Asset price bubbles can arise unintentionally when one uses continuous-time diffusion processes to model financial quantities. We propose a flexible damped diffusion framework that is able to break many types of bubbles and preserve the martingale pricing approach. Damping can be done on either...

I first introduce the early-stage and modern classical asset pricing and portfolio theories. These include: the capital asset pricing model (CAPM), the arbitrage pricing theory (APT), the consumption capital asset pricing model (CCAPM), the intertemporal capital asset pricing model (ICAPM), and...

We develop a new closed-form approximation method for pricing spread options. Numerical analysis shows that our method is more accurate than existing analytical approximations. Our method is also extremely fast, with computing time more than two orders of magnitude shorter than one-dimensional...

We develop an asymptotic expansion technique for pricing timer options under general stochastic volatility models around small volatility of variance. Closed-form approximation formulas have been obtained for the Heston model and the 3/2-model. The approximation has an easy-to-understand...

We develop an approximation technique for pricing finite-maturity timer options under Heston-like stochastic volatility models. By approximating the distributions of the accumulated variance and the random variance budget exceeding time, we obtain analytic expressions for timer option prices...

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...