Title: Corrections in Heston model derivations for bond options

Authors: Satrajit Mandal; Sujoy Bhattacharya

Addresses: Vinod Gupta School of Management, Indian Institute of Technology, Kharagpur, West Bengal 721302, India ' Vinod Gupta School of Management, Indian Institute of Technology, Kharagpur, West Bengal 721302, India

Abstract: A closed form solution for European call option price has been first proposed by Black and Scholes. Later, Heston modified the model by replacing the constant volatility with a stochastic volatility and applied it on bond options. However, for bond options, we found that the mathematical derivations of the partial differential equations involving probabilities for the call option expiring in the money obtained by Heston contain some errors. This paper rectifies the errors and a new PDE has been derived. The paper uses important theories of stochastic calculus and portfolio theory such as Ito's lemma, portfolio hedging while formulating the PDE for the option price probabilities.

Keywords: option; Black and Scholes; Heston; stochastic volatility; Ito's lemma.

DOI: 10.1504/IJBD.2018.097402

International Journal of Bonds and Derivatives, 2018 Vol.4 No.1, pp.1 - 9

Received: 21 Feb 2018
Accepted: 22 Mar 2018
Published online: 21 Jan 2019 *

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