An approximation method for pricing continuous barrier options under multi-asset local stochastic volatility models
（First Version : 2016年10月30日）
This paper presents a new approximation method for pricing multi-asset continuous single barrier options under general local stochastic volatility models. The formula applies an asymptotic expansion technique and an approximation for the hitting probability. This method focuses on local stochastic volatility models with unknown characteristic function and transition density function. To the best of our knowledge, our approximation formula is the first to achieve analytic approximations for continuous barrier options prices in this environment. In numerical experiments, we examine the validity of the formula.