Published Online: 15 MAY 2010
Copyright © 2010 John Wiley & Sons, Ltd. All rights reserved.
Encyclopedia of Quantitative Finance
How to Cite
Friz, P. K. and Ressel, M. K. 2010. Moment Explosions. Encyclopedia of Quantitative Finance. .
- Published Online: 15 MAY 2010
Let (St)t ≥ 0 be the discounted price process in a stochastic volatility model. A moment explosion takes place, if the moment of some given order u ∈ ℝ becomes infinite (“explodes”) after some finite time T*(u). Moment explosions are closely related to the shape of the implied volatility surface, where they can be used to obtain approximations for deep in-the-money and out-of-the-money strikes. Furthermore, moment explosions may lead to infinite prices of derivatives with superlinear payoff, and to the breakdown of error estimates for numerical approximation schemes. Comparison results for parabolic partial differential equations (PDEs) combined with an exponentially affine ansatz for the solution, allow to link explosion times to the blow-up time of ordinary differential equations of the (generalized) Riccati type.
- moment explosion;
- stochastic volatility;
- Heston model;
- SABR model;
- affine stochastic volatility model;
- implied volatility surface;
- smile asymptotics;
- (generalized) Riccati equation