4_Options_sol.pdf

Put call parity for european options 4 trading

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Put-Call parity for European options 4. Trading strategies involving options: 1. Synthetic forward 2. Synthetic Stock 3. Stock/Options Combinations 4. Spreads Fin330 27

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Put-Call Parity for European options l Consider two portfolios: l Portfolio A : a European call + a zero coupon bond that pays K at time T . l Portfolio B : a European put + a share of the stock. l Payoffs at maturity T : Fin330 28 S T >K S T <K Portfolio A: Call option Zero coupon bond Total Portfolio B: Put option Share Total
Put-Call Parity for European options l Consider two portfolios: l Portfolio A : a European call + a zero coupon bond that pays K at time T . l Portfolio B : a European put + a share of the stock. l Payoffs at maturity T : Fin330 29 S T >K S T <K Portfolio A: Call option S T – K 0 Zero coupon bond K K Total S T K Portfolio B: Put option 0 K – S T Share S T S T Total S T K

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Put-Call Parity for European options l Since the two portfolios have the same payoffs at T , they must cost the same at time 0 ! l Cost at time 0 : l Portfolio A: c + Ke -rT ; l Portfolio B: p + S 0 . l Therefore, we have: Fin330 30
Put-Call Parity for European options l What could investors do if: c + Ke -rT > p + S 0 l Buy portfolio B and sell portfolio A = Long a share + long put + borrow Ke -rT + sell call l Arbitrage opportunity of type “money today”. l What could investors do if: c + Ke -rT < p + S 0 Fin330 31

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Outline 1. Options: definition and payoffs 2. Factors affecting option prices 3. Put-Call parity for European options 4. Trading strategies involving options: 1. Synthetic forward 2. Synthetic Stock 3. Stock/Options Combinations 4. Spreads Fin330 32
l A synthetic (long) forward contract can be created by buying a call and selling a put on the same underlying asset, with each option having the same strike price and time to expiration. l What is the difference between the synthetic forward contract and a standard forward contract? Payoff at t=0 Payoff at t=T Synthetic Standard Payoffs K S T K S T + = K S T Creating Synthetic Forwards Fin330 33

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l A synthetic (long) forward contract can be created by buying a call and selling a put on the same underlying asset, with each option having the same strike price and time to expiration. l What is the difference between the synthetic forward contract and a standard forward contract? Payoff at t=0 Payoff at t=T Synthetic p – c S T – K Standard 0 S T – F 0 Creating Synthetic Forwards K Payoffs S T Long call K S T Short put K S T Long forward + = 34 Fin330
Creating Synthetic Forwards l Payoff (in PV terms) from the forward contract: PV(S T – F 0 ) = PV(S T ) – F 0 e -rT = PV(S T ) – S 0 l Payoff (in PV terms) from the synthetic forward contract: p – c + PV(S T – K) = p – c + PV(S T ) – Ke -rT l Equalize the payoffs and rearrange: p+S 0 = Ke -rT + c l Recognize the put-call parity! Fin330 35

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Outline 1.
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• Spring '16
• Chang
• Options, Strike price, put-call parity

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