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Quantitative Finance · Glossaire

Qu'est-ce que « Curve Jacobian » ?

Definition 3.3 Rates, Credit, XVA and Risk · Chapitre 3 — Rates Risk

The curve Jacobian is the matrix Jkj=∂mk/∂zjJ_{kj} = \partial m_k/\partial z_j of the derivatives of the model quotes of the input instruments with respect to the curve’s pillar parameters, at the calibrated curve; its inverse gives how the pillars move when the quotes move, δz=J−1δq\delta z = J^{-1}\delta q.

Two coordinate systems for one risk. Calibration maps quotes to pillars, pricing maps pillars to value; the Jacobian of the calibration carries a ladder from one system to the other ().
Figure 3.2. Two coordinate systems for one risk. Calibration maps quotes to pillars, pricing maps pillars to value; the Jacobian of the calibration carries a ladder from one system to the other (Proposition 3.4).
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