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 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 develops a new scheme for improving an approximation method of a probability density function, which is inspired by the idea in best approximation in an inner product space. Moreover, we applies “Dykstra's cyclic projections algorithm” for its implementation. Numerical examples...

This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More generally, we also derive an error estimate for an asymptotic expansion around a partially elliptic...