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In mathematical finance, the SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for " stochastic alpha , beta , rho ", referring to the parameters of the model.
When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. [ 1 ] : 394 For direct modeling of simple forward rates the Brace–Gatarek–Musiela model represents an example.
Starting from a constant volatility approach, assume that the derivative's underlying asset price follows a standard model for geometric Brownian motion: = + where is the constant drift (i.e. expected return) of the security price , is the constant volatility, and is a standard Wiener process with zero mean and unit rate of variance.
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Bill James, who coined the term "sabermetrics". Sabermetrics (originally SABRmetrics) is the original or blanket term for sports analytics in the US, the empirical analysis of baseball, especially the development of advanced metrics based on baseball statistics that measure in-game activity.
In the Black–Scholes model, the theoretical value of a vanilla option is a monotonic increasing function of the volatility of the underlying asset. This means it is usually possible to compute a unique implied volatility from a given market price for an option. This implied volatility is best regarded as a rescaling of option prices which ...
The model is at times classified as a stochastic volatility model, although according to the definition given here, it is a local volatility model, as there is no new randomness in the diffusion coefficient. This model and related references are shown in detail in the related page.
Modern Pricing of Interest-Rate Derivatives: The LIBOR Market Model and Beyond. 2002. Wiley. ISBN 0-691-08973-6; Volatility and Correlation: The Perfect Hedger and the Fox. 2004. Wiley. ISBN 0-470-09139-8; The SABR/LIBOR Market Model: Pricing, Calibration and Hedging for Complex Interest-Rate Derivatives. 2009. Wiley. ISBN 0-470-74005-1