Pricing double-barrier options under a flexible jump diffusion model

In this paper we present a Laplace transform-based analytical solution for pricing double-barrier options under a flexible hyper-exponential jump diffusion model (HEM). The major theoretical contribution is that we prove non-singularity of a related high-dimensional matrix, which guarantees the existence and uniqueness of the solution.  

双障碍幂型期权定价公式

为了进一步完善障碍期权理论,更好地适应金融市场的需求,本文在完全市场条件下,利用连续时间的双障碍幂型期权买权过程的鞅性和等价鞅测度变换的方法,得到了双障碍幂型期权定价模型的显式解.  

基于指数障碍期权的抛物方程的存在性和唯一性

考虑了一类基于指数障碍期权的拟线性抛物型方程.首先在b(t,x)=c(t,x)=0情形下运用标准的Schauder理论证明了该抛物型方程问题存在一个属于Cα,1+α/2的唯一解.其次,运用变换的方法将该结论推广到了一般方程.  

A New Approach to Pricing Double-Barrier Options with Arbitrary Payoffs and Exponential Boundaries

Abstract

We consider in this article the arbitrage free pricing of double knock-out barrier options with payoffs that are arbitrary functions of the underlying asset, where we allow exponentially time-varying barrier levels in an otherwise standard Black–Scholes model. Our approach, reminiscent of the method of images of electromagnetics, considerably simplifies the derivation of analytical formulae for this class of exotics by reducing the pricing of any double-barrier problem to that of pricing a related European option. We illustrate the method by reproducing the well-known formulae of Kunitomo and Ikeda (1992 Kunitomo, N. and Ikeda, M. 1992. Pricing options with curved boundaries. Mathematical Finance, 2: 276–298.  [Google Scholar]) for the standard knock-out double-barrier call and put options. We give an explanation for the rapid rate of convergence of the doubly infinite sums for affine payoffs in the stock price, as encountered in the pricing of double-barrier call and put options first observed by Kunitomo and Ikeda (1992 Kunitomo, N. and Ikeda, M. 1992. Pricing options with curved boundaries. Mathematical Finance, 2: 276–298.  [Google Scholar]).  

跳跃扩散下双障碍期权定价的数值解

提出了一种求解带有跳跃的双障碍期权定价模型的数值方法.算法采用了Crank-Nicolson有限差分格式和复化梯形公式对模型进行离散,对离散后的线性系统采用GMRES迭代法求解,并且构造了一个新的预处理算子以加速迭代法的收敛.数值实验验证了该方法能快速求解模型并达到二阶收敛精度.  

双重障碍期权定价

提出双重障碍期权定价的离散放法,反复使用反射原理计算触及障碍的轨线数,并拓展:Boyle-Lau方法计算时步数,而从减少传统Cox-Ross-Rubinstein二项式算法的偏差,数值模拟结果验证所提出离散方法的准确和有效性.