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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 Bayesian update؟

Definition 30.3 Markets II: Rates, FX and Credit · الفصل 30 — Market-Making Games

A Bayesian update revises a probability distribution over an unknown value after an observation, in proportion to how likely the observation would be under each value: posterior ∝\propto prior ×\times likelihood.

Distribution of the sum of five cards dealt from a 52-card deck, aces counting 1 and kings 13: mean 35 (dashed), standard deviation 8.03, from 6 to 64. Exact, by counting. Data: the chapter’s tutorial.
Figure 30.1. Distribution of the sum of five cards dealt from a 52-card deck, aces counting 1 and kings 13: mean 35 (dashed), standard deviation 8.03, from 6 to 64. Exact, by counting. Data: the chapter’s tutorial.
One game at a width of 11.5: the maker’s expected value of the sum before each round, updated by Bayes’ rule after every trade and pass, against the true sum, 31. Early buys push the estimate up; the sales that follow bring it down towards the truth. The maker ends the game with a profit of 18.6. Data: the chapter’s tutorial, seeded.
Figure 30.2. One game at a width of 11.5: the maker’s expected value of the sum before each round, updated by Bayes’ rule after every trade and pass, against the true sum, 31. Early buys push the estimate up; the sales that follow bring it down towards the truth. The maker ends the game with a profit of 18.6. Data: the chapter’s tutorial, seeded.

أمثلة

Example 30.4 (The first trade)

The maker opens 30 at 40, a width of 10. An uninformed trader trades with probability e−10/8=0.29e^{-10/8} = 0.29. If someone buys at 40, it was an informed trader with probability 0.31; the maker’s expected value of the sum rises from 35 to 38.13, and its next market is centred there. After a sale at 30 it falls to 31.87; after a pass it stays at 35, since a pass is equally likely from a high or a low sum.

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