有交易成本的GARCH-扩散期权定价模型

GARCH diffusion option pricing model with transaction costs

基于GARCH-扩散过程,把规范的B lack-Scholes期权定价模型推广到存在交易成本的情形.首先给出了有交易成本的期权定价的非线性偏微分方程,然后用泰勒展开技术对方程的解进行逼近,最后与Leland的期权定价模型进行了比较.结果表明,有交易成本的GARCH-扩散期权定价模型具有较好的定价性能.

Based on GARCH （generalized autoregressive condition heteroscedasticity model） diffusion process, the canonical Black-Scholes option pricing model is extended a situation with transaction cost. Firstly, the option pricing model with transaction cost is built by the GARCH diffusion process, and the nonlinear partial differential equation is given. Then the solution of this equation is approximated by the Talayor expansions technology. Finally, this pricing model is compared with Leland＇ model. The result shows that the GARCH diffusion option pricing model is efficient in option pricing.