Kenichiro Shiraya

An approximation formula for basket option prices under local stochastic volatility with jumps

This paper develops a new approximation formula for pricing basket options in a local-stochastic volatility model with jumps. In particular, the model admits local volatility functions and jump components in not only the underlying asset price processes, but also the volatility processes. To the best of our knowledge, the proposed formula is the first one which achieves an analytical approximation for the basket option prices under this type of the models.Moreover, in numerical experiments, we provide approximate prices for basket options on the WTI futures and Brent futures based on the parameters through calibration to the plain-vanilla option prices, and confirm the validity of our approximation formula.

Pricing and hedging of long-term futures and forward contracts by a three-factor model

This paper demonstrates the 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 data well. Furthermore, it shows how to hedge based on a three-factor model and confirms that using three different futures contracts to hedge long-term contracts outperforms the traditional parallel hedge based on a single futures position by time series data and simulation. It also finds that the three-factor model outperforms the two-factor version with respect to the replication of actual term structures and that stochastic mean reversion models outperform constant mean reversion models in Out of Sample hedges.

A General Control Variate Method for Multi-dimensional SDEs: An Application to Multi-asset Options under Local Stochastic Volatility with Jumps Models in Finance

This paper presents a new control variate method for general multi-dimensional stochastic differential equations (SDEs) including jumps in order to reduce the variance of Monte Carlo method. Our control variate method is based on an asymptotic expansion technique, and does not require an explicit characteristic function of SDEs. This is an extension of previous researches using asymptotic expansions to obtain the control variates for such general models. Moreover, in our control variate method, the regression estimators can be chosen for each number of jump times with a stratified sampling, and improve the efficiency of the variance reduction. This paper also provides the asymptotic bias and variance of our method in terms of its terminal time and a small noise parameter used in an asymptotic expansion method.

An asymptotic expansion for local-stochastic volatility with jump models

This paper develops an asymptotic expansion method for general stochastic differential equations with jumps and their functions. By applying the method, we derive an explicit approximation formula for pricing options on functions of multiple assets under local-stochastic volatility with jump models. Moreover, we present numerical examples for pricing basket options based on the parameters calibrated to the actual market data, which confirms the validity of our method in practice.