SABR : a stochastic volatility model in practice

Bogatyreva, Natalya S.; Grandez, Rodrigo; Rodríguez Apolinar, Sergio; Soldevilla, Abraham

SABR : a stochastic volatility model in practice

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Bogatyreva, N, Grandez, R, Rodríguez Apolinar, S, Soldevilla, A. SABR : a stochastic volatility model in practice. 2019. handle: http://hdl.handle.net/10230/43328

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Abstract

The Black and Scholes model (BS) assumes that the volatility of an asset is constant over the trading period. As a result, BS returns a flat volatility surface. This assumption fails to capture the asset’s volatility dynamics (smile), which is particularly important if we want to price complex derivatives. Local Volatility (LV) models captures the volatility smile, but not the price dynamics. In this project, we study the SABR (Stochastic Alpha, Beta, Rho) model, a stochastic volatility (SV) model designed to describe the implied volatility (IV) surface capturing both the smile and price dynamics. We calibrate its parameters, compute the IV using its closed-form solution and Monte Carlo Methods (MCM), and compare our results with real market data. Finally, we discuss our results and their implementations to practitioners.