Pricing of Derivatives on Mean-Reverting Assets

As already mentioned by Lo and Wang (1995) there is an apparent paradox if we derive standard option pricing formulae for an underlying mean-reverting drift. While the drift has an in?uence on the long-run behavior of the underlying, the option price becomes independent of the drift of the price process itself. Using the continuous-time pricing framework this leads to option prices which are much too large for more distant maturities. One possible solution for this paradox is the assumption that the market is incomplete. As shown by Ross (1997), in an inc- plete market the mean reversion remains in the drift of the risk-adjusted process under the equivalent martingale measure. However, mean reversion in the drift complicates the solution process for option pricing considerably. Lutzcontributestothisresearchinseveralrespects.Usingstate-of-the-artFourier inversion techniques he extends the mean-reverting one-factor diffusion setting of Schwartz (1997) and Ross (1997) and discusses processes with stochastic volatility, different jump components, a stochastic equilibrium level and deterministic seas- alities. This leads to new and rather complex models, where the resulting Riccati systems are dif?cult to solve. While giving new analytic solutions in some cases Lutz shows that numerical procedures for the Riccati systems are often superior in terms of numerical ef?ciency. I recommend this research monograph to everybody who deals with the speci?c peculiarities of mean-reversionin option pricing. T¨ ubingen, Rainer Schobel ¨ May 2009 vii Acknowledgements The research presented in this Ph.D. thesis has been carried out at the College of EconomicsandBusinessAdministrationattheEberhardKarlsUniversityTubi ¨ ngen.