New Acceleration Schemes with the Asymptotic Expansion in Monte Carlo Simulation (Revised in June 2005, subsequently published in "Advances in Mathematical Economics", Vol.8, 411-431, 2006. )

In the present paper, we propose a new computational technique with the Asymptotic Expansion (AE) approach to achieve variance reduction of the Monte-Carlo integration appearing especially in finance. We extend the algorithm developed by Takahashi and Yoshida (2003) to the second order asymptotics. Moreover, we apply the AE to approximate time dependent differentials of the target value in Newton (1994)'s scheme. Our numerical examples include pricing of average and basket options when the underlying state variables follow Constant Elasticity of Variance (CEV) processes.

"New Acceleration Schemes with the Asymptotic Expansion in Monte Carlo Simulation"

In the present paper, we propose a new computational technique with the Asymptotic Expansion (AE) approach to achieve variance reduction of the Monte-Carlo integration appearing especially in finance. We extend the algorithm developed by Takahashi and Yoshida (2003) to the second order asymptotics. Moreover, we apply the AE to approximate time dependent differentials of the target value in Newton (1994)'s scheme. Our numerical examples include pricing of average, basket and swap options when the underlying state variables follow Constant Elasticity of Variance (CEV) processes.

A New Computational Scheme for Computing Greeks by the Asymptotic Expansion Approach (Special Issue on Mathematical Finance, Published in "Asia-Pacific Financial Markets", Vol.11, 393-430, 2006. )

We developed a new scheme for computing ?Greeks?of derivatives by an asymptotic expansion approach. In particular, we derived analytical approximation formulae for deltas and Vegas of plain vanilla and average European call options under general Markovian processes of underlying asset prices. Moreover, we introduced a new variance reduction method of Monte Carlo simulations based on the asymptotic expansion scheme. Finally, several numerical examples under CEV processes confirmed the validity of our method.

Elucidating Dark Energy with Future 21 cm Observations at the Epoch of Reionization

We investigate how precisely we can determine the nature of dark energy such as the equation of state (EoS) and its time dependence by using future observations of 21 cm fluctuations at the epoch of reionization (6.8 <~ z <~ 10) such as Square Kilometre Array (SKA) and Omniscope in combination with those from cosmic microwave background, baryon acoustic oscillation, type Ia supernovae and direct measurement of the Hubble constant. We consider several parametrizations for the EoS and find that future 21 cm observations will be powerful in constraining models of dark energy, especially when its EoS varies at high redshifts.Comment: 35 pages, 12 figure