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Quantitative Finance · शब्दावली

Backward-looking caplet क्या है?

Definition 10.2 Rates, Credit, XVA and Risk · अध्याय 10 — Modelling Overnight-Rate Products

A backward-looking caplet pays δmax⁡(R(S,E)−K,0)\delta\max(R(S,E)-K,0) at EE (or a few days later) on the compounded rate of its own period.

A forward-looking rate carries risk until the start of its period and is known from then on; a compounded overnight rate keeps moving until the last fixing at the end, so an option on it carries risk through its whole accrual period.
Figure 10.1. A forward-looking rate carries risk until the start of its period and is known from then on; a compounded overnight rate keeps moving until the last fixing at the end, so an option on it carries risk through its whole accrual period.
Caplets of a two-year cap at 3.75% on USD 100 million, on compounded SOFR and on a term rate for the same quarters. The current quarter has a caplet only in the backward-looking cap; each later backward-looking caplet is worth more by its period’s in-arrears variance. Data: chapter 1’s curve, Hull–White =3\%, =90 basis points; the chapter’s tutorial.
Figure 10.2. Caplets of a two-year cap at 3.75% on USD 100 million, on compounded SOFR and on a term rate for the same quarters. The current quarter has a caplet only in the backward-looking cap; each later backward-looking caplet is worth more by its period’s in-arrears variance. Data: chapter 1’s curve, Hull–White κ=3%\kappa=3\%, σ=90\sigma=90 basis points; the chapter’s tutorial.

उदाहरण

Example 10.4 (A two-year SOFR cap)

On chapter 1’s SOFR curve with κ=3%\kappa=3\% and σ=90\sigma=90 basis points, a two-year cap on three-month compounded SOFR at 3.75% on USD 100 million costs USD 288 963: eight caplets from USD 13 623 (the current quarter) to 53 846 (Figure 10.2). The same cap on a three-month term rate, whose first caplet has already fixed, costs USD 250 741: the backward-looking cap is USD 38 222 more expensive, of which 13 623 is the first caplet and 24 599 the in-period variance of the other seven. A Monte Carlo of the short rate with 260 steps a year reprices the caplet on the fifth quarter (USD 40 944) to within a fifth of a standard error.

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