Asymptotic Expansion Approaches in Finance: Applications to Currency Options

Akihiko Takahashi and Kohta Takehara
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Akihiko Takahashi: Faculty of Economics, University of Tokyo
Kohta Takehara: Graduate School of Economics, University of Tokyo

No CIRJE-F-654, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This chapter presents a basic of the methodology so-called an asymptotic expansion approach, and applies this method to approximation of prices of currency options with a libor market model of interest rates and stochastic volatility models of spot exchange rates. The scheme enables us to derive closed-form approximation formulas for pricing currency options even with high flexibility of the underlying model; we do not model a foreign exchange rate's variance such as in Heston [27], but its volatility that follows a general time-inhomogeneous Markovian process. Further, the correlations among all the factors such as domestic and foreign interest rates, a spot foreign exchange rate and its volatility, are allowed. At the end of this chapter some numerical examples are provided and the pricing formula is applied to the calibration of volatility surfaces in the JPY/USD option market.

Pages: 51 pages
Date: 2009-08
New Economics Papers: this item is included in nep-cba and nep-rmg
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