(a) Make use of an arbitrage argument to derive the put-call parity formula C+Ke
ID: 2788153 • Letter: #
Question
(a) Make use of an arbitrage argument to derive the put-call parity formula C+Ker(Tt) = P+X(t), relating the time t prices of a European call option C and a European put option P, both with the same expiry date T and the same strike price K, on an underlying asset whose current price is X(t). The risk-free interest rate is r. (a) Make use of an arbitrage argument to derive the put-call parity formula C+Ker(Tt) = P+X(t), relating the time t prices of a European call option C and a European put option P, both with the same expiry date T and the same strike price K, on an underlying asset whose current price is X(t). The risk-free interest rate is r. (a) Make use of an arbitrage argument to derive the put-call parity formula C+Ker(Tt) = P+X(t), relating the time t prices of a European call option C and a European put option P, both with the same expiry date T and the same strike price K, on an underlying asset whose current price is X(t). The risk-free interest rate is r.Explanation / Answer
Outcome at T
Protective put Put expire in Money Call expire in money
Asset Xt Xt
Long Put K- Xt 0
Total K Xt
Fiduciary call
Long call 0 Xt-K
Risk free bond K K
Total K Xt
When put in the money protective put=Fiduciary call=K
When Call in the money protective put=Fiduciary call=XT
If protective put not equal to fiduciary call arbitrager will create synthetic position and use arbitrage technique that is buy cheap sell high to bring price back where Protective put=fiduciary call
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.