Question

What is the delta of a short position in 600 European call options on silver futures? The options mature in 8 months and the silver futures contract matures in 9 months. The current 9 month futures price is $30.00 per ounce. The exercise price of the option is $31.00 per ounce. The risk-free interest rate is 5% per year and the volatility is 20 percent per year.

Answer 1

Delta is defined as rate of change of derivative's price compared to that of underlying.

Give facts

Option Period= 8 months

Silver future contract period= 9 months

Futures Price( S)= 30

Exercise Price (X)= 31

Risk Free Rate (Rf)= 5%

Volatility= 20%

Delta= e^-rt*N(d1)

d1= $\fn_jvn (ln(s/x)+(r+\sigma ^{2}/2 )t)/\sigma\sqrt{t}$

= $\fn_jvn (ln(30/31)+(.05+.20^{^{2}}/2 ).6667)/.20\sqrt{0.6667}$

=$\fn_jvn 0.013869 /0.1633$

=$\fn_jvn 0.0849$

N(d1)= 0.5338

and Delta of Option is

$\fn_jvn e^{^{-.05*0.6667}}(0.5338)$

0.9672*0.5338

=0.5163

The delta of a short position in 600 futures options is therefore= 309.78