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Quantitative Finance · Glosarium

Apa itu Garman–Kohlhagen model?

Dikenal juga sebagai: Garman--Kohlhagen model

Definition 20.1 Derivatives and Volatility · Bab 20 — FX Derivatives

The Garman–Kohlhagen model is Black–Scholes for an exchange rate SS (units of the quote currency per unit of the base currency): the base currency is an asset paying a continuous yield equal to its interest rate rfr_f, the quote currency’s rate rdr_d discounts, and a call on the base currency is worth e−rfTS Φ(d1)−e−rdTK Φ(d2)e^{-r_fT}S\,\Phi(d_1)-e^{-r_dT}K\,\Phi(d_2) with d1,2=(ln⁡(F/K)±12σ2T)/(σT)d_{1,2}=\bigl(\ln(F/K)\pm\frac12\sigma^2T\bigr)/(\sigma\sqrt T) and F=Se(rd−rf)TF=Se^{(r_d-r_f)T}.

Contoh

Example 20.2 (The broker’s screen)

At one year the market implies an at-the-money volatility of 5.32% (delta-neutral straddle strike 6.871, against a forward of 6.861). The 25-delta risk reversal is +1.89+1.89 volatility points and the butterfly +0.46+0.46, with the 25-delta strikes at 6.662 and 7.177. At 10 delta the risk reversal is +3.77+3.77 and the butterfly +1.71+1.71 (strikes 6.442 and 7.702).

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