Moment Explosions in Discrete Time Stochastic Processes | Hanlon Financial Systems Center

Moment Explosions in Discrete Time Stochastic Processes

Moment Explosions in Discrete Time Stochastic Processes

seminar date: 
Thursday, March 17, 2016 - 5:45pm
seminar location: 
Dan Pirjol, JP Morgan

It is known that stochastic volatility models with log-normally distributed volatility in continuous time have moment explosions.

Popular models of this type are the Hull-White, the Chesney-Scott, and the log-normal SABR models, which are widely used in financial practice. Similar explosions are observed also empirically in Monte Carlo simulations when the models are discretized in time by Euler-Maruyama discretization. Under certain conditions the asset price moments explode to very large numerical values, which is observed in simulations as a rapid increase in the frequency of tail events. The talk shows that this phenomenon is related to non-analytical behavior of the Lyapunov exponents of the asset price moments, and presents the conditions under which it appears in the uncorrelated Hull-White model.



Dan Pirjol works in the Model Risk Group at JP Morgan, covering valuation models in commodities. Previously he was with Markit and Merrill Lynch in various roles in modeling and model risk, after doing research in theoretical high energy physics. He is interested in applications of methods from mathematical physics and probability to problems in mathematical finance.