Research On Pricing Of High-dimensional Basket Options

From solving stochastic partial differential equations to statistical simulation, from European Options can be exercised only on the expiration date to the American Options can be exercised at any time up to expiration, from Standard Options to Multi-asset Options, options pricing is a new topic in the field of financial derivative all the time. With the continuous development of financial markets, derivational financial instrument is deemed to effective tool for eluding risks by trader in financial market, One of the core topics in modern financial theories is the determination of Options price.On February 9, 2015 on the Shanghai Futures Exchange launched an ETF50 Basket Options with 50 stocks as underlying assets, this moment herald a high-dimensional basket Options pricing era. High-dimensional basket Options is different from the standard Options, the underlying assets’ price would influence each others, the joint distribution of the underlying asset’ price is non-normal distribution, the change of basket price affects the risk-free rate, so the option pricing method to the standard Options cannot be directly extended to high-dimensional basket Options pricing.In this paper, based on the monte carlo simulation pricing method, according to several features of high-dimensional basket Options, redesigned the simulation method, monte carlo simulation pricing method was put forward.Natural basket HS300 ETF combination, for example and is compared with the results of classical BS Options pricing model, the experimental results show that the improved monte carlo simulation pricing method is an effective attempt of high-dimensional basket Options pricing, provides a new theoretical framework for the basket Options.