Corrections in Heston model derivations for bond options. (2018)

• Record Type: Journal Article
• Authors: Mandal, Satrajit; Bhattacharya, Sujoy
• Is Part Of: International journal of bonds and derivatives. Volume 4:Number 1(2019)
• Page Start: 1
• Page End: 9
• Publication Date: 2018
• Subjects: option -- Black and Scholes -- Heston -- stochastic volatility -- Ito's lemma; Bonds -- Periodicals; Derivative securities -- Periodicals; Capital market -- Periodicals; 332.63205
• Languages: English
• ISSNs: 2050-2281

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.