Mixing SABR Models for Negative Rates

a b s t r a c tIn this work, we propose a one time-step Monte Carlo method for the SABR model. We base our approach on an accurate approximation of the cumulative distribution function of the time-integrated variance (conditional on the SABR volatility), using Fourier techniques and a copula. Resulting is a fast simulation algorithm which can be employed to price European options under the SABR dynamics. Our approach can thus be seen as an alternative to Hagan's analytic formula for short maturities that may be employed for model calibration purposes.

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“…Fig. 5 a gives convergence results for Set I, where an analytic solution is given by Antonov [7] ( ρ = 0 ). In Fig.…”

Section: Pricing European Options By the One-step Sabr Methodsmentioning

confidence: 99%

“…In [2] , Oblój provided a correction to the Hagan formula but the same drawbacks remained. In order to improve the approximation for the SABR implied volatility, different techniques have been proposed in the literature, based on either perturbation theory [3,4] , heat kernel expansions [5,6] or model map techniques [7] .…”

Section: Introductionmentioning

confidence: 99%

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

Leitao

Grzelak

Oosterlee

2017

Applied Mathematics and Computation

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“…This formula, also known as the Hagan formula, may however sometimes lead to arbitrage possibilities for low strikes, as one can observe by examining the corresponding PDF [36]. The Hagan formula is not accurate for pricing options with long maturities [1,18,36]. As no analytic expression for the bivariate ChF of the SABR model is available, it may be difficult to calculate accurate reference values for our purposes.…”

Section: The Two-dimensional Cos Methodsmentioning

confidence: 99%

“…The ChF of the Heston model is known, which ensures the availability of accurate reference prices for European and Bermudan options. The FSDEs can be written in the form of Formula (1), that is,…”

Section: The Two-dimensional Cos Methodsmentioning

confidence: 99%

“…Many pricing methods for SABR-like models have been presented in the literature, like [2,9,16,18,27], however, many of those methods are mainly accurate for valuing European options with short maturities under the SABR model. In [1] a pricing method is given, which is accurate for options with long maturities, but this method is not applicable for all parameter sets [1]. When we work on the risk neutral measure, we can simply use the COS method, for European and Bermudan options.…”

Section: Introductionmentioning

confidence: 99%

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The COS method for option valuation under the SABR dynamics

Have

Oosterlee

2017

International Journal of Computer Mathematics

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In this paper, we consider the COS method for pricing European and Bermudan options under the stochastic alpha beta rho (SABR) model. In the COS pricing method, we make use of the characteristic function of the discrete forward process. We observe second-order convergence by using a second-order Taylor scheme in the discretization, or by using Richardson extrapolation in combination with a Euler-Maruyama discretization on the forward process. We also consider backward stochastic differential equations under the SABR model, using the discretized forward process and Fourier-cosine expansion for the occurring expectations. For this purpose, we extend the so-called BCOS method from one to two dimensions. ARTICLE HISTORY

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Forecasting negative yield‐curve distributions

Jun

Lebreton²,

Rakotondratsimba

2020

Journal of Forecasting

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Negative interest rates have been present in various marketplaces since mid-2014, following the negative interest rate policy (NIRP) adopted by the European Central Bank to raise economic growth. The well-known historical approach (HA) appears to be a good resource. By tweaking the HA, we derive a very tractable data-driven tool that allows practitioners to generate yield-curve distributions at future discrete time horizons. We thereby provide a robust and easy-to-understand forecasting model, suitable for the NIRP context, allowing an appreciation of its predictive power.Besides the methodological development herein, various numerical illustrations are presented to shed light on the benefits (and limitations) of this forecasting approach.

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Mixing SABR Models for Negative Rates

Cited by 22 publications

References 8 publications

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options

The COS method for option valuation under the SABR dynamics

Forecasting negative yield‐curve distributions

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