What is the delta of a short position in 1,000 European call options on Silver futures? The options mature in 8 months and the futures contract underlying the option matures in 9 months. The current 9-month futures price is €8 per ounce, the exercise price of the options is €8, the risk-free rate is 12% per annum, and the volatility of silver is 18% per annum.
Computation of Delta of short position in european futures option:
The formula is e-rt N(d1)
F0 (Stock Price) = 8
K (Strike Price) = 8
r (Risk-free interest) = 12%
σ (Volatility of stock) = 18%
T (Time to maturity) = 8/12 = 0.6667
d1 = {[ln X(F0/K)] + [(σ2/2) X T]} / σ X √T
= {[ln X(8/8)] + [(0.182/2) X 0.6667]} / 0.18 X √0.6667
= 0.0735
N(d1) = 0.5293 and the delta is computed as follows:
e-0.12 X 0.6667 X 0.5293 = 0.4886
The delta of a short term position in a 1000 futures option is = -488.6
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