Deriscope ## The Excel Derivatives Periscope

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Vol_Spec

*Vol Spec* is a Type that represents a collection of specification parameters being used by Vol objects in defining the exact type of volatility that these objects represent.

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 *Quotable* by the key *Risk Factor*

It is assumed that the value *x1* of the Quotable in *Ref Quotable* follows the jump-diffusion process:

*dx1 = μ1dt + σ1dw1 + dN1*

where *μ1* = drift, *t* = time, *σ1* = overall volatility, *w1* = wiener process, *N1* = pure jump process.

It is similarly assumed that the value *x2* of the Quotable in *Risk Factor* follows the jump-diffusion process:

*dx2 = μ2dt + σ2dw2 + dN2*

We can always decompose as *σ1dw1 = σ1'dw2 + σ1''dw3* where *dw3* is orthogonal to *dw2*, so that

*dx1 = μ1dt + σ1'dw2 + σ1''dw3 + dN1*

This final equation describes how the value *x1* of *Ref Quotable* is evolved against the non-jump random increment *dw2* of the value *x2* of *Risk Factor*

The quantity *σ1'* is exactly the volatility described here.