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Traditional methods for the stochastic alpha beta rho model tend to focus on expansion approximations that are inaccurate in the long maturity ‘wings’. However, if the Brownian motions driving the forward and its volatility are uncorrelated, option prices are analytically tractable. In the correlated case, model parameters can be mapped to a mimicking uncorrelated model for accurate option pricing.

Numerix authors Dr. Alexander Antonov, SVP of Quantitative Research, Dr. Michael Konikov, Executive Director Quantitative Development, andDr. Michael Spector, Director of Quantitative Research explain how in this cutting edge research published in Risk Magazine.

Highlights include an analysis of the following:

• Stochastic Alpha Beta Rho (SABR) model and its widespread usage to capture volatility skew and smile effects of interest rate options
• How traditional methods focus on expansion approximations that are not accurate when it comes to the longer maturity ‘wings’
• How model parameters can be mapped to a mimicking uncorrelated model for accurate option pricing
• How the Numerix approach is precise and near arbitrage-free, consistent with theoretical SABR, and still reasonably fast