At time = 0, for a put option at exercise price (X) on a newly issued forward contact at FT (the forward price at time = 0), a portfolio with equal value could be constructed from being long in:
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Utilizing the basic put/call parity equation, we're looking for a portfolio that is equal to the portfolio mentioned in the stem (a put option). The put-call parity equation is c0 + (X – FT) / (1+R)T = p0. Since (X – FT) / (1+R) is actually just the present value of the bond at expiration, the relationship can be simplified to long call + long bond = put.
Put-call parity for options on forward contracts at the initiation of the option where the forward price at that time (time=0) is FT, can best be expressed as:
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Put call parity for stocks (with discrete time discounting) is c0 + X / (1 + R)T ? S0 = p0. Noting that for the forward contract on an asset with no underlying cash flows, S0 = FT / (1 + R)T, and substituting, we get c0 + (X ? FT) / (1 + R)T = p0.
Which of the following would have the same value at t = 0 as an at-the-money call option on a forward contract priced at FT (the forward price at time = 0)?
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Put-call parity for options on forward contracts is c0 + (X – FT) / (1+R)T = p0. Since X = FT for an at-the-money option, the put and the call have the same value for an at-the-money option.
Which of the following is a correct specification of put-call parity for options on futures?
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Begin with put-call parity for a stock, and substitute
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