Why would the option-adjusted spread vary across dealer firms?

What will be an ideal response?

As discussed below, the option-adjusted spread will vary across dealer firms because each dealer will make their own volatility assumptions.

In the Monte Carlo model, the OAS is the spread K that when added to all the spot rates on all interest-rate paths will make the average present value of the paths equal to the observed market price (plus accrued interest). The spread among dealer firms will differ to the extent interest-rate paths and their volatility assumptions differ.

The typical model that Wall Street firms and commercial vendors use to generate random interest-rate paths takes as input today's term structure of interest rates and a volatility assumption. The term structure of interest rates is the theoretical spot rate (or zero-coupon) curve implied by today's Treasury securities. The volatility assumption determines the dispersion of future interest rates in the simulation. The simulations should be normalized so that the average simulated price of a zero-coupon Treasury bond equals today's actual price.

Each model has its own model of the evolution of future interest rates and its own volatility assumptions. Typically, there are no significant differences in the interest-rate models of dealer firms and vendors, although their volatility assumptions can be significantly different.