Allowing for Stochastic Interest Rates in the Black–Scholes Model

Carl Chiarella*, Xue Zhong He, Christina Sklibosios Nikitopoulos

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingChapterpeer-review

Abstract

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.

Original languageEnglish
Title of host publicationDynamic Modeling and Econometrics in Economics and Finance
PublisherSpringer Science and Business Media Deutschland GmbH
Pages405-417
Number of pages13
DOIs
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameDynamic Modeling and Econometrics in Economics and Finance
Volume21
ISSN (Print)1566-0419
ISSN (Electronic)2363-8370

Keywords

  • Implied Volatility
  • Interest Rate
  • Option Price
  • Stochastic Differential Equation
  • Stock Option

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