Put-Call Parity

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Think Question??. Suppose the futures and options markets for May-10 KCBT Wheat are trading at the following prices:May-10 Wheat Futures:6.05May-10 Wheat 6.00 Call Option:40 centsMay-10 Wheat 6.00 Put Option:60 centsCan you take a position in these markets to make a risk-free profit at exp

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Put-Call Parity

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1. Put-Call Parity

2. Think Question?? Suppose the futures and options markets for May-10 KCBT Wheat are trading at the following prices: May-10 Wheat Futures: 6.05 May-10 Wheat 6.00 Call Option: 40 cents May-10 Wheat 6.00 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.

3. Buy 6.00 Call Option for .40: Profit/Loss at Expiration

4. Sell 6.00 Put Option for .60: Profit/Loss at Expiration

5. Buy 6.00 Call Option for .40

6. Buy 6.00 Call Option for .40 + Sell 6.00 Put Option for .60

7. Sell Futures at 6.05

8. Sell Futures at 6.05

9. Long Call + Short Put + Short Futures

10. PUT-CALL PARITY Call Premium Put Premium = Futures Price Strike Price Applies to calls and puts with the same strike price only.

11. May-08 Wheat KCBT Options May Futures 9.024 (1/10/08)

12. 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

13. Hedging Example 1 Mar 1: Sell Sep-10 KCBT Wheat Futures @ 6.05 to hedge New-Crop Wheat Production Mar 31: Bearish Acreage Intentions Report Apr 1: Sep-10 Futures = 5.80 (+25 cent profit) Buy a 5.80 Call Option for .48 => Long a 5.80 Put at .23 premium

14. Hedging Example 2 Mar 1: Forward Contracted Grain Mar 31: Bullish Acreage Intentions Report Apr 1: Want to re-own the grain with a 6.00 Sep-10 Call Option (not traded) Buy a 6.00 Put for .60 Buy (go long) Futures at 6.30 =>Long a Synthetic 6.00 Call @ ????? (C-P) = (F-S) Or, C = (F-S) + P = 30 cents

15. Put-Call Parity Summary Guarantees No-Arbitrage Equilibrium Prices Between Calls, Puts and Futures Can Create a Synthetic position from two other assets.

16. How are Options Prices Determined? There is a supply and a demand curve for options. Major suppliers offset options risks against each other using a large portfolio Agricultural options are a small part Commodities serve as an inflation hedge. Black-Scholes Option Pricing Formula

17. Black Scholes Option Pricing Calls = [F-S]*[N(F,S,T,v)]*[1-e-rT] Puts = [S-F]*[N(F,S,T,-v)]*[1-e-rT] r = risk-free interest rate T = time to expiration (number of days/365) v = the standard deviation of the futures price S = option strike price F = price of underlying futures contract As v increases, both options prices increase. As F, T and r increase or as S declines, calls more expensive and puts cheaper.

18. Options Pricing Imperfections The Assumptions are Incorrect The distribution is not normal (heavy tails) In the late 1990s, many fortunes lost The markets are thin Underlying smooth market conditions are false. Alternative models work a bit better. In actuality, financial firms shade prices, adding a cushion. This seems more art than science and is controlled by the firm.

19. Option Pricing for Hedgers Financial Firms are willing to supply options at a cost. Volatility is a key driver of willingness. Options markets are imperfect. Thin markets are expensive.

20. Dairy Options Pilot Program Subsidized Puts for Milk, Four Rounds High Subsidies (80% plus costs), Brokers closely consulted Brokers sold high dollar puts/quick fills Price Errors (|Actual Theory|) considered DOPP Puts quite expensive Used every (1000s) of trades

21. Average Pricing Errors for DOPP, Puts and Calls by Round

23. Some Brokers Had High Prices Hypothesis 1: Brokers are overcharging dairy producers Hypothesis 2: Dairy farmers have reduced incentives for low options prices, want quick fills, and are willing to have brokers fill puts at higher prices. Tests for repeat customers supports #2.

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