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...

This paper proposes a new hedging scheme of European derivatives under uncertain volatility environments, in which a weighted variance swap called the polynomial variance swap is added to the Black-Scholes delta hedging for managing exposure to volatility risk. In general, under these...

This paper proposes a continuous-time term-structure model under stochastic differential utility with non-unitary elasticity of intertemporal substitution (EIS, henceforth) in a representative-agent endowment economy with mean-reverting expectations on real output growth and inflation. Using...

An asymptotic expansion scheme in finance initiated by Kunitomo and Takahashi [15] and Yoshida[68] is a widely applicable methodology for analytic approximation of the expectation of a certain functional of diffusion processes. [46], [47] and [53] provide explicit formulas of conditional...

This paper studies portfolio selection and performance analysis of hedge funds whose locations or investment targets are Asia-Pacific region. Utilizing Eurekahedge database, we investigate the characteristics of the funds' returns and optimization methods to create a fund of funds. Moreover, we...

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...

There are now available wide variety of swap products which exchange Libors with different currencies and tenors. Furthermore, the collateralization is becoming more and more popular due to the increased attention to the counter party credit risk. These developments require clear distinction...

This paper proposes a new three-factor model with stochastic mean reversions for commodity prices and derives the closed-form solution for the term structure of futures prices. Moreover, it is confirmed that the prices of crude oil and copper futures prices estimated by our model replicate the...

This paper proposes a new scheme for static hedging of European path-independent derivatives under stochastic volatility models. First, we show that pricing European path-independent derivatives under stochastic volatility models is transformed to pricing those under one-factor local volatility...

Recently, not only academic researchers but also many practitioners have used the methodology so-called "an asymptotic expansion method" in their proposed techniques for a variety of financial issues. e.g. pricing or hedging complex derivatives under high-dimensional stochastic environments....