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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 Accrued interest, clean and dirty price؟

يُعرف أيضًا باسم: accrued interest · dirty price · clean price

Definition 3.3 Markets II: Rates, FX and Credit · الفصل 3 — Government Bonds

Between two coupon dates the seller of a bond has earned part of the next coupon, and the buyer pays it to her: this is accrued interest, A=cf (1−w)A = \frac{c}{f}\,(1 - w) under actual/actual, where ww is the fraction of the current period still to run. The dirty price (or full, or invoice price) is what changes hands; the clean price quoted on screens is the dirty price less accrued interest.

A settlement between coupon dates. The seller is paid the fraction 1 - w of the coming coupon as accrued interest; the buyer receives the whole coupon. The street convention discounts each later flow over w, 1 + w, 2 + w, … periods.
Figure 3.1. A settlement between coupon dates. The seller is paid the fraction 1−w1 - w of the coming coupon as accrued interest; the buyer receives the whole coupon. The street convention discounts each later flow over ww, 1+w1 + w, 2+w2 + w, … periods.

أمثلة

Example 3.4 (Forty-one days)

A note paying 4.25% semiannually on 15 February and 15 August settles on 25 September 2026. The current period runs 184 days, of which 41 have elapsed: A=2.125×41/184=0.473505A = 2.125 \times 41/184 = 0.473505 per 100, USD 4 735 per million, USD 47 351 on the trade of the opening paragraph.

Example 3.10 (The ten-year note)

At 4.200% the note of Example 3.4 has a clean price of 100.397405 (100-12+), a dirty price of 100.870911, a Macaulay duration of 8.142 years, a modified duration of 7.975, a DV01 of USD 804 per million and a convexity of 75.8. A 100-basis-point rise costs 7.675 points; duration alone predicts 8.044, duration and convexity together 7.662 (Figure 3.2).

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