## Vol Spec

**is a direct subtype of Financial with functions Vol Spec Functions, keys Vol Spec keys and example object VolSpec that represents a collection of specification parameters being used by Vol objects in defining the exact type of volatility that these objects represent.**

*Vol Spec*A formal description follows:

In order to properly define a volatility of some stochastic process against some risk factor, two separate stochastic processes must be first defined.

The first is the process where the volatility applies. It is supplied as an object of type Quotable by the key

*Ref Quotable*The second is the reference process defining the risk factor. It is supplied as an object of also type

**by the key**

*Quotable*

*Risk Factor*It is assumed that the Quotable Value

**of the Quotable in**

*x1***follows the jump-diffusion process:**

*Ref Quotable*

*dx1 = μ1dt + σ1dw1 + dN1*where

**= drift,**

*μ1***= time,**

*t***= overall volatility,**

*σ1***= wiener process,**

*w1***= pure jump process.**

*N1*It is similarly assumed that the value

**of the Quotable in**

*x2***follows the jump-diffusion process:**

*Risk Factor*

*dx2 = μ2dt + σ2dw2 + dN2*We can always decompose as

**where**

*σ1dw1 = σ1'dw2 + σ1''dw3***is orthogonal to**

*dw3***, so that**

*dw2*

*dx1 = μ1dt + σ1'dw2 + σ1''dw3 + dN1*This final equation describes how the value

**of**

*x1***is evolved against the non-jump random increment**

*Ref Quotable***of the value**

*dw2***of**

*x2*

*Risk Factor*The quantity

**is exactly the volatility described here.**

*σ1'*