This paper offers a new approach for pricing options on assets with stochastic volatility. We start by taking as given the prices of a few simple, liquid European options. More specifically, we take as given the “surface†of Black-Scholes implied volatilities for European options with...

This paper explicitly solves a dynamic portfolio choice problem in which an investor allocates his wealth between a riskless and a risky asset. The solution shows that insights gained from studying static portfolio choice problems do not necessarily carry over to dynamic choice settings. For...

An inherent risk facing investors in financial markets is that a major event may trigger a large abrupt change in stock prices and market volatility. This paper studies the implications of jumps in prices and volatility on investment strategies. Using the event-risk framework of Duffie, Pan, and...

We characterize the joint dynamics of expected returns, stochastic volatility, and prices. In particular, with a given dividend process, one of the processes of the expected return, the stock volatility, or the price-dividend ratio fully determines the other two. For example, the stock...