Question

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.

Answer 1

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