Advertisement

Review of Derivatives Research

, Volume 12, Issue 2, pp 141–167 | Cite as

Asset pricing under information with stochastic volatility

  • Bertram Düring
Article

Abstract

Based on a general specification of the asset specific pricing kernel, we develop a pricing model using an information process with stochastic volatility. We derive analytical asset and option pricing formulas. The asset prices in this rational expectations model exhibit crash-like, strong downward movements. The resulting option pricing formula is consistent with the strong negative skewness and high levels of kurtosis observed in empirical studies. Furthermore, we determine credit spreads in a simple structural model.

Keywords

Pricing kernel Stochastic volatility Asset pricing Option pricing Credit spreads 

JEL Classifications

G12 G13 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ait-Sahalia Y., Lo A.W. (2000) Nonparametric risk management and implied risk aversion. Journal of Econometrics 94: 9–51CrossRefGoogle Scholar
  2. Albrecher H., Mayer P., Schoutens W., Tistaert J. (2007) The little Heston trap. Wilmott 1: 83–92Google Scholar
  3. Bakshi G., Cao C., Chen Z. (1997) Empirical performance of alternative option pricing models. Journal of Finance 52(5): 2003–2049CrossRefGoogle Scholar
  4. Benninga S., Mayshar J. (2000) Heterogeneity and option pricing. Review of Derivatives Research 4: 7–27CrossRefGoogle Scholar
  5. Bick A. (1987) On the consistency of the Black–Scholes model with a general equilibrium framework. Journal of Financial and Quantitative Analysis 22: 259–275CrossRefGoogle Scholar
  6. Black F., Scholes M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81: 637–654CrossRefGoogle Scholar
  7. Brennan M.J. (1979) The pricing of contingent claims in discrete time models. Journal of Finance 34: 53–68CrossRefGoogle Scholar
  8. Câmara A. (2003) A generalization of the Brennan–Rubinstein approach for the pricing of derivatives. Journal of Finance 58: 805–819CrossRefGoogle Scholar
  9. Câmara A. (2005) Option prices sustained by risk-preferences. Journal of Business 78: 1683–1708CrossRefGoogle Scholar
  10. Campbell J.Y., Cochrane J.H. (1999) By force of habit: A consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107: 205–251CrossRefGoogle Scholar
  11. Cochrane, J. H. (2001). Asset pricing. Princeton University Press.Google Scholar
  12. Collin-Dufresne P., Goldstein R. (2001) Do credit spreads reflect stationary leverage ratios?. Journal of Finance 56: 1928–12957Google Scholar
  13. Daniel K., Hirshleifer D., Subrahmanyam A. (2001) Overconfidence, arbitrage, and equilibrium asset pricing. Journal of Finance 56: 921–965CrossRefGoogle Scholar
  14. Düring B., Lüders E. (2005) Option prices under generalized pricing kernels. Review of Derivatives Research 8(2): 97–123CrossRefGoogle Scholar
  15. Franke G., Huang J., Stapleton R. (2007) Two-dimensional risk-neutral valuation relationships for the pricing of options. Review of Derivatives Research 9(3): 213–237CrossRefGoogle Scholar
  16. Franke G., Stapleton R.C., Subrahmanyam M.G. (1999) When are options overpriced? The Black–Scholes Model and alternative characterisations of the pricing kernel. European Finance Review 3: 79–102CrossRefGoogle Scholar
  17. Heston S.L. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6(2): 327–343CrossRefGoogle Scholar
  18. Huang, J-Z., & Huang, M. (2003). How much of the corporate-treasury yield spread is due to credit risk? working paper.Google Scholar
  19. Jackwerth J.C. (2000) Recovering risk aversion from option prices and realized returns. Review of Financial Studies 13: 433–451CrossRefGoogle Scholar
  20. Kahl, C., & Jäckel, P. (2005). Not-so-complex logarithms in the Heston model. Wilmott, September, 94–103.Google Scholar
  21. Longstaff F.A., Schwartz E.S. (1995) A simple approach to valuing risky fixed and floating rate debt. Journal of Finance 50: 789–819CrossRefGoogle Scholar
  22. Lüders, E., & Franke, G. (2004). Predictability, excess volatility and stock market crashes in rational expectations models, working paper, CoFE discussion paper 04/05, University of Konstanz.Google Scholar
  23. Merton R.C. (1974) On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29: 449–470CrossRefGoogle Scholar
  24. Pham H., Touzi N. (1996) Equilibrium state prices in a stochastic volatility model. Mathematical Finance 6: 215–236CrossRefGoogle Scholar
  25. Rosenberg J.V., Englem R.F. (2002) Empirical pricing kernels. Journal of Financial Economics 64: 341–732CrossRefGoogle Scholar
  26. Rubinstein M. (1976) The valuation of uncertain income streams and the pricing of options. Bell Journal of Economics and Management Science 7: 407–425Google Scholar
  27. Schroder M. (2004) Risk-neutral parameter shifts and derivatives pricing in discrete time. Journal of Finance 59: 2375–2402CrossRefGoogle Scholar
  28. Vitiello, L. & Poon, S. (2006). A general equilibrium and preference free model for pricing options under transformed gamma distribution, working paper.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Institut für Analysis und Scientific ComputingTechnische Universität WienWienAustria

Personalised recommendations