This paper develops a general pricing method for multi-asset cross currency options, whose underlying asset consists of multiple different assets, and the evaluation currency is different from the ones used in the most liquid market of each asset; the examples include cross currency options,...

This paper presents a new approximation formula for pricing swaptions and caps/floors under the LIBOR market model of interest rates (LMM) with the local and affine-type stochastic volatility. In particular, two approximation methods are applied in pricing, one of which is so called...

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. It also examines the relation of our model with Schwartz(1997) type models that explicitly include interest rates and...

This paper shows pricing and hedging efficiency of a three factor stochastic mean reversion Gaussian model of commodity prices using oil and copper futures and forward contracts. The model is estimated using NYMEX WTI (light sweet crude oil) and LME Copper futures prices and is shown to fit the...

This study proposes a new approximation formula for pricing average options on commodities under a stochastic volatility environment. In particular, it derives an option pricing formula under Heston and an extended λ‐SABR stochastic volatility models (which includes an extended SABR model as...

This paper studies impacts of imperfect collateralization on derivatives values. Firstly, we present a general framework for the analysis in a multi-dimensional dif fusion setting, and then calclate pre-default values of forwards and options for the numerical experiments. In particular, we...

This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in a stochastic volatility model. In particular, the integration-by-parts formula in Malliavin calculus and the push-down of Malliavin weights are...

This paper proposes a general approximation method for the solutions to second order parabolic partial differential equations (PDEs) by an extension of Leandre's approach and the Bismut identity in Malliavin calculus. We show two types of its applications, new approximations of derivatives...

This paper proposes a new analytical approximation scheme for the representation of the forward- backward stochastic differential equations (FBSDEs) of Ma and Zhang (2002). In particular, we obtain an error estimate for the scheme applying Malliavin calculus method for the forward SDEs combined...

This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into two parts, namely "dominant" linear and "small" nonlinear...