Published on October 4, 2007
Put-Call Parity: Put-Call Parity Think Question??: Think Question?? Suppose the futures and options markets for May-07 KCBT Wheat are trading at the following prices: May-07 Wheat Futures: 505 cents May-07 Wheat 500 Call Option: 6 cents May-07 Wheat 500 Put Option: 4 cents Can you take a position in these markets to make a risk-free profit at expiration? Describe your position in each market and compute the expected profit at expiration of the options. Hint: your position will involve the futures, call and put market. Buy 300 Call Option for 6:Profit/Loss at Expiration: Buy 300 Call Option for 6: Profit/Loss at Expiration Sell 300 Put Option for 4:Profit/Loss at Expiration: Sell 300 Put Option for 4: Profit/Loss at Expiration Buy 300 Call Option for 6+ Sell 300 Put Option for 4:: Buy 300 Call Option for 6 + Sell 300 Put Option for 4: Buy 300 Call Option for 6+ Sell 300 Put Option for 4: Buy 300 Call Option for 6 + Sell 300 Put Option for 4 ‘Synthetic’ Long Futures Position at 302 502 = Strike + Call Prem – Put Prem Sell Futures at 305: Sell Futures at 305 Sell Futures at 305: Sell Futures at 305 Long (Synthetic) Futures at 302 Long Call + Short Put + Short Futures: Long Call + Short Put + Short Futures Guaranteed 3 Cent Profit PUT-CALL PARITY: PUT-CALL PARITY Call Premium – Put Premium = Futures Price – Strike Price Applies to calls and puts with the same strike price only. May-07 Wheat CBT OptionsMay Futures 487.5: May-07 Wheat CBT Options May Futures 487.5 Implication of Put-Call Parity: Implication of Put-Call Parity Any Two Positions Can Make A Third! EXAMPLES: Short Futures + Long Call = Long Put Long Futures + Long Put = Long Call Hedging Example 1: Hedging Example 1 Mar 1: Sell Sep-07 KCBT Wheat Futures @ 535 to hedge New-Crop Wheat Production Mar 31: Bullish Acreage Intentions Report Apr 1: Sep-07 Futures = 510 (+25 cent profit) Buy a 520 Call Option for 18 => Long a 520 Put at –7 premium Hedging Example 2: Hedging Example 2 Mar 1: Forward Contracted Grain Mar 31: Bullish Acreage Intentions Report Apr 1: Want to re-own the grain with a 500 Sep-03 Call Option (not traded) Buy a 500 Put for 14 Buy Futures at 510 =>Long a ‘Synthetic’ 500 Call @ ????? (C-P) = (F-S) Or, C = (F-S) + P = 24 cents Put-Call Parity Summary: Put-Call Parity Summary Guarantees No-Arbitrage Equilibrium Prices Between Calls, Puts and Futures Can Create a ‘Synthetic’ position from two other assets.