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Quantitative Finance · Glossaire

Qu'est-ce que « Option cost » ?

Definition 12.6 Rates, Credit, XVA and Risk · Chapitre 12 — Mortgage Modelling

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 κ=3%\kappa = 3\%, σ=90\sigma = 90 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 −123-123, 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.

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