Allowing for Stochastic Interest Rates in the Black–Scholes Model

Carl Chiarella, Xuezhong (Tony) He () and Christina Sklibosios Nikitopoulos
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Christina Sklibosios Nikitopoulos: University of Technology Sydney

Chapter Chapter 19 in Derivative Security Pricing, 2015, pp 405-417 from Springer

Abstract: 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.

Keywords: Interest Rate; Stochastic Differential Equation; Option Price; Stock Option; Implied Volatility (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:dymchp:978-3-662-45906-5_19

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DOI: 10.1007/978-3-662-45906-5_19

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