This paper proposes a new Markov chain approach to second order weak approximation of stochastic differential equations driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order and any discrete moment matched random...

This paper shows an efficient second order discretization scheme of expectations of stochastic differential equations. We introduce smart Malliavin weight which is given by a simple polynomials of Brownian motions as an improvement of the scheme of Yamada (2017). A new quasi Monte Carlo...

This paper provides a systematic empirical analysis of the effects of the M&A on target firm’s employment in Japan. It may contribute to the Japanese literature by capturing the dynamic employment impacts of firm acquisition using latest micro data. Our main findings are: the immediate effects...

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula in Malliavin calculus is effectively applied in an asymptotic expansion approach. First, the paper derives...

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 new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach....