The option cost of a mortgage security is its zero-volatility spread (the spread that reprices it on the single path of forward rates) minus its option-adjusted spread: the value, in spread, of the borrowers’ prepayment options that volatile rates make valuable.
Exemples
Example 12.7 (A premium pool at par)
A pool with a WAC of 6.0%, a coupon of 5.5%, 348 months left, on chapter 1’s SOFR curve (ten-year par rate 3.80% in the model’s annual convention, so a mortgage rate of 5.55% and an incentive of 0.45%), with Hull–White , basis points and 4 000 paths, priced at 100: its option-adjusted spread is 146 basis points, its zero-volatility spread 181, and its option cost 34. Its effective duration is 4.99 years, its effective convexity , its weighted-average life 6.4 years. Without burnout the same pool at the same spread would be worth 99.20: faster prepayment of a premium pool returns principal at par sooner.