Interest Rate Modelling (Finance and Capital Markets Series)

2.4 Value of any contingent claim in equilibrium

Now comparing the drift coefficients in (2.10) and (2.3) we have:

Making use of (2.11) yields:

Rearranging terms we have a partial differential equation for the price of any contingent claim ^[5] :

This valuation equation holds for any contingent claim. Specific terminal and boundary conditions as well as the structure of , the payout flow, define the unique characteristics of a claim.

^[5] First group the coefficients of F _W and make use of (2.8) to give: