Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

An Asymptotic Expansion Approach to Pricing Financial Contingent Claims

An Asymptotic Expansion Approach to Pricing Financial Contingent Claims We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applicable to a wide range of valuation problems including contingent claims associated with stocks, foreign exchange rates, the term structure of interest rates, and even their combinations. We illustrate our method by discussing the Black-Scholes economy when the underlying asset prices follow the continuous diffusion processes, which are not necessarily time-homogeneous. The standard Black-Scholes model on stocks and the Cox-Ingersoll-Ross model on the spot interest rate are simple examples. Then we shall give a series of examples on the valuation formulae including plain vanilla options, average options, and other contingent claims. We shall also give some numerical evidence of the accuracy of the approximations we have obtained for practical purposes. Our approach can be rigorously justified by an infinite dimensional mathematics, the Malliavin-Watanabe-Yoshida theory recently developed in stochastic analysis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Asia-Pacific Financial Markets Springer Journals

An Asymptotic Expansion Approach to Pricing Financial Contingent Claims

Takahashi, Akihiko
Asia-Pacific Financial Markets , Volume 6 (2) – Sep 29, 2004
Download PDF
37 pages

Loading next page...
 
/lp/springer-journals/an-asymptotic-expansion-approach-to-pricing-financial-contingent-FktiqB00Ml
Publisher
Springer Journals
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Finance; Finance, general; Macroeconomics/Monetary Economics//Financial Economics; International Economics; Econometrics; Economic Theory/Quantitative Economics/Mathematical Methods
ISSN
1387-2834
eISSN
1573-6946
DOI
10.1023/A:1010080610650
Publisher site
See Article on Publisher Site

Abstract

We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applicable to a wide range of valuation problems including contingent claims associated with stocks, foreign exchange rates, the term structure of interest rates, and even their combinations. We illustrate our method by discussing the Black-Scholes economy when the underlying asset prices follow the continuous diffusion processes, which are not necessarily time-homogeneous. The standard Black-Scholes model on stocks and the Cox-Ingersoll-Ross model on the spot interest rate are simple examples. Then we shall give a series of examples on the valuation formulae including plain vanilla options, average options, and other contingent claims. We shall also give some numerical evidence of the accuracy of the approximations we have obtained for practical purposes. Our approach can be rigorously justified by an infinite dimensional mathematics, the Malliavin-Watanabe-Yoshida theory recently developed in stochastic analysis.

Journal

Asia-Pacific Financial Markets – Springer Journals

Published: Sep 29, 2004

References

  • Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system
    Fujikoshi, Y.; Morimune, K.; Kunitomo, N.; Taniguchi, M.
  • Option prices with stochastic volatilities: An equilibrium analysis
    He, H.
  • A variable reduction technique for pricing average-rate options
    He, H.; Takahashi, A.
  • Bond pricing and the term structure of interest rates: A new methodology for contingent claims valuation
    Heath, D.; Jarrow, R.; Morton, A.
  • Stochastic Differential Equations and Diffusion Processes
    Ikeda, N.; Watanabe, S.
  • Pricing average options
    Kunitomo, N.; Takahashi, A.
  • Essays on the valuation problems of contingent claims
    Takahashi, A.
  • Lectures on Stochastic Differential Equations and Malliavin Calculus
    Watanabe, S.
  • Analysis ofWiener functionals (Malliavin Calculus) and its applications to heat kernels
    Watanabe, S.
  • Asymptotic expansions for statistics related to small diffusions
    Yoshida, N.
  • Asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of Malliavin-Watanabe
    Yoshida, N.
  • Malliavin calculus and asymptotic expansions for martingales
    Yoshida, N.