A low-bias simulation scheme for the SABR stochastic volatility model

Bin Chen; Cornelis W. Oosterlee; Hans Van Der Weide

doi:10.1142/S0219024912500161

A low-bias simulation scheme for the SABR stochastic volatility model

Bin Chen^*, Cornelis W. Oosterlee, Hans Van Der Weide

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.

Original language	English
Article number	1250016
Journal	International Journal of Theoretical and Applied Finance
Volume	15
Issue number	2
DOIs	https://doi.org/10.1142/S0219024912500161
Publication status	Published - Mar 2012
Externally published	Yes

Keywords

Discretization scheme
integrated variance
Monte Carlo
SABR model
small noise expansion
square Bessel process

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10.1142/S0219024912500161

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title = "A low-bias simulation scheme for the SABR stochastic volatility model",

abstract = "The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.",

keywords = "Discretization scheme, integrated variance, Monte Carlo, SABR model, small noise expansion, square Bessel process",

author = "Bin Chen and Oosterlee, {Cornelis W.} and {Van Der Weide}, Hans",

year = "2012",

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doi = "10.1142/S0219024912500161",

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AU - Chen, Bin

AU - Oosterlee, Cornelis W.

AU - Van Der Weide, Hans

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N2 - The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.

AB - The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.

KW - Discretization scheme

KW - integrated variance

KW - Monte Carlo

KW - SABR model

KW - small noise expansion

KW - square Bessel process

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JO - International Journal of Theoretical and Applied Finance

JF - International Journal of Theoretical and Applied Finance

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ER -

A low-bias simulation scheme for the SABR stochastic volatility model

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Keywords

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