Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach

Many derivatives products are directly or indirectly associated with integrated diffusion processes. We develop a general perturbation method to price those derivatives. We show that for any positive diffusion process, the hitting time of its integrated process is approximately normally distributed when the diffusion coefficient is small. This result of approximate normality enables us to reduce many derivative pricing problems to simple expectations. We illustrate the generality and accuracy of this probabilistic approach with several examples in the Heston model, including variance derivatives, European vanilla options, timer forwards, and timer options. Major advantages of the proposed technique include extremely fast computational speed, ease of implementation, and analytic tractability.