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Quantitative Finance · Begrippenlijst

Wat is Greeks?

Ook bekend als: vega · theta · rho · vanna · volga

Definition 4.1 Derivatives and Volatility · Hoofdstuk 4 — Greeks and the Hedging P&L

The Greeks of a position are the partial derivatives of its value V(t,S,σ,r)V(t,S,\sigma,r) with respect to the inputs of the pricing model: delta Δ=∂SV\Delta=\partial_SV and gamma Γ=∂SSV\Gamma=\partial_{SS}V; the vega V=∂σV\mathcal V=\partial_\sigma V; the theta Θ=∂tV\Theta=\partial_tV, the change of value with calendar time, all else fixed; the rho Rho=∂rV\mathrm{Rho}=\partial_rV; and the second-order cross-sensitivities vanna Vanna=∂SσV\mathrm{Vanna}=\partial_{S\sigma}V, the change of delta with volatility, and volga Volga=∂σσV\mathrm{Volga}=\partial_{\sigma\sigma}V, the change of vega with volatility.

Voorbeelden

Example 4.6 (The desk’s month)

The one-month at-the-money straddle on a share at 100 is worth 4.6059 at 20 volatility and 5.7570 at 25, with zero rates. A desk short 1 000 straddles (multiplier 100) expects to lose (5.7570−4.6059)×100 000(5.7570-4.6059)\times100\,000, about USD 115 100, when realised volatility comes in at 25. Its vega, 0.2302 per point per straddle, times five points gives nearly the same number: for small changes the expected loss is vega times the volatility gap.

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