The Escape Problem Under Stochastic Volatility: The Heston Model

29 Pages Posted: 22 Jul 2008

See all articles by Jaume Masoliver

Jaume Masoliver

University of Barcelona - Department of Physics

Josep Perelló

University of Barcelona - Department of Physics

Date Written: July 7, 2008

Abstract

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which amounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility - a ratio of the three parameters that appear in the Heston model - and analyze their form in several asymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.

JEL Classification: C00

Suggested Citation

Masoliver, Jaume and Perello, Josep, The Escape Problem Under Stochastic Volatility: The Heston Model (July 7, 2008). Available at SSRN: https://ssrn.com/abstract=1162704 or http://dx.doi.org/10.2139/ssrn.1162704

Jaume Masoliver

University of Barcelona - Department of Physics ( email )

Barcelona, E-08028
Spain
00 34 3 402 11 59 (Phone)
00 34 3 402 11 49 (Fax)

Josep Perello (Contact Author)

University of Barcelona - Department of Physics ( email )

Diagonal, 647
Barcelona, E-08028
Spain
+34 9 34021150 (Phone)
+34 34021149 (Fax)

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