The Valuation of American-style Swaptions in a Two-factor Spot-futures Model PDF Download

Author: Sandra Peterson
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 0

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Author: Sandra Peterson
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 53

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Author: Sandra Peterson
Publisher:
ISBN:
Category :
Languages : en
Pages : 40

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We build a no-arbitrage model of the term structure of interest rates using two stochastic factors, the short-term interest rate and the premium of the futures rate over the short-term interest rate. The model provides and extension of the lognormal interest rate model of Black and Karasinski (1991) to two factors, both of which can exhibit mean-reversion. The method is computationally efficient for several reasons. First, the model is based on Libor futures prices, enabling us to satisfy the no-arbitrage condition without resorting to iterative methods. Second, we modify and implement the binomial approximation methodology of Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) to compute a multiperiod tree of rates with the no-arbitrage property. The method uses a recombining two-dimensional binomial lattice of interest rates that minimizes the number of states and term structures over time. In addition to these computational advantages, a key feature of the model is that it is consistent with the observed term structure of futures rates as well as the term structure of volatilities implied by the prices of interest rate caps and floors. These prices are shown to be highly sensitive to the existence of the second factor and its volatility characteristics.

Author: Sandra Peterson
Publisher:
ISBN:
Category :
Languages : en
Pages : 50

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We build a multi-factor, no-arbitrage model of the term structure of interest rates. The stochastic factors are the short-term interest rate and the premia of the futures rates over the short-term interest rate. In the three-factor version of the model, for example, the first factor is the three-month LIBOR, the second factor is the premium of the first futures LIBOR over spot LIBOR, and the third factor is the incremental premium of the second futures over the first. The model provides an extension of the lognormal interest rate model of Black and Karasinski (1991) to multiple factors, each of which can exhibit mean-reversion. The method is computationally efficient for several reasons. First, since our model is based on LIBOR futures prices, we can satisfy the no-arbitrage condition without resorting to iterative methods. Second, we modify and implement the binomial approximation methodology of Nelson and Ramaswamy (1990) and Ho, Stapleton and Subrahmanyam (1995) to compute a multi-period tree of rates with the no-arbitrage property.The method uses a recombining two or three-dimensional binomial lattice of interest rates that minimizes the number of states and term structures over time. In addition to these computational advantages, a key feature of the model is that it is consistent with the observed term structure of futures rates as well as the term structure of volatilities implied by the prices of interest rate caps and floors. We use the model to price European-style, Bermudan-style, and American-style swaptions.To implement the methodology, we first calibrate the model to the caplet implied-volatility curve on a given day, and then use the model to price European-style swaptions. We find that the two-factor model, where the LIBOR mean reverts rapidly to a slowly mean-reverting second factor overprices the swaptions relative to market quotations. However, introducing a third factor significantly reduces the overpricing. Finally, we re-calibrate the two-factor model simultaneously to caplet and swaption prices and use the model output to price Bermudan-style swaptions.

Author: New York University. Salomon Center
Publisher:
ISBN:
Category : Finance
Languages : en
Pages : 44

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Author: Viral V. Acharya
Publisher:
ISBN:
Category : Banking law
Languages : en
Pages : 78

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Author: Jilong Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 19

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In this paper a pricing formula is derived for futures options in Schwartz 1997 two factor model with time dependent spot volatility. The pricing formula can be used like the Black-Scholes formula with observed volatility directly. Also, it can be used to find backwards the results of time dependent spot volatility with a few market data. The results of time dependent spot volatility can be easily and quickly obtained in Matlab. We also explain why the result of time dependent spot volatility needs to be tested theoretically and show how to make sure its correctness both in theory and practise.

Author: Roy C. Smith
Publisher:
ISBN:
Category :
Languages : en
Pages : 58

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Author: Sanjay K. Nawalkha
Publisher: John Wiley & Sons
ISBN: 0470140062
Category : Business & Economics
Languages : en
Pages : 722

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Praise for Dynamic Term Structure Modeling "This book offers the most comprehensive coverage of term-structure models I have seen so far, encompassing equilibrium and no-arbitrage models in a new framework, along with the major solution techniques using trees, PDE methods, Fourier methods, and approximations. It is an essential reference for academics and practitioners alike." --Sanjiv Ranjan Das Professor of Finance, Santa Clara University, California, coeditor, Journal of Derivatives "Bravo! This is an exhaustive analysis of the yield curve dynamics. It is clear, pedagogically impressive, well presented, and to the point." --Nassim Nicholas Taleb author, Dynamic Hedging and The Black Swan "Nawalkha, Beliaeva, and Soto have put together a comprehensive, up-to-date textbook on modern dynamic term structure modeling. It is both accessible and rigorous and should be of tremendous interest to anyone who wants to learn about state-of-the-art fixed income modeling. It provides many numerical examples that will be valuable to readers interested in the practical implementations of these models." --Pierre Collin-Dufresne Associate Professor of Finance, UC Berkeley "The book provides a comprehensive description of the continuous time interest rate models. It serves an important part of the trilogy, useful for financial engineers to grasp the theoretical underpinnings and the practical implementation." --Thomas S. Y. Ho, PHD President, Thomas Ho Company, Ltd, coauthor, The Oxford Guide to Financial Modeling

Author: Raoul Pietersz
Publisher:
ISBN: 9789058920997
Category :
Languages : en
Pages : 209

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