Stochastic Volatility Models - Computational Methods for Quantitative Finance - page 122

Fig. 9.3 Option price ( top )
and free boundary ( bottom )
for the Heston model
9.7 Further Reading
Background information to stochastic volatility, in general, can be found in Shepard
[151] and the references therein. Stochastic volatility (diffusion models) connected
to derivative pricing is considered in Fouque et al. [68]. The diffusion SV mod-
els we have considered in this chapter can be extended by adding jumps. Bates
[13, 14], for example, adds log-normal jumps to the Heston model. The model of
Barndorff-Nielsen and Shepard (BNS) [10] describes the volatility as non-Gaussian
mean reverting OU process. Introducing SV into an exponential Lévy model via
time change was suggested by Carr et al. [37]. The pricing of European and Ameri-
can options via finite difference or finite element methods for diffusion SV models
can be found in Achdou and Tchou [2], Ikonen and Toivanen [90]aswellasZvan
et al. [166]. Benth and Groth [16] consider option pricing in the BNS model under
the minimal entropy EMM. Stochastic volatility models with jumps are described
in Chap. 15.