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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 Forward-rate correlation؟

Definition 8.11 Rates, Credit, XVA and Risk · الفصل 8 — Forward-Rate and Market Models

The forward-rate correlation ρij\rho_{ij} of a market model is the instantaneous correlation of the Brownian motions driving FiF_i and FjF_j. It is usually parametrised, for example ρij=e−β∣Ti−Tj∣\rho_{ij} = e^{-\beta|T_i-T_j|}, and reduced to two or three factors by keeping the leading eigenvectors of the matrix (the principal components of chapter 3), which speeds simulation and removes noise.

Correlation of the first annual forward with the others under the exponential parametrisation _ij=e- |T_i-T_j| for three values of . Data: the chapter’s tutorial.
Figure 8.4. Correlation of the first annual forward with the others under the exponential parametrisation ρij=e−β∣Ti−Tj∣\rho_{ij}=e^{-\beta|T_i-T_j|} for three values of β\beta. Data: the chapter’s tutorial.
Five-year-expiry swaption volatilities from two market models that reprice the same caplets. Decorrelating the forwards lowers the volatility of longer swap rates; Rebonato’s formula (lines) tracks Monte Carlo (marks). Data: the chapter’s tutorial.
Figure 8.5. Five-year-expiry swaption volatilities from two market models that reprice the same caplets. Decorrelating the forwards lowers the volatility of longer swap rates; Rebonato’s formula (lines) tracks Monte Carlo (marks). Data: the chapter’s tutorial.

أمثلة

Example 8.12 (Same caplets, different swaptions)

Calibrate the model to the same caplets with β=0.02\beta=0.02 (forwards nearly perfectly correlated) and with β=0.40\beta=0.40 (the one-year and nine-year forwards correlated at 0.04). The swaption expiring in five years into one year is priced at 25.0% of Black volatility by both (it is one forward); into five years, at 22.1% and 17.3% (Figure 8.5). On EUR 100 million, at the money (forward 2.933%, annuity 4.102), that is EUR 2.35 million against 1.84 million: 22% apart for the same caplets. Monte Carlo confirms Rebonato’s formula to within its standard errors.

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