Go to Deriscope's documentation start pageVol_Spec__Vol_Type

*Vol Type* refers to List of definitions of what "volatility" exactly (mathematically) means in the context of a given stochastic process, a given risk factor and some fixed future time.

Available *Vol Type* types:

*Black*

Appropriate when the value *x(T)* of the Quotable in Key Vol Spec::Ref Quotable at a given time *T* with respect to the given risk factor is distributed in any fashion.

Then the *Black* volatility is defined as the function *σ(K)* defined by requiring that the equality *E{ max(x(T)-K,0) } = Black(K,σ)* holds for all real values K.

Here *E* denotes the Expectation operator with respect to a measure where x behaves as martingale and *Black(K,σ)* is defined to equal *E{ max(y(T)-K,0) }* for some *y* diffused as *dy = σydw*

In the trivial case where all strikes *K* map to the same flat value *σ*, the value at time *T* is the single number *σ*.

*SABR*

Appropriate when the value *x(T)* of the Quotable in Key Vol Spec::Ref Quotable at a given time *T* with respect to the given risk factor derives from the following SDE:

*dx = α(x^β)dw*

where*w* is a Wiener process, *β* is constant and *α* is the forward's stochastic volatility, which itself follows the SDE:

*dα = ναdω*

where *v* is constant and *ω* is another Wiener process having correlation *ρ* with *w*. Web reference available here

Due to the absence of a drift term, *x* represents the value of some forward, such as a forward rate or a forward stock price.