جميع الكتب

مهني

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
التطبيقات حول المدرب تسجيل الدخول ابدأ القراءة

Quantitative Finance · المسرد

ما معنى Annuity and par swap rate؟

يُعرف أيضًا باسم: annuity · par swap rate

Definition 9.5 Markets II: Rates, FX and Credit · الفصل 9 — Interest-Rate Swaps

For fixed-leg payment dates t1,…,tnt_1, \dots, t_n with accrual fractions δi\delta_i and discount factors P(ti)P(t_i), the annuity is A=∑iδiP(ti)A = \sum_i \delta_i P(t_i), the value of receiving 1 a year on the fixed leg’s schedule. The par swap rate is the fixed rate at which the swap is worth zero at inception.

The curve bootstrapped from six illustrative par rates. Zero rates are smooth; forward rates are flat between pillars and jump at them, an artefact of interpolating the logarithm of discount factors linearly: every choice of interpolation is a choice of forward curve, and One Quant Book 6 treats better ones. Data: the chapter’s tutorial.
Figure 9.2. The curve bootstrapped from six illustrative par rates. Zero rates are smooth; forward rates are flat between pillars and jump at them, an artefact of interpolating the logarithm of discount factors linearly: every choice of interpolation is a choice of forward curve, and One Quant Book 6 treats better ones. Data: the chapter’s tutorial.
Bucketed DV01 of two payer swaps of USD 100 million: the change in value when each input par rate rises by a basis point and the curve is rebuilt. The par ten-year loads only its own pillar. The five-year swap starting in five years is long ten-year rates and short five-year rates: it is a bet on the forward, and its hedge is a pair of par swaps. Data: the chapter’s tutorial.
Figure 9.3. Bucketed DV01 of two payer swaps of USD 100 million: the change in value when each input par rate rises by a basis point and the curve is rebuilt. The par ten-year loads only its own pillar. The five-year swap starting in five years is long ten-year rates and short five-year rates: it is a bet on the forward, and its hedge is a pair of par swaps. Data: the chapter’s tutorial.

أمثلة

Example 9.8 (A ten-year swap)

With illustrative par rates of 3.90, 3.85, 3.83, 3.85, 3.92 and 4.05% at one, two, three, five, seven and ten years, the ten-year par rate is 4.05% by construction, the annuity is 8.228 and the swap’s DV01 on USD 100 million is USD 82 278 by NA×10−4N A \times 10^{-4}, and USD 82 262 when the curve is rebuilt after bumping each input by a basis point. All of it falls on the ten-year pillar: a par swap is hedged exactly by the swap that built its pillar.

اقرأ في الفصل →

مصطلحات ذات صلة