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Quantitative Finance · Begrippenlijst

Wat is Hedging P&L?

Ook bekend als: hedging P\&L

Definition 4.4 Derivatives and Volatility · Hoofdstuk 4 — Greeks and the Hedging P&L

The hedging P&L of a delta-hedged option is the change of value of the option together with its hedge and its financing. For a long option hedged at volatility σ\sigma it is, to second order over each interval, the cash gamma times the difference between the squared return and the variance the hedge assumed:

P&L[0,T]=∫0Ter(T−t)12ΓtSt2(σreal,t2−σ2)dt,\pnl_{[0,T]}=\int_0^Te^{r(T-t)}\tfrac12\Gamma_tS_t^2\bigl(\sigma_{\mathrm{real},t}^2-\sigma^2\bigr)dt ,

where σreal,t2dt=(dSt/St)2\sigma^2_{\mathrm{real},t}dt=(dS_t/S_t)^2 is the instantaneous realised variance.

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