37 lines
2.7 KiB
Plaintext
37 lines
2.7 KiB
Plaintext
484
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A Complete Guide to the Futures mArket
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and selling “overpriced” options would be justified only if empirical evidence supported the conten-
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tion that, on balance, the model’s volatility assumptions proved to be better than implied volatility in
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predicting actual volatility levels.
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If a model’s volatility estimates were demonstrated to be superior to implied volatility estimates,
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it would suggest, from a strict probability standpoint, a bullish trader would be better off selling puts
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than buying calls if options were overpriced (based on the fair value figures indicated by the model),
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and buying calls rather than selling puts if options were underpriced. Similarly, a bearish trader would
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be better off selling calls than buying puts if options were overpriced, and buying puts rather than
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selling calls if options were underpriced. The best strategy for any individual trader, however, would
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depend on the specific profile of his price expectations (i.e., the probabilities the trader assigns to
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various price outcomes).
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■ Delta (the Neutral Hedge Ratio)
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Delta, also called the neutral hedge ratio, is the expected change in the option price given a one-unit
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change in the price of the underlying futures contract. For example, if the delta of an August gold
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call option is 0.25, it means that a $1 change in the price of August futures can be expected to result
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in a $0.25 change in the option premium. Thus, the delta value for a given option can be used to
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determine the number of options that would be equivalent in risk to a single futures contract for small
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changes in price. It should be stressed that delta will change rapidly as prices change. Thus, the delta
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value cannot be used to compare the relative risk of options versus futures for large price changes.
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Table 34.3 illustrates the estimated delta values for out-of-the-money, at-the-money, and in-the-
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money call options for a range of times to expiration. Where did these values come from? They are
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derived from the same mathematical models used to determine a theoretical value for an option pre-
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mium given the relationship between the strike price and the current price of futures, time remaining
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table 34.3 Change in the premium of an e-Mini S&p 500 Call Option for 20.00 ($1000) Move in the
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Underlying Futures Contracta
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Increase in the 2000 call option premium if the futures price rises:
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From 1900 to 1920 From 2000 to 2020 From 2100 to 2120
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Time to expiration $ Delta $ Delta $ Delta
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1 week $10 0.01 $500 0.5 $1,000 1
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1 month $120 0.12 $510 0.51 $870 0.87
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3 months $260 0.26 $510 0.51 $750 0.75
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6 months $330 0.33 $520 0.52 $690 0.69
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12 months $390 0.39 $520 0.52 $650 0.65
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aAssumed volatility: 15 percent; assumed interest rate: 2 percent per year.
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Source: CMe Group (www .cmegroup.com). |