基于近似对冲跳跃风险的美式看跌期权定价及数值解法研究

The Prcing of American Put Options and Numerical Solution Based on Approximating Hedge Jump Risk

考虑了基于近似对冲跳跃风险的美式看跌期权定价问题。首先,运用近似对冲跳跃风险、广义It公式及无套利原理,得到了跳-扩散过程下的期权定价模型及期权价格所满足的偏微分方程。然后建立了美式看跌期权定价模型的隐式差分近似格式,并且证明了该差分格式具有的相容性、适定性、稳定性和收敛性。最后,数值实验表明,用本文方法为跳-扩散模型中的美式期权定价是可行的和有效的。

In this paper,the pricing for American put option is considered based on approximating hedge jump risk. Firstly,the options pricing model and the partial differential equation of the options pricing model are derived in the jump-diffusion process,by applying the generalized It formula and no-arbitrage principle,based on approximating hedge jump risk. The approximate implicit difference scheme of American put option pricing model is developed,and consistency,well-posedness,stability and convergence of the difference scheme are also proved in this paper. Lastly,the numerical experiments show that this method is an effective and feasible way for pricing American options in jump-diffusion model.