Option Pricing in Periods of Negative or Low- Interest Rates: Case of European Type of Options

Abstract

The negative interest rates policy that was implemented to help the economy to recover from a recession, pushed the market to revise some pricing models. The Black Scholes model in the current situation where rates are below zero fails to price interest rate options since it only allows positive rates in its formula. Besides the Black Scholes model, the Heston Cox Ingersoll also doesn’t allow negative inputs of interest rates. Deloitte in February 2016 introduced a new pricing regime based on inserting a shifting parameter to existing pricing models like the Black Scholes and the SABR models. This work, analyses the performance of the shifted Black Scholes model in the negative rate environment. In this study, we also conduct a comparative study of pricing models, by providing their performance based on speed, complexity, and market applicability. According to empirical findings, the shifted Black Scholes model performs very well in the negative rate environment. Even though finding the right shift parameter and generating the implied volatility can be challenging, the shifted Black Scholes, especially when backed with the Montecarlo simulation, is equipped with enough tools to price interest rate options when rates are below zero.