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1 Markets I: The Ecosystem and Exchange-Traded Marketsالأسواق عبر الإنترنت 2 Markets II: Rates, FX and Creditالأسواق عبر الإنترنت 3 Markets III: Commodities, Energy and Cryptoالأسواق عبر الإنترنت 4 Quantitative Methodsالأساليب عبر الإنترنت 5 Derivatives and Volatilityالمشتقات عبر الإنترنت 6 Rates, Credit, XVA and Riskالفائدة والائتمان والمخاطر عبر الإنترنت 7 Research Craft: Predictors, Backtests, Measurement, Portfoliosالبحث عبر الإنترنت 8 Strategies I: Equities and Futuresالاستراتيجيات عبر الإنترنت 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desksالاستراتيجيات عبر الإنترنت 10 Microstructure and Executionالتنفيذ عبر الإنترنت 11 Market Making and High-Frequency Tradingصناعة السوق عبر الإنترنت 12 Machine Learning for Marketsتعلم الآلة عبر الإنترنت 13 Low-Latency Softwareالتكنولوجيا عبر الإنترنت 14 Networks, Hardware and Trading Infrastructureالتكنولوجيا عبر الإنترنت 15 Research, Data and Risk Platformsالتكنولوجيا عبر الإنترنت 16 The Desk and the Firmالشركة عبر الإنترنت 17 The Industry: Firms, Roles and Careersالمسارات المهنية عبر الإنترنت 18 The Interview Bookالمسارات المهنية عبر الإنترنت
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Quantitative Finance · المسرد

ما معنى Backward-looking caplet؟

Definition 10.2 Rates, Credit, XVA and Risk · الفصل 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.

أمثلة

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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