Location of Repository

This paper proposes an asymptotic expansion scheme of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. In particular, we derive closed-form approximation formulas for the density functions of the underlying assets and for pricing currency options based on the third order asymptotic expansion scheme; we do not model a foreign exchange rate's variance such as in Heston[1993], but its volatility that follows a general time-inhomogeneous Markovian process, and we allow the correlations among all the factors, that is domestic and foreign interest rates, a spot foreign exchange rate and its volatility. Finally, we provide numerical examples and apply the pricing formula to the calibration of volatility surfaces in the JPY/USD option market.

OAI identifier:

Provided by:
Research Papers in Economics

Downloaded from
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2007/2007cf474.pdf

- [1992a], ”Asymptotic Expansion for Small Diﬀusions via the Theory of
- [1992b], “Asymptotic Expansions for Statistics Related to Small Diﬀusions,”
- [2004b], “An Asymptotic Expansion for a Black-Scholes Type Model,”
- (1991). [2006]ɼ“A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach,” Asia-Paciﬁc Financial Markets,
- A Closed-Form Solution for Options with Stochastic Volatility
- (2005). A multi-currency model with FX volatility skew,” Working paper.
- (2003). A New Approximate Swaption Formula in the LIBOR Market Model: An Asymptotic Expansion Approach,”
- (2005). A Note on Computing Greeks by an Asymptotic Expansion Scheme,”
- An Asymptotic Expansion Approach to Pricing
- (1999). An Asymptotic Expansion Approach to Pricing Contingent
- An Asymptotic Expansion Scheme for Optimal
- (1987). Analysis of Wiener Functionals (Malliavin Calculus) and Its Applications to Heat Kernels,”
- (2004). Applications of the Asymptotic Expansion Approach based on Malliavin-Watanabe Calculus
- Bond Pricing and the Term Structure of Interest Rates:
- (1997). Closed Form Solutions for Term Structure Derivatives with Long-normal Interest Rates,”
- (2001). Cross-currency LIBOR market models,” Working paper,
- (1991). Currency Option Pricing with Stochastic Domestic and Foreign Interest-Rates,”
- (1995). Discrete-time valuation of American options with stochastic interest rates,”
- E.[2002], “A Multi-currency Extension of the Lognormal Interest Rate Market Model,” Finance and Stochastics,
- (1995). Essays on the Valuation Problems of Contingent Claims,”
- Finite Dimensional Realizations of Interest Rate Models with Jumps and an Asymptotic Expansion for the Black-Scholes Model with Generalized Volatility,” Unpublished Ph.D. Dissertation,
- (1983). Foreign currency options,”
- Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options,”
- (2005). Monte Carlo Simulation with Asymptotic Method,”
- Numerical Procedures for Implementing Term Structure Models I: Single-factor Models,”
- (1997). Numerical valuation of cross-currency swaps and swaptions,”
- (2003). On Validity of the Asymptotic Expansion Approach in Contingent Claim Analysis,”
- (1987). Optimal Portfolio and Consumption Decisions for a ‘small investor’ on a Finite Horizon,”
- (2005). Pricing Contingent Claims with Credit Risk: Asymptotic Expansion Approach,”
- (1991). Pricing Cross-Currency Options,”
- (1991). Pricing Foreign-Currency Options Under Stochastic Interest-Rates,”
- (2001). The Aysmptotic Expansion Approach to the Valuation
- (1983). The Pricing of Call and Put Options on Foreign-Exchange,”
- (1976). The Pricing of Commodity Contracts,”
- (1973). Theory of Rational Option Pricing”,
- (1999). Valuation of Cross-currency Derivatives with Stochastic Interest Rates in a Three-factor Model,”
- Volatility and Correlation,”

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.