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...

The Sato process associated with self decomposable laws at unit time is further generalized to an additive process with arbitrary innovation term structures. A second generalization to additive processes consistent with bilateral gamma marginal distributions is also made. The Sato process is a...

Daily return distributions are modeled by pure jump limit laws that are selfdecomposable laws. The returns may be seen as composed of a sum of independent and identically distributed increments or as a selfsimilar law scaling the sum of exponentially weighted past shocks or a combination...

Comparisons are made of the CBOE skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies may be attributed to strike discretization in evaluating prices of powered returns. The remedy...

The bilateral gamma model for returns is naturally derived from the lognormal model. Maximizing entropy in a random time change delivers the symmetric variance gamma model. The asymmetric variance gamma follows on incorporating skewness. Differential speeds for the upward and downward motions...

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...

Market clichés assert that markets take escalators up and elevators down. The observation suggests differentiating models for up and down moves. Non-diffusive models allow for this and we model the move as the difference of two independent mean reverting increasing processes driven by gamma...