Conclusion

In this thesis, we discussed and extended existing pricing models for derivatives on mean-reverting assets. The pricing formulas are based on the Fourier inversion approach of Heston (1993), whereas the specification of the underlying price process traces back to the incomplete market setup in Ross (1997) and model 1 in Schwartz (1997). In Chap. 2, we discussed the sources and empirical evidence of mean reversion in asset prices. As sources of mean reversion, we identified convenience yield effects and negative correlation between prices and risk premia as well as interest rates. We shortly addressed convenience yield models as a second alternative to achieve mean reversion in prices through an additional subordinated process. Compared with the modeling of mean reversion by an OU price process, convenience yield models show less stringent mean reversion unless the (log-) price is directly included in the convenience yield process. The fact that the model manages with less parameters could be an advantage of OU price processes compared with convenience yield models. Furthermore, the convenience yield is not an observable economic variable, which makes it difficult to judge whether the model setup matches the empirical facts or not.