This paper reviews the asymptotic expansion approach based on Malliavin-Watanabe Calculus in Mathematical Finance. We give the basic formulation of the asymptotic expansion approach and discuss its power and usefulness to solve important problems arised in nance. As illustrations we use three...

This paper develops a Fourier transform method with an asymptotic expansion approach for option pricing. The method is applied to European currency options with a libor market model of interest rates and jump-diffusion stochastic volatility models of spot exchange rates. In particular, we derive...

This paper proposes a new method to a bond portfolio problem in a multi-period setting. In particular, we apply a factor allocation approach to constructing the optimal bond portfolio in a class of multi-factor Gaussian yield curve models. In other words, we consider a bond portfolio problem in...

This paper studies the probability distribution and option pricing for drawdown in a stochastic volatility environment. We derive an analytical approximation formula for them by applying a singular perturbation method ([12]). Then, numerical examples show that the instantaneous correlation...

This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for the valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general...

We shall propose a new computational scheme with the asymptotic method to achieve variance reduction of Monte Carlo simulation for numerical analysis especially in finance. We not only provide general scheme of our method,@but also show its effectiveness through numerical examples such as...

This paper proposes a new scheme for the static replication of European options and their portfolios. First, we derive a general approximation formula for efficient static replication as an extension of Carr and Chou [1997, 2002] and Carr and Wu [2002]. Second, we present a concrete procedure...

This paper formulates and analyzes a dynamic optimization problem of bond portfolios within Markovian Heath-Jarrow-Morton term structure models. In particular, we investigate optimal yield curve strategies analytically and numerically, and provide theoretical justification for a typical strategy...

This paper proposes a new method to a bond portfolio problem in a multi-period setting. In particular, we apply a factor allocation approach to constructing the optimal bond portfolio in a class of multi-factor Gaussian yield curve models. In other words, we consider a bond portfolio problem in...

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...