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Stochastic Volatility Models

In: Pricing of Derivatives on Mean-Reverting Assets

Author

Listed:
  • Björn Lutz

    (Hauck & Aufhäuser Asset)

Abstract

So far, the characteristic function of the log-price at maturity was used without further specifications. In the following chapters, we derive characteristic functions for different settings. Once the characteristic function is obtained, it can be applied in the pricing equations as presented in Chap. 3. We will focus on the pricing of commodity contingent claims. Applications of mean-reverting OU processes for commodity prices were done by Schwartz (1997) and Ross (1997), among others. In both papers, futures prices and hedge ratios are derived, but no stochastic volatility is incorporated. Schwartz (1997) also provides an empirical survey for the proposed models. The commodities involved are crude oil, copper, and gold. Longstaff and Schwartz (1995) apply an Ornstein–Uhlenbeck (OU) model without stochastic volatility to price credit spread options. Following Zhu (2000), Tahani (2004) extends their proposal by incorporation of square-root and OU-stochastic volatility, respectively. In our stochastic volatility models, we will refer to the results and interpretations of Tahani.

Suggested Citation

  • Björn Lutz, 2010. "Stochastic Volatility Models," Lecture Notes in Economics and Mathematical Systems, in: Pricing of Derivatives on Mean-Reverting Assets, chapter 0, pages 55-79, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-02909-7_4
    DOI: 10.1007/978-3-642-02909-7_4
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