Pricing Discrete Barrier Options With A Hyper-expential Jump-diffusion Model

As an important member of the derivatives, Barrier options can control the benefits and risks of the investors within a certain range. And it's much more cheaper than the standard options,for this reason,barrier options becomes more and more popular.On the one hand,most of the barrier options research is based on the standard BS model, is rare to see research on more complex model. One the other hand, barrier option pricing usually assumes the continuous monitoring of the barrier. However, barrier options traded in markets are discretely monitored and in this case there are no closed form solutions available. Based on the above two aspects, we introduce the continuity correction formula for hyper-exponential jump diffusion model on the basis of the predecessors' double exponential. Due to the introduction of the jump, the proof of the original continuous correction model no longer apply, so, we adjust the prove of the continuous correction model, Then, we apply continuous correction model to both the single and double monitored barrier options. We somehow expand the coverage of the original corrected diffusion method. At the end of this paper, we use the Euler algorithm to invert the two-dimensional Laplace transform, by taking different monitoring frequency and jumping intensity, we can show that the continuous correction based on the hyper-exponential jump diffusion model is correct and useful under a low jumping intensity.