Valuation Commentary

How to Validate an Interest Rate Model
by Alex Levin

Part III: Validation of option values

With the last several articles having been written about prOAS, I got derailed from this model validation sequel. It is time to resume the efforts and bring forth perhaps the most intriguing subject: calibration of volatility to rate options. Indeed, MBS are short of a prepayment option, and everyone knows that the options are driven by volatility. Perhaps the most stunning discovery (at least, from a practitioner's standpoint) made by Black and Scholes is that the price of an option and volatility are two sides of one coin - nothing else is uncertain: stock's price, strike and discount factor are all undisputed.

Usually, rate models are calibrated to the option market meaning they are supposed to value most important rate options within a tolerance. Given the fact that mortgage prepay option is just a special call option, "anything less will be uncivilized".

Instruments matter
Before you choose a vendor for OAS or just a rate model, ask whether its system accepts swaptions volatilities (or prices) for calibration. In Levin [2002, 2004] we pointed out that caps are not priced in unison with swaptions by typical diffusion models. Cap volatility structure exhibits a prominent hump explained by the jumpy nature of short rates. Hence, calibrating a diffusion model to caps understates options on long rates, which the prepay option is. Do not fall in a trap of belief that short rate and long rates should agree on volatility by "the arbitrage argument". Only a multi-factor jump-diffusion model (or a model with other forms of non-Brownian stochastic volatility) can capture both caps and swaptions; such a model would be an extreme rarity in the business - even at MBS desks of major street firms. >>>