We present a valuation framework that captures the main characteristics of employee stock options (ESOs), which financial regulations now require to be expensed in firms' accounting statements. The value of these options is much less than Black-Scholes prices for corresponding market-traded...

We study the problem of hedging early exercise (American) options with respect to exponential utility within a general incomplete market model. This leads us to construct a duality formula involving relative entropy minimization and optimal stopping. We further consider claims with multiple...

This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF...

We analyze the American option valuation problem with the forward performance criterion introduced by Musiela and Zariphopoulou (2008). In this framework, utility evolves forward in time without reference to a specific future time horizon. Moreover, risk preferences change with stochastic market...

We discuss the valuation of credit derivatives in extreme regimes such as when the time-to-maturity is short, or when payoff is contingent upon a large number of defaults, as with senior tranches of collateralized debt obligations. In these cases, risk aversion may play an important role,...