Quadratic Term Structure Models
Quadratic Term Structure Models

Author: Dong-Hyun Ahn

Publisher:

Published: 2000

Total Pages: 52

ISBN-13:

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We identify and characterize a class of term structure models where bond yields are quadratic functions of the Markov process. We label this class as the 'quadratic class' and aim to lay a solid theoretical foundation for its future empirical application. We contribute to the literature in three aspects: (i) We identify the necessary and sufficient conditions for the quadratic class in terms of the Markov process, the instantaneous interest rate, and the pricing kernel. (ii) We characterize the properties of the bond yields and forward rates in terms of their moment conditions and characteristic functions. (iii) We provide closed-form solutions to a wide variety of fixed income derivatives.

Dynamic Term Structure Modeling
Dynamic Term Structure Modeling

Author: Sanjay K. Nawalkha

Publisher: John Wiley & Sons

Published: 2007-05-23

Total Pages: 722

ISBN-13: 0470140062

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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

Closed-Form Solutions for Pricing Credit-Risky Bonds and Bond Options
Closed-Form Solutions for Pricing Credit-Risky Bonds and Bond Options

Author: Leonard Tchuindjo

Publisher:

Published: 2013

Total Pages:

ISBN-13:

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This paper proposes closed-form solutions for pricing credit-risky discount bonds and their European call and put options in the intensity-based reduced-form framework, assuming the stochastic dynamics of both the risk-free interest rate and the credit-spread are driven by two correlated Ho-Lee models [T.S.Y. Ho, S.B. Lee, Term structure movements and pricing interest rates contingent claims, Journal of Finance 41 (5) (1986) 1011-1029]. The results are easily to implement, and require very few parameters which are directly implied from market data.

Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates
Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates

Author: Kristian R. Miltersen

Publisher:

Published: 2006

Total Pages:

ISBN-13:

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We derive a unified model which gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds. The crucial assumption is that forward rates with a compounding period that matches the contract, which we want to price, is log normally distributed. Moreover, this assumption is shown to be consistent with the Heath-Jarrow-Morton model for a specific choice of volatility.

Pricing of Bond Options
Pricing of Bond Options

Author: Detlef Repplinger

Publisher: Springer Science & Business Media

Published: 2008-08-15

Total Pages: 141

ISBN-13: 3540707298

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A major theme of this book is the development of a consistent unified model framework for the evaluation of bond options. In general options on zero bonds (e.g. caps) and options on coupon bearing bonds (e.g. swaptions) are linked by no-arbitrage relations through the correlation structure of interest rates. Therefore, unspanned stochastic volatility (USV) as well as Random Field (RF) models are used to model the dynamics of entire yield curves. The USV models postulate a correlation between the bond price dynamics and the subordinated stochastic volatility process, whereas Random Field models allow for a deterministic correlation structure between bond prices of different terms. Then the pricing of bond options is done either by running a Fractional Fourier Transform or by applying the Integrated Edgeworth Expansion approach. The latter is a new extension of a generalized series expansion of the (log) characteristic function, especially adapted for the computation of exercise probabilities.

Pricing Swaptions and Coupon Bond Options in Affine Term Structure Models
Pricing Swaptions and Coupon Bond Options in Affine Term Structure Models

Author: David Schrager

Publisher:

Published: 2005

Total Pages: 29

ISBN-13:

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We propose an approach to find an approximate price of a swaption in Affine Term Structure Models. Our approach is based on the derivation of approximate dynamics in which the volatility of the Forward Swap Rate is itself an affine function of the factors. Hence we remain in the affine framework and well known results on transforms and transform inversion can be used to obtain swaption prices in ways similar to bond options (i.e. caplets). We demonstrate that we can also obtain a closed form formula for the approximate price which is based on square-root dynamics for the swap rate. The latter approximation is extremely fast while remaining accurate. The method can be easily generalized to price options on coupon bonds. Computational time compares favorably with other approximation methods. Numerical results on the quality of the approximation are excellent. Our results show that in Affine models, analogously to the LIBOR Market Model, LIBOR and Swap rates are driven by approximately the same type of (in this case affine) dynamics.