Black’s model in a negative interest rate environment, with application to OTC derivatives

The most common application of Black’s formula is interest rate derivatives pricing.\r\nBlack’s model, a variant of Black-Scholes option pricing model, was first introduced\r\nby Fischer Black in 1976. In recent market conditions, where global interest rates are\r\nat very low levels and in some markets are currently zero or negative, Black model—\r\nin its canonical form—fails to price interest rate options since positive interest rates\r\nare assumed in its formula. In this paper we propose a heuristic method that, without\r\nexplicit assumptions about the forward rate generating process, extends the cumulative\r\nstandard normal distribution domain to negative interest rates and allows Black’smodel\r\nto work in the conventional way. Furthermore, we provide the derivations of the so\r\ncalled five Greek letters that enable finance professionals to evaluate the sensitivity\r\nof an option to various parameters. Along with the description of the methodology,\r\nwe present an extensive simulation study and a comparison with the Normal model\r\nwhich is widely used in the negative environment option pricing problems.