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Quantitative Finance · Glossaire

Qu'est-ce que « Fair-price filter » ?

Definition 2.5 Market Making and High-Frequency Trading · Chapitre 2 — Fair Value

A fair-price filter treats the efficient price as a hidden state, a random walk with variance qq per second, and every source’s price as an observation of it with noise variance rjr_j. On an observation yy from source jj at time tt, the previous update having been at t′t', it propagates and updates:

Σ←Σ+q (t−t′),K=ΣΣ+rj,P^t←P^t+K (y−P^t),Σ←(1−K) Σ.\Sigma\leftarrow\Sigma+q\,(t-t'),\qquad K=\frac{\Sigma}{\Sigma+r_j},\qquad \hat P_t\leftarrow\hat P_t+K\,(y-\hat P_t),\qquad \Sigma\leftarrow(1-K)\,\Sigma .
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