeking to exploit the profit potential of interest rate dependent options were forced to hunt through esoteric journals for a crumb or two of practical knowledge about their use. This accessible book narrows the information gap. Written in easy-to-follow, non-technical language, it logically reviews all the most commonly used interest rate option models, showing how each one can be applied and implemented for specific market applications. DR. RICARDO REBONATO (London, England) is head of Research, Debt Capital Markets at Barclays de Zoete Wedd Ltd.

Download or read book A Pricing Model for American Options with Stochastic Interest Rates written by Albert Jan Menkveld and published by . This book was released on 1998 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete Time Valuation of American Options with Stochastic Interest Rates written by Kaushik I. Amin and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop an arbitrage-free discrete time model to price American-style claims for which domestic term structurerisk, foreign term structure risk and currency risk are important. This model combines a discrete version of the Heath, Jarrow, Morton (1992) term structure model with the binomial model of Cox, Ross, and Rubinstein (1979). It converges (weakly) to the continuous time models in Amin and Jarrow (1991, 1992). The general model is quot;path dependentquot; and can be implemented with arbitrary volatility functions to value claims with maturity up to five years. The model is illustrated with applications to long-dated American currency warrants and a cross-rate swap from the quanto class.

Download or read book Pricing American Options in Regime Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pricing problem for American options in Markov-modulated Lévy models is solved. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization procedure for regime-switching models. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. In contrast with the earlier version of the method, an explicit algorithm is formulated for wide classes of Lévy processes, and FFT and iFFT are used.

Download or read book Pricing American Options with Stochastic Interest Rates written by Kaushik Ishwar Amin and published by . This book was released on 1992 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Pricing Model for American Options with Stochastic Interest Rates written by Ton Vorst and published by . This book was released on 2008 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop a new method to value American stock options with stochastic interest rates. We construct a binomial tree for the stock price divided by the price of the zero coupon bond that matures at the maturity date of the option. In fact, we construct a tree for the so-called forward risk adjusted measure. In each node of the tree the quotient of the stock price and bond price is constant and there are combinations of stock and bond prices for which immediate exercise is optimal and other combinations for which this is not the case. We derive for each node in the tree an analytic expression for the expected immediate exercise premium conditional on this quotient of stock and bond prices. This immediate exercise premium is added to the value that is derived from the familiar backward procedure. Both European and American option prices depend on the correlation between the interest rate process and the stock price process. It is interesting to see that with increasing correlation between the interest rate process and the stock price process, and hence a decreasing correlation between bond and stock prices, the values of European options increase, while the values of the early exercise premium decrease. For American options this might result in a non-monotonic relation between the correlation coefficient and the option price. Furthermore, there is evidence that the early exercise premium due to stochastic interest rates is much larger than established before by other researchers. Finally, we also consider the influence of the shape of the initial term structure.

Download or read book An Investigation of the Impact of Stochastic Interest Rates on the Pricing of Equity Options written by Peter Carayannopoulos and published by . This book was released on 1993 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Interest Rate Modeling With Fixed Income Derivative Pricing Third Edition written by Nicolas Privault and published by World Scientific. This book was released on 2021-09-02 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the mathematics of stochastic interest rate modeling and the pricing of related derivatives, based on a step-by-step presentation of concepts with a focus on explicit calculations. The types of interest rates considered range from short rates to forward rates such as LIBOR and swap rates, which are presented in the HJM and BGM frameworks. The pricing and hedging of interest rate and fixed income derivatives such as bond options, caps, and swaptions, are treated using forward measure techniques. An introduction to default bond pricing and an outlook on model calibration are also included as additional topics.This third edition represents a significant update on the second edition published by World Scientific in 2012. Most chapters have been reorganized and largely rewritten with additional details and supplementary solved exercises. New graphs and simulations based on market data have been included, together with the corresponding R codes.This new edition also contains 75 exercises and 4 problems with detailed solutions, making it suitable for advanced undergraduate and graduate level students.

Download or read book Pricing American Options Under Stochastic Volatility and Stochastic Interest Rates written by Jannick B. G. Schreiner and published by . This book was released on 2012 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: