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Quantitative Finance · Begrippenlijst

Wat is Spot, forward and premium-adjusted delta?

Ook bekend als: spot delta · forward delta · premium-adjusted delta

Definition 19.1 Markets II: Rates, FX and Credit · Hoofdstuk 19 — The FX Options Market

The spot delta of an FX option is the amount of the base currency, per unit of notional, to trade in the spot market to hedge it: ϕe−rfTN(ϕd1)\phi e^{-r_f T} N(\phi d_1), with ϕ=1\phi = 1 for a call and −1-1 for a put. The forward delta is the amount to trade in the forward market, ϕN(ϕd1)\phi N(\phi d_1). The premium-adjusted delta corrects either for a premium paid in the base currency, which is itself a position in that currency: ϕe−rfT(K/F)N(ϕd2)\phi e^{-r_f T} (K/F) N(\phi d_2) (spot) or ϕ(K/F)N(ϕd2)\phi (K/F) N(\phi d_2) (forward).

Voorbeelden

Example 19.6 (Two smiles from one screen)

USDJPY three months: ATM 9.5%, risk reversal −1.2-1.2 (dollar puts over), butterfly 0.3. By Equation 19.1 the 25-delta dollar call is at 9.2% and the put at 10.4%. With regular spot deltas their strikes are 160.85 and 150.71; with premium-adjusted spot deltas, the pair’s convention, 160.68 and 150.52. A trader who priced the 150.71 put at 10.4% while the market meant 150.52 would misprice it by the smile’s slope over 19 pips of strike (Figure 19.2).

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