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Question :
What are the parameters affecting European option price on a futures contract? What happens to option prices when one of these parameters changes with all the others remaining the same?
A European option may be exercised only at the expiry date of the option, i.e. at a single pre-defined point in time. The pay-off – when it occurs – is via:
Max [ (S X), 0 ], for a call option
Max [ (X S), 0 ], for a put option:
(Where K is the Strike price and S is the spot price of the underlying asset)
And Call put Parity relation follows
C- P = S X exp (-rt)
For a European option on the underlying futures, F, satisfies:
C = F*N([d(N1)]) X*N([d(N2)]),
where:
[d(N1)] = [ln (F/X) + 1/2 s2*t]/ (s t1/2)
[d.(N2)] = [d(N1)] – (s t1/2)
F = futures price;
X = exercise price;
C = call price;
t = time to maturity; and
s = instantaneous volatility
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