As is well known, the classic Black­Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non­normal return innovations. Second,...

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular...

Levy processes can capture the behaviors of return innovations on a full range of financial securities. Applying stochastic time changes to the Levy processes randomizes the clock on which the processes run, thus generating stochastic volatilities and stochastic higher return moments. Therefore,...

In 1993, the Chicago Board of Options Exchange (CBOE) introduced the CBOE Volatility Index. This index has become the de facto benchmark for stock market volatility. On September 22, 2003, the CBOE revamped the definition and calculation of the volatility index, and back-calculated the new index...

We apply stochastic time change to Levy processes to generate a wide variety of tractable option pricing models. In particular, we prove a fundamental theorem that transforms the characteristic function of the time-changed Levy process into the Laplace transform of the stochastic time under...

We propose a direct and robust method for quantifying the variance risk premium on financial assets. We theoretically and numerically show that the risk-neutral expected value of the return variance, also known as the variance swap rate, is well approximated by the value of a particular...

The U.S. agency mortgage backed securities (MBS) market is deep and highly liquid, yet modeling MBS is extremely challenging. This paper applies market participants' desired requirements for a good pricing model to MBS pricing models provided by six of the top MBS dealers. We find that five out...

This paper presents a model on contagion in nancial markets. We use a bank run framework as a mechanism to initiate a crisis and argues that liquidity crunch and imperfect information are the key culprits for a crisis to be contagious. The model proposes that a crisis is more likely to be...

The U.S. agency mortgage backed securities (MBS) market is deep and highly liquid, yet modeling MBS is extremely challenging. This paper applies market participants' desired requirements for a good pricing model to MBS pricing models provided by six of the top MBS dealers. We find that five out...

Option prices vary with not only the underlying asset price, but also volatilities and higher moments. In this paper, we use a portfolio of options to seclude the value change of the portfolio from the impact of volatility and higher moments. We apply this portfolio approach to the price...