@inbook{c610da4ed642414996e65a340d05b289,
title = "Allowing for Stochastic Interest Rates in the Black–Scholes Model",
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.",
keywords = "Implied Volatility, Interest Rate, Option Price, Stochastic Differential Equation, Stock Option",
author = "Carl Chiarella and He, {Xue Zhong} and Nikitopoulos, {Christina Sklibosios}",
note = "Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",
year = "2015",
doi = "10.1007/978-3-662-45906-5_19",
language = "English",
series = "Dynamic Modeling and Econometrics in Economics and Finance",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "405--417",
booktitle = "Dynamic Modeling and Econometrics in Economics and Finance",
}