The effects of negative interest rates on the estimation of option sensitivities: The impact of switching from a log-normal to a normal model

Giribone, Pietro; Ligato, Simone; Mulas, Martina

doi:10.1142/s2424786317500153

Cited by 5 publications

(3 citation statements)

References 2 publications

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“…The five Greek letters (or simply the Greeks) represent the sensitivity of the option price with respect to the parameters that define the model of the underlying asset. Each letter measures a different risk dimension in an option position [(see Giribone et al (2017), Hull ( 2018)] and is evaluated as an appropriate partial derivatives of the option price. In this section we derive the mathematical formulas of the first-order (delta, theta, vega and omega) and the second-order (gamma) Greeks both for a single caplet and floorlet option 4 .…”

Section: Greek Lettersmentioning

confidence: 99%

“…Moreover, they carry out an empirical investigation to higlight the differences between estimation using some quasi-closed formulas for pricing an American option and the stochastic trinomial trees algorithm. Giribone et al (2017) investigate the effects of negative rates on the calculation of option sensitivities by comparing the log-normal and the normal framework, both from the practical and the theoretical viewpoint. Moreover, Recchioni et al (2017) use an adjusted Heston model (Grzelak and Oosterlee 2011) to investigate if models allowing for negative interest rates can improve option pricing and implied volatility forecasting.…”

Section: Introductionmentioning

confidence: 99%

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

Bramante

Dallago²,

Facchinetti

2021

Comput Manag Sci

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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.

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Section: Greek Lettersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Bramante

Dallago²,

Facchinetti

2021

Comput Manag Sci

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“…From the financial standpoint, it is therefore necessary to check to what extent the existing pricing models can be adapted to incorporate negative nominal rates. This aspect has been already investigated in some research papers: [3] and [4] discuss the issue for options written on interest rates, both from the practical and the theoretical viewpoint; [5], focusing on foreign exchange and index options investigate whether the use of models allowing for negative interest rates can improve option pricing and implied volatility forecasting; [6], discusses a new closed form for option pricing that leads to sensitively lower the error in European options pricing. Besides, [7] adapts the Nelson-Siegel model [8] to include the negative interest.…”

Section: Introductionmentioning

confidence: 99%

The Effects of Negative Nominal Rates on the Pricing of American Calls: Some Theoretical and Numerical Insights

Cafferata¹,

Giribone²,

Resta³

2017

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The article investigates the effects played on options pricing by negative risk-free rates when the underlying is an equity with null dividends. In such anomalous conditions, in fact, the fair value at early exercise of the American Call would not match the value of the European Call with the same financial features. We originally motivate this assumption with theoretical arguments. We then move to an empirical investigation where we put at work some quasi-closed formulas for pricing an American option and the stochastic trinomial trees algorithm. We then draw the conclusion that from a numerical viewpoint, the bias between the fair value of the American Call and the value of the corresponding. European Call is mainly due to approximation errors, which can be mitigated when Trinomial Stochastic Trees are used.

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Critical analysis of the most widespread methodologies for the simulation of the short rate dynamics under extreme market conditions

Giribone¹

2020

RMM

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This study proposes an analysis of the main drawbacks emerged when adopting the traditional short rate dynamics under extreme market conditions such as under negative interest rates. In fact, this condition has led to invalidate the use of the majority of the most popular stochastic differential equations (SDE) reported in the scientific literature. The first part of the paper makes an overall introduction to the problem, analyzing it from different perspectives. Given that the author dealt with these topics in previous research items, the objective of the paper is to focus on only one of these aspects which was not scrutinized before and to examine it in full detail. As a result, the most popular stochastic dynamics are shown in the second part and the problems raised by their numerical integration are then discussed. Starting from the equations for which it is feasible to implement a numerical scheme for their solution, the problem thus becomes how to find a reasonable estimation for the SDE parameters. The third section deals with the problems occurred in the application of Maximum Likelihood Estimation (MLE) caused by the negative interest rates during the implementation of the well-established approaches. For every analyzed dynamics a real market case is provided. The paper highlights the appropriateness of the Hull-White model which can be considered a feasible and reliable solution for simulating short rates also under extreme market conditions.

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The effects of negative interest rates on the estimation of option sensitivities: The impact of switching from a log-normal to a normal model

Cited by 5 publications

References 2 publications

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

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

The Effects of Negative Nominal Rates on the Pricing of American Calls: Some Theoretical and Numerical Insights

Critical analysis of the most widespread methodologies for the simulation of the short rate dynamics under extreme market conditions

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