Location of Repository

Approximate solution to a hybrid model with stochastic volatility: a singular-perturbation strategy

By T Fatima, L Grzelak and H Hendriks


We study a hybrid model of Schobel-Zhu-Hull-White-type from a singular-perturbation-analysis perspective. The merit of the paper is twofold: On one hand, we find boundary conditions for the deterministic non-linear degenerate parabolic partial differential equation for the evolution of the stock price. On the other hand, we combine two-scales regular- and singular-perturbation techniques to find an approximate solution to the pricing PDE. The aim is to produce an expression that can be evaluated numerically very fast

Topics: Discrete, None/Other, Finance
Year: 2009
OAI identifier: oai:generic.eprints.org:595/core70

Suggested articles



  1. (2004). A partial differential equation connected to option pricing with stochastic volatility: regularity results and discretization. doi
  2. (2008). An Introduction to Stochastic Differential Equations. Department of Mathematics,
  3. (2006). Application of Perturbation Methods to Modeling Correlated Defaults in Financial Markets.
  4. (1999). Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications. doi
  5. (2007). Correlations and bounds for stochastic volatility models. doi
  6. (1985). Diffusion in fissured media. doi
  7. (2008). Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process. doi
  8. (2004). Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, doi
  9. (2005). Matched asymptotic expansions in financial engineering. doi
  10. (2003). Multiscale stochastic volatility asymptotics. doi
  11. (2009). On the Heston model with stochastic interest rates. SSRN: http://ssrn.com/abstract=1382902, doi
  12. (2004). On the pricing and hedging of volatility derivatives. doi
  13. (1987). Option pricing when the variance changes randomly: theory, estimation, and an application. doi
  14. (2008). Pricing of Bond Options, doi
  15. (2003). Stochastic Differential Equations. doi
  16. (1995). The Mathematics of Financial Derivatives. doi
  17. (2002). Variational analysis for the stochastic Black and Scholes equation with stochastic volatility. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.