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Term Structure Of Vanilla Options

Author

Listed:
  • DORJE C. BRODY

    (Department of Mathematics, Imperial College, London SW7 2AZ, UK)

  • IRENE C. CONSTANTINOU

    (Blackett Laboratory, Imperial College, London SW7 2BZ, UK)

  • BERNHARD K. MEISTER

    (Department of Physics, Renmin University of China, Beijing 100872, China)

Abstract

Every maturity-dependent derivative contract entails a term structure. For example, when the value of the portfolio consisting of a long position in a stock and a short position in a vanilla option is expressed in units of its instantaneous exercise value, the resulting quantity defines a discount function. Thus, the derivative of the discount function with respect to the time left until maturity defines a term structure density function, and the "hazard rate" associated with the discount function determines the forward rates for the vanilla option portfolio. The dynamics associated with these quantities are obtained in the complete market setting. In particular, one can model vanilla options based on the associated forward rates. The formulation based on forward rates for options extends the approach based on modeling the implied volatility process. As an illustrative example, the initial term structure of the Black–Scholes model is considered. It is shown in this example that the implied volatility smile has the effect of making the option forward rates homogeneous across different strikes.

Suggested Citation

  • Dorje C. Brody & Irene C. Constantinou & Bernhard K. Meister, 2007. "Term Structure Of Vanilla Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(08), pages 1323-1337.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:08:n:s0219024907004676
    DOI: 10.1142/S0219024907004676
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