PutCall Parity

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Put-Call Parity
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Think Question??

• Suppose the futures and options markets for
  May-08 KCBT Wheat are trading at the following
  prices
• May-07 Wheat Futures 9.05
• May-07 Wheat 9.00 Call Option 40 cents
• May-07 Wheat 9.00 Put Option 60 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.

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Buy 9.00 Call Option for .40Profit/Loss at
Expiration
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Sell 9.00 Put Option for .60Profit/Loss at
Expiration
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Buy 9.00 Call Option for .40
Sell 9.00 Put Option for .60
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Buy 9.00 Call Option for .40 Sell 9.00 Put
Option for .60
Synthetic Long Futures Position at 8.80
8.80 Strike Call Prem
Put Prem
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Sell Futures at 9.05
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Sell Futures at 9.05
Long (Synthetic) Futures at 8.80
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Long Call Short Put Short Futures
Guaranteed 25 Cent Profit
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PUT-CALL PARITY

• Call Premium Put Premium
• Futures Price Strike Price
• Applies to calls and puts with the same strike
  price only.

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May-08 Wheat KCBT OptionsMay Futures 9.024
(1/10/08)
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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

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Hedging Example 1

• Mar 1 Sell Sep-08 KCBT Wheat Futures _at_ 8.35 to
  hedge New-Crop Wheat Production
• Mar 31 Bearish Acreage Intentions Report
• Apr 1 Sep-08 Futures 8.10 (25 cent profit)
• Buy a 8.20 Call Option for .48
• gt Long a 8.20 Put at .23 premium

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Hedging Example 2

• Mar 1 Forward Contracted Grain
• Mar 31 Bullish Acreage Intentions Report
• Apr 1 Want to re-own the grain with a 9.00
  Sep-08 Call Option (not traded)
• Buy a 9.00 Put for .60
• Buy (go long) Futures at 9.10
• gtLong a Synthetic 9.00 Call _at_ ?????
• (C-P) (F-S)
• Or, C (F-S) P 70 cents

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Put-Call Parity Summary

• Guarantees No-Arbitrage Equilibrium Prices
  Between Calls, Puts and Futures
• Can Create a Synthetic position from two other
  assets.