This paper shows that the VIX market contains information on the variance of the S&P 500 returns, which is not already spanned by the S&P 500 market. We estimate a flexible affine model based on a joint time series of underlying indexes and option prices on both markets. We find that including...

We analyze the impact of funding costs and margin requirements on prices of index options traded on the CBOE. We propose a model that gives upper and lower bounds for option prices in the absence of arbitrage in an incomplete market with differential borrowing and lending rates. We show that...

As is well known, the classic Black-Scholes 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 non-normal return innovations. Second,...

We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of at-the-money and out-of-the-money options as the option maturity approaches zero. We show that these prices converge...

We consider the hedging of derivative securities when the price movement of the underlying asset can exhibit random jumps. Under a one factor Markovian setting, we derive a spanning relation between a long term option and a continuum of short term options. We then apply this spanning relation to...

We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts...

We develop a simple robust test for the presence of continuous and discontinuous (jump) com­ponents in the price of an asset underlying an option. Our test examines the prices of at­the­money and out­of­the­money options as the option maturity approaches zero. We show that these prices...

We derive discrete markov chain approximations for continuous state equilibrium term structure models. The states and transition probabilities of the markov chain are chosen effciently according to a quadrature rule as in Tauchen and Hussey (1991). Quadrature provides a simple yet method which...

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,...