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 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 Pricing American Options with Stochastic Interest Rates written by Kaushik I. 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 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:
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 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 Pricing American Options Under Stochastic Volatility and Stochastic Interest Rates written by Alexey Medvedev and published by . This book was released on 2007 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pricing American Call Options with Dividend and Stochastic Interest Rates written by Shu-Ing Liu and published by . This book was released on 2009 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article presents a closed form solution for pricing American stock call options with one known dividend under the Ho-Lee stochastic interest rate assumptions. Both the closed-form pricing formula and delta hedge ratio formula for the discussed American stock call options are derived. The correlation between the underlying stock price process and the discount factor process is suitably established. Numerical analyses demonstrate that there are some crucial parameters, the correlation coefficient between the stock price process and the discount factor process, and the amount of dividend, that have an impact on the option price and the delta hedge ratio. These results provide researchers and participants with some pricing and hedging applications in the real financial market.
Download or read book American Spread Option Pricing with Stochastic Interest Rates written by An Jiang and published by . This book was released on 2016 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial markets, spread option is a derivative security with two underlying assets and the payoff of the spread option depends on the difference of these assets. We consider American style spread option which allows the owners to exercise it at any time before the maturity. The complexity of pricing American spread option is that the boundary of the corresponding partial differential equation which determines the option price is unknown and the model for the underlying assets is two-dimensional.
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 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 Option Pricing Interest Rates and Risk Management written by Elyès Jouini and published by Cambridge University Press. This book was released on 2001 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 handbook surveys the state of practice, method and understanding in the field of mathematical finance. Every chapter has been written by leading researchers and each starts by briefly surveying the existing results for a given topic, then discusses more recent results and, finally, points out open problems with an indication of what needs to be done in order to solve them. The primary audiences for the book are doctoral students, researchers and practitioners who already have some basic knowledge of mathematical finance. In sum, this is a comprehensive reference work for mathematical finance and will be indispensable to readers who need to find a quick introduction or reference to a specific topic, leading all the way to cutting edge material.
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 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 Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.
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 The Valuation of American Options with Stochastic Interest Rates written by Teng Suan Ho and published by . This book was released on 1996 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
