This paper derives a pricing model for employee stock options (ESO) that includes default risk and considers employee sentiment. Using ESO data from 1992 to 2004, the study finds that the average executive's subjective value is about 55% of the Black-Scholes value. Only employees who over-estimate firm returns (or insiders who know that the firm is under-valued) by about 10% per annum will prefer ESOs over cash compensation. Our model also shows that work incentives offered by ESOs may be far lower than those implied by Black-Scholes but that ESOs may induce less risk-taking behavior, contrary to typical moral hazard arguments. Findings may impact relevant accounting regulations as well as compensation decisions.

We provide closed-form solutions for a continuous time, Markov-modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications. We further demonstrate that the two-state model provides the leptokurtic return features, volatility smile, and volatility clustering observed empirically for the Dow Jones Industrial Average (DJIA) and its component stocks. Using 10years of stock return data, we confirm the existence of jump intensity switching and clustering, illustrate transition probabilities, and verify superior empirical fit over competing Poisson-style models.

Credit ratings group firms by risk, yet yields are shown to overlap between firms of adjacent ratings. We model this by considering the residual risk arising from differences in the parameters of each firm's value process for firms with the same rating. To do so, our framework simultaneously incorporates jump default with Markov-governed likelihoods and continuous defaults in a default-barrier framework. We provide closed-form approximations for expected default time and tail probabilities, and empirically fit the S-shaped yield curve, intra-rating spread, and inter-rating overlap. Results are robust to time period, rating system, sub-rating, and common characteristics such as liquidity.

We provide methodologies to price discretely monitored exotic options when the underlying evolves according to a double exponential jump diffusion process. We show that discrete barrier or lookback options can be approximately priced by their continuous counterparts’ pricing formulae with a simple continuity correction. The correction is justified theoretically via extending the corrected diffusion method of Siegmund (1985). We also discuss the jump effects on the performance of this continuity correction method. Numerical results show that this continuity correction performs very well especially when the proportion of jump volatility to total volatility is small. Therefore, our method is sufficiently of use for most of time.