The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the...

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...

Recently academic researchers and practitioners have use the asymptotic expansion method to examine a variety of financial issues under high-dimensional stochastic environments. This methodology is mathematically justified by Watanabe theory (Watanabe, 1987), and Malliavin calculus (Yoshida,...