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 Two-factor Gaussian model؟

Definition 7.13 Rates, Credit, XVA and Risk · الفصل 7 — Short-Rate Models

The two-factor Gaussian model (G2++) sets rt=φ(t)+xt+ytr_t = \varphi(t)+x_t+y_t with dx=−κ1x dt+σ1dW1dx = -\kappa_1x\,dt+\sigma_1dW^1, dy=−κ2y dt+σ2dW2dy = -\kappa_2y\,dt+\sigma_2dW^2, d⟨W1,W2⟩=ρ dtd\langle W^1,W^2\rangle = \rho\,dt, and φ\varphi fitted to the curve. The correlation of changes of the zero rates of maturities τ1\tau_1 and τ2\tau_2 is

∑a,bba(τ1)bb(τ2)cab∑a,bba(τ1)bb(τ1)cab ∑a,bba(τ2)bb(τ2)cab,ba(τ)=B(κa,τ)τ,\frac{\sum_{a,b}b_a(\tau_1)b_b(\tau_2)c_{ab}}{\sqrt{\sum_{a,b}b_a(\tau_1)b_b(\tau_1)c_{ab}\,\sum_{a,b}b_a(\tau_2)b_b(\tau_2)c_{ab}}}, \quad b_a(\tau)=\frac{B(\kappa_a,\tau)}{\tau},

with c11=σ12c_{11}=\sigma_1^2, c22=σ22c_{22}=\sigma_2^2, c12=c21=ρσ1σ2c_{12}=c_{21}=\rho\sigma_1\sigma_2.

Correlation of instantaneous changes of the two-year zero rate with zero rates of other maturities: one in any one-factor model, decaying with maturity in the two-factor model of . Data: the chapter’s tutorial.
Figure 7.5. Correlation of instantaneous changes of the two-year zero rate with zero rates of other maturities: one in any one-factor model, decaying with maturity in the two-factor model of Example 7.14. Data: the chapter’s tutorial.

أمثلة

Example 7.14 (Decorrelating the curve)

With a slow factor (κ1=2%\kappa_1=2\%, σ1=75\sigma_1=75 basis points), a fast one (κ2=50%\kappa_2=50\%, σ2=90\sigma_2=90 basis points) and ρ=−0.8\rho=-0.8, the model’s correlation between the two- and ten-year zero rates is 0.774, close to the Treasury estimate, and between the two- and thirty-year 0.687 (Figure 7.5). The strongly negative ρ\rho is typical: the fast factor moves the front against the slow factor to produce slope moves.

اقرأ في الفصل →