सभी किताबें

1 Primary & Middle School Mathematicsकक्षा 1–9 ऑनलाइन 2 High School Mathematicsकक्षा 10–12 ऑनलाइन 3 University Mathematics — Year 1स्नातक वर्ष 1 ऑनलाइन 4 University Mathematics — Year 2स्नातक वर्ष 2 ऑनलाइन 5 University Mathematics — Year 3स्नातक वर्ष 3 ऑनलाइन

1 Primary & Middle School Physicsकक्षा 1–9 ऑनलाइन 2 High School Physicsकक्षा 10–12 ऑनलाइन 3 University Physics — Year 1स्नातक वर्ष 1 ऑनलाइन 4 University Physics — Year 2स्नातक वर्ष 2 ऑनलाइन 5 University Physics — Year 3स्नातक वर्ष 3 ऑनलाइन

1 Primary & Middle School Biologyकक्षा 1–9 ऑनलाइन 2 High School Biologyकक्षा 10–12 ऑनलाइन 3 University Biology — Year 1स्नातक वर्ष 1 ऑनलाइन 4 University Biology — Year 2स्नातक वर्ष 2 ऑनलाइन 5 University Biology — Year 3स्नातक वर्ष 3 ऑनलाइन

1 Markets I: The Ecosystem and Exchange-Traded Marketsबाज़ार ऑनलाइन 2 Markets II: Rates, FX and Creditबाज़ार ऑनलाइन 3 Markets III: Commodities, Energy and Cryptoबाज़ार ऑनलाइन 4 Quantitative Methodsविधियाँ ऑनलाइन 5 Derivatives and Volatilityडेरिवेटिव्स ऑनलाइन 6 Rates, Credit, XVA and Riskब्याज दरें, क्रेडिट और जोखिम ऑनलाइन 7 Research Craft: Predictors, Backtests, Measurement, Portfoliosअनुसंधान ऑनलाइन 8 Strategies I: Equities and Futuresरणनीतियाँ ऑनलाइन 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desksरणनीतियाँ ऑनलाइन 10 Microstructure and Executionनिष्पादन ऑनलाइन 11 Market Making and High-Frequency Tradingमार्केट मेकिंग ऑनलाइन 12 Machine Learning for Marketsमशीन लर्निंग ऑनलाइन 13 Low-Latency Softwareतकनीक ऑनलाइन 14 Networks, Hardware and Trading Infrastructureतकनीक ऑनलाइन 15 Research, Data and Risk Platformsतकनीक ऑनलाइन 16 The Desk and the Firmफ़र्म ऑनलाइन 17 The Industry: Firms, Roles and Careersकरियर ऑनलाइन 18 The Interview Bookकरियर ऑनलाइन

सभी गेम Math Fuse Word Reactor Atlas Dash

ऐप्स परिचय

Coach

English Français Español Nederlands Português हिन्दी العربية Bahasa Indonesia

लॉग इन पढ़ना शुरू करें

Quantitative Finance · शब्दावली

Multivariate Hawkes process क्या है?

Definition 7.7 Quantitative Methods · अध्याय 7 — Point Processes and Hawkes Processes

A multivariate Hawkes process has components $N^{(1)}, \dots, N^{(d)}$ with intensities $\lambda^{(i)}_t = \mu_i + \sum_j\sum_{t^{(j)}_k < t}g_{ij}(t - t^{(j)}_k)$ ; the branching matrix is $G = (\lVert g_{ij}\rVert_1)$ , and a stationary version exists when its spectral radius is below one.

Left: one minute of a simulated trading day with = 0.1, = 0.7 and = 1 per second (branching ratio 0.7): the intensity jumps by at each event (ticks) and decays toward the baseline (dashed). Right: variance-to-mean ratio of the counts in bins of length , from the covariance density and in the simulated day, against one for a Poisson process (dashed), rising to 1/(1 - 0.7)2 = 11.1. Data: the chapter’s tutorial, seeded. — Figure 7.2. Left: one minute of a simulated trading day with $\mu = 0.1$ , $\alpha = 0.7$ and $\beta = 1$ per second (branching ratio 0.7): the intensity jumps by $\alpha$ at each event (ticks) and decays toward the baseline (dashed). Right: variance-to-mean ratio of the counts in bins of length $\tau$ , from the covariance density and in the simulated day, against one for a Poisson process (dashed), rising to $1/(1 - 0.7)^2 = 11.1$ . Data: the chapter’s tutorial, seeded.

उदाहरण

Example 7.8 (Buys and sells that excite each other)

Let buys and sells each have baseline $0.1$ per second and exponential kernels with $\beta = 1$ , a buy raising the buy intensity by $0.2$ and the sell intensity by $0.4$ , and symmetrically. The branching matrix $G = \bigl(\begin{smallmatrix}0.2 & 0.4\\0.4 & 0.2\end{smallmatrix}\bigr)$ has eigenvalues $0.6$ and $-0.2$ , so the process is stable; taking expectations as in Proposition 7.5, the mean intensities solve $\bar\lambda = \mu + G\bar\lambda$ , giving $\bar\lambda = (I_2 - G)^{-1}\mu = (0.25, 0.25)$ per second. Cross-excitation dominates: of the triggered activity on each side, two thirds comes from the other side’s trades.

अध्याय में पढ़ें →