This study formalizes the departure between risk-neutral and physical index return volatilities, termed volatility spreads. Theoretically, the departure between risk neutral and physical index volatility is connected to the higher-order physical return moments and the parameters of the pricing...

This article presents a framework for studying the role of recovery on defaultable debt prices (for a wide class of processes describing recovery rates and default probability). These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be...

This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the...

This article studies the valuation of options written on the average level of a Markov process. The general properties of such options are examined. We propose a closed-form characterization in which the option payoff is contingent on cumulative catastrophe losses. In our framework, the loss...

This article investigates, both theoretically and empirically, the economics of stock market crashes. Using more than 100 years of daily data on the DJIA (and shorter series on NASDAQ, IBM, and Caterpillar), we first document empirically that (a) the probability of a daily stock market decline...

This paper proposes a methodology for the valuation of contingent securities. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans the payoff universe of most, if not all, derivative assets. In one specific application, from the...

This paper studies the structure of stock market crashes, rallies, their jump arrival rates, and extremes. Large market moves are characterized in a pure-jump modeling framework. Based on both raw and devolatized returns, it is shown empirically that crashes are more severe in intensity than...

Models which hypothesize that returns are pure jump processes with independent increments have been shown to be capable of capturing the observed variation of market prices of vanilla stock options across strike and maturity. In this paper, these models are employed to derive in closed form the...

This paper shows that a continuum of options and a continuum of characteristic functions are equivalent classes of spanning securities, for a wide class of payoff functions. In particular, it establishes how the characteristic function (of the future uncertainty) is basis augmenting and spans...

We define the class of local Levy processes. These are Levy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded...