Tuesday, February 21, 2012

Put-call parity for European options

Put-call parity for European options with the same strike price and time to expiration is
Call - put = present value of (forward price - strike price)
Equation for put-call parity:
C(K, T) - P(K, T) = PV0,T(F0,T - K) = e-rT(F0,T - K)
Meaning of variables:
K = strike price of the options
T = time to expiration of the options
C(K, T) = price of a European call with strike price K and time to expiration T.
P(K, T) = price of a European put with strike price K and time to expiration T.
F0,T = forward price for the underlying asset.
PV0,T = the present value over the life of the options.
e-rT*F0,T = prepaid forward price for the asset.
e-rT*K= prepaid forward price for the strike.
r = the continuously compounded interest rate.
Source: McDonald, R.L., Derivatives Markets (Second Edition), Addison Wesley, 2006, Ch. 9, p. 282.

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