【简报】天美制作果冻视频系列学术研究讨会 （183）
2016-05-17 00:00:00
2016年5月17日星期二，来自香港投资银行的Jaehyuk Choi在汇丰商学院337教室为师生报告了他的论文 ‘’Sum of All Black Scholes’’
Jaehyuk Choi是量化策略分析师在香港投资银行。他获得了麻省理工学院博士是麻省理工学院的（MIT）应用数学博士学位。
Abstract:
This study considers pricing options under multivariate Black- Scholes models such as basket options, spread options and discretely monitored Asian options. We present an efficient multidimensional integration method against the common view that the exact pricing is computationally prohibitive due to the curse of dimensionality. The key of our approach is to find an optimal rotation of the factor matrix under which the first dimension is approximately perpendicular to the exercise boundary. Then we integrate the option payoff, analytically on the first dimension (with a numerically solved exercise point) and with Gauss-Hermite quadratures on the remaining dimensions. The numerical examples show that the quadrature integration requires only a few points per dimension or can be even truncated for low-varying factors. In essence we express the price of an option on a weighted sum of asset prices as a weighted sum of a minimal but accurate set of Black-Schole-like prices, thereby generalizing the Black-Scholes formula to the multivariate cases.
