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...

Most existing hedging theories are derived under strong, idealistic assumptions on both the underlying security price dynamics and the trading environments. Practical concerns such as contract availability, transaction cost, and uncertainty regarding the security price dynamics impose severe...

We model term structure dynamics using a recursive cascade of heterogeneously persistent factors. The cascade naturally orders the factors by their adjustment speeds, and generates smooth zero-coupon bond prices and forward curves in closed form. For a class of specifications, the number of...

Most existing hedging approaches are based on neutralizing risk exposures defined under a pre-specified model. This paper proposes a new, simple, and robust hedging approach based on the affinity of the derivative contracts. As a result, the strategy does not depend on assumptions on the...

This paper examines several US monthly financial time series data using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with...