# Chapter 131 CHAPTER 13 Options on Futures In this chapter, we discuss option on futures contracts....

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### Transcript of Chapter 131 CHAPTER 13 Options on Futures In this chapter, we discuss option on futures contracts....

- Slide 1
- Chapter 131 CHAPTER 13 Options on Futures In this chapter, we discuss option on futures contracts. This chapter is organized into: 1. Characteristics of Options on Physicals and Options on Futures. 2. The Market for Options on Futures 3. Pricing of Options on Futures 4. Price Relationship Between Options on Physicals and Options on Futures 5. Put-Call Parity for Options on Futures 6. Options on Futures and Synthetic Futures 7. Risk Management with Options on Futures
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- Chapter 132 Characteristics of Options on Physicals and Options Futures Recall from Chapter 12 that options are written for a pre- specified amount of a pre-specified asset at a pre-specified price that can be bought or sold at a pre-specified time period. Call Options The buyer of a call option has the right but not the obligation to purchase. The seller of a call option has the obligation to sell. Put Options. The buyer of a put option has the right but not the obligation to sell. The seller of a put option has the obligation to purchase.
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- Chapter 133 Characteristics of Options on Physicals and Options Futures Prices of options on futures are closely related to prices of options on the underlying good. Call Option on Futures Upon exercising a option on futures, the call owner: Receives a long position in the underlying futures at the settlement price prevailing at the time of exercise. Receives a payment that equals the settlement price minus the exercise price of the option on futures. The call owner would not exercise if the futures settlement price did not exceed the exercise price. Upon exercise, the call seller: Receives a short position in the underlying futures at the settlement price prevailing at the time of exercise. Pays the long trader the futures settlement price minus the exercise price.
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- Chapter 134 Characteristics of Options on Physicals and Options Futures On February 1, a trader buys a call option on a MAR euro futures contract with an exercise price of $0.44 per euro. On February 15, the call owner decides to exercise the call option. The futures settlement price is $.48. After gathering all the information, the owner has: Future settlement price = $.48 The exercise price= $.44/euro The euro futures maturing= March Euro contract amount = 125,000 euros Upon exercise, the call owner: Receives a long position in the MAR euro futures contract. Receives a payment = F 0 E $.48 -.44 (125,000) = $5000 Upon exercise, the call seller: Receives a short position in the euro futures. Pay $5,000. The traders can offset or hold their futures positions.
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- Chapter 135 Characteristics of Options on Physicals and Options Futures Put Option on Futures Upon exercising a option on futures, the put owner: Receives a short position in the underlying futures contract at the settlement price prevailing at the time of exercise. Receives a payment that equals the exercise price minus the futures settlement price. The put owner would not exercise unless the exercise price exceeded the futures settlement price. Upon exercise, the put seller: Receives a long position in the underlying futures contract. Pays the exercise price minus the settlement price.
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- Chapter 136 Characteristics of Options on Physicals and Options Futures On April 1, a trader buys a put option on a MAY wheat futures contract. The exercise price is $2.40/bushel and wheat contract is for 5,000 bushels. On April 4, the owner of the call option decides to exercise. The futures settlement price is $2.32/bushel. Exercise price = $2.40/bushel Wheat contract = 5,000 bushels Futures settlement price = $2.32/bushel. The wheat futures matures= May Upon exercise, the put owner: Receives a short position MAY Wheat futures contract. Receives a payment = F 0 E $2.40-$2.32 (5,000) = $400 Upon exercise, the put seller: Receives a long position MAY Wheat futures contract. Pays $400. The traders can offset or hold their futures positions.
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- Chapter 137 Characteristics of Options on Physicals and Options Futures The following table summarizes the option examples discussed previously. The overall profitability of the transactions depends upon the original premium and the prices that become available before expiration of the option.
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- Chapter 138 The Market of Options on Futures Figure 13.1 presents some illustrative quotations for options on futures. Insert figure 13.1 here
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- Chapter 139 The Market of Options on Futures Table 13.1 shows the trading volume for options on futures by type of commodity in the fiscal year ending September 30, 1995.
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- Chapter 1310 The Market of Options on Futures
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- Chapter 1311 The Market of Options on Futures
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- Chapter 1312 The Market of Options on Futures
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- Chapter 1313 Pricing Options on Futures Recall from Chapter 12: European Options European options can be exercised only on the maturity date. American Options American options can be exercised any time prior to maturity. The Black-Scholes model focus best on European options which avoids problems with early exercise and dividends. When there is a dividend and the dividend rate varies, the Black-Scholes model is not suitable for valuing options on futures. The Black-Scholes model can be modified for forward option pricing.
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- Chapter 1314 Graphical Approach to American Options on Futures Figure 13.2 illustrates how European options prices are good approximations for American futures option prices Insert figure 13.2 here
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- Chapter 1315 Black-Scholes Model for Options on Forward Contracts The Black-Scholes equation for option on forward contracts is: Where r = risk-free rate of interest t = time until expiration for the forward and the option F 0,t = forward price for a contract expiring at time t = standard deviation of the forward contracts price If there were no uncertainty, N(d 1 *) and N(d 2 *) will equal 1 and the equation would simplify to: C f = e -rt [F 0,t - E]
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- Chapter 1316 European Versus American Option on Futures European Options Early exercise of an option on a non-dividend paying stock is not recommended: Recall that upon exercising, the call owner receives the intrinsic value (S E). Exercising a call discards the excess value of the option over and above S E. American Options Early exercise of a dividend paying futures option has benefits and costs Benefit: exercise provides an immediate payment of F E which can earn interest until expiration e rt [F - E]. Cost: sacrifice of option value over and above intrinsic value F E.
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- Chapter 1317 Approximating European and American Futures Option Values Table 13.2 compares the theoretical values for European and American options on futures. The table assumes that the option on futures expires in half a year and has an exercise price of $100. The risk-free rate of interest is 8% and the standard deviation of the percentage change in the futures price is 0.2.
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- Chapter 1318 Efficiency of The Option on Futures Market Most tests of efficiency examine whether market prices match the prices of a theoretical model. A test of market prices against a theoretical model is a joint test of the market's efficiency and the model's ability to correctly represent the price. The results of Whaleys test for efficiency are presented in Table 13.3. The differences between the theoretical and market price are significant here.
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- Chapter 1319 Efficiency of The Option on Futures Market Some of the studies summarized in Table 13.4 compare actual prices with Black model prices.
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- Chapter 1320 Price Relationship Between Options on Physicals and Options on Futures In this section, the pricing relationship between options on physicals and options on futures is considered, specifically for call options. The analysis is organized as follows: 1. European options 2. American options on underlying assets with no cash flow 3. American options on underlying assets with cash flow
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- Chapter 1321 Price Relationship Between Options on Physicals and Options on Futures The following assumption will be held for this analysis: 1. The options have the same expiration and exercise price. 2. The options are on the same underlying commodity. One option is on the commodity itself. One option is on the futures on the commodity.
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- Chapter 1322 European Options on Physicals and Futures Recall from Chapter 12 that at expiration a call option on the physical will be worth: S - E For European options on futures, exercise can occur only at expiration, so it must be that: F t,t - E = S t - E For European options the exercise value for options on physicals and options on futures is the same.
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- Chapter 1323 American Options on Physicals and Futures with No Underlying Cash Flows For American options, any difference in value between options on physicals and options on futures results from the early exercise privilege. Table 13.5 shows the exercise values that the option on the futures can have given the option on physicals in percentage terms. The risk-free rate is assumed to be 15% and the percentage change in the underlying assets is.25.
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