An asymptotic expansion approach to currency options with a market model of interest rates under stochastic volatility processes of spot exchange rates. (English) Zbl 1151.91545
Summary: 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 a third order asymptotic expansion scheme; we do not model a foreign exchange rate’s variance such as in [S. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options”, Rev. Financ. Stud. 6, No. 2, 327–343 (1993; doi:10.1093/rfs/6.2.327)], 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. Finally, numerical examples are provided and the pricing formula are applied to the calibration of volatility surfaces in the JPY/USD option market.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91B26 | Auctions, bargaining, bidding and selling, and other market models |
Keywords:
asymptotic expansion; currency options; Libor market model; Malliavin calculus; stochastic volatilityReferences:
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