Put-Call Parity for Options on Forwards

  • An option can be created for a forward contract.

  • Recall that at contract initiation a forward will have a value of zero.

  • European options on forwards will have the same price as European options on futures contracts; but American options on forwards will have a different price from American options on futures.

  • The payoff values for options on forwards are:

Call payoff = Max[0,ST-X]

Put payoff = Max [0,X-ST]

ST = Underlying's price at expiration

X = Strike price of option

  • Put-Call Parity for Options on Forwards:

p0 = c0 + ((X - F(0,T))/(1+rF)T)

  • p0 = Today's price for a European put on a futures contract

  • c0 = Today's price for a European call on a futures contract

  • X = The strike price

  • F(0,T) = Price at time "0" for a forward expiring at time "T"

  • X - F(0,T) = The face value in long position of a zero coupon bond

Excluding storage costs, F(0,T) can be substituted with the formula for pricing a forward: S0(1+rF)T

With the put call parity formula and forward pricing formula, investors can apply the put call parity relationship to exploit mispricings.

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