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Allowing for Stochastic Interest Rates in the Black–Scholes Model

In: Derivative Security Pricing

Author

Listed:
  • Carl Chiarella

    (University of Technology Sydney)

  • Xue-Zhong He

    (University of Technology Sydney)

  • Christina Sklibosios Nikitopoulos

    (University of Technology Sydney)

Abstract

Interest rate stochastic Black–Scholes model stochastic interest rates The discussion in Chaps. 12 and 15 considered a relaxation of one of the key assumptions of the Black–Scholes framework, namely that the asset price changes follow a geometric Brownian motion. Another crucial assumption is the assumption of a constant interest rate over the life of the option. In this chapter we consider the specific case of stock options and retain all the assumptions of the original Black–Scholes model, except that we now allow interest rates to vary stochastically. Along the lines of Merton (Bell J Econ Manag Sci 4:141–183, 1973b), we develop the appropriate hedging argument to derive the stock option pricing partial differential equation and provide the technical details of its solution.

Suggested Citation

  • Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Allowing for Stochastic Interest Rates in the Black–Scholes Model," Dynamic Modeling and Econometrics in Economics and Finance, in: Derivative Security Pricing, edition 127, chapter 0, pages 405-417, Springer.
    • Handle: RePEc:spr:dymchp:978-3-662-45906-5_19
    DOI: 10.1007/978-3-662-45906-5_19
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