We consider a system where the asset values of firms are correlated with the default thresholds. We first evaluate the probability of default of a single firm under the correlated assets assumptions. This extends Merton’s probability of default of a single firm under the independent asset...

In this paper, we study the optimal stopping time and the optimal stopping boundary for the perpetual Russian option under the diffusion process. The general continuation region is characterized by a function b(p; t) depending on both variables t and the maximum value of the stock and initial...

It is well-known that the market prices of options produce implied volatilities that inexplicably vary by exercise price in a pattern often referred to as the volatility smile. This paper shows that not only do market prices produce volatility smiles, but so do model prices. This result occurs...

Based on a sequence of discretized American option price processes under the multinomial model proposed by Maller, Solomon and Szimayer (2006), the sequence converges to the counterpart under the original Lévy process in distribution for almost all time. We prove a weak convergence in this case...