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. Black’s model, a variant of Black-Scholes option pricing model, was first introduced by Fischer Black in 1976. In recent market conditions, where global interest rates are at very low levels and in some markets are...

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Bibliographic Details
Published in:Computational management science 2022, Vol.19 (1), p.25-39
Main Authors: Bramante, Riccardo, Dallago, Gimmi, Facchinetti, Silvia
Format: Article
Language:English
Subjects:
Business and Management
Canonical forms
Central banks
Heuristic methods
Interest rates
Normal distribution
Operations Research/Decision Theory
Optimization
Original Paper
Parameter sensitivity
Pricing
Put & call options
Securities prices
Stochastic models
Volatility
Citations: Items that this one cites
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Summary:The most common application of Black’s formula is interest rate derivatives pricing. Black’s model, a variant of Black-Scholes option pricing model, was first introduced by Fischer Black in 1976. In recent market conditions, where global interest rates are at very low levels and in some markets are currently zero or negative, Black model—in its canonical form—fails to price interest rate options since positive interest rates are assumed in its formula. In this paper we propose a heuristic method that, without explicit assumptions about the forward rate generating process, extends the cumulative standard normal distribution domain to negative interest rates and allows Black’s model to work in the conventional way. Furthermore, we provide the derivations of the so called five Greek letters that enable finance professionals to evaluate the sensitivity of an option to various parameters. Along with the description of the methodology, we present an extensive simulation study and a comparison with the Normal model which is widely used in the negative environment option pricing problems.
ISSN:1619-697X
1619-6988
DOI:10.1007/s10287-021-00408-6