41 lines
3.4 KiB
Plaintext
41 lines
3.4 KiB
Plaintext
483
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AN INTrOduCTION TO OPTIONS ON FuTureS
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investing the cash received and so is willing to accept less; the value of the options fall.
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However, in futures markets, part of the value of distant contracts in a carry market
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reflects the interest costs associated with owning the commodity. An increase in the
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interest rate might cause the futures price to increase, leading to the value of existing
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calls going up. The net effect on calls is ambiguous, but puts should decline in value
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with increasing interest rates, as the effects are reinforcing.
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■ Theoretical versus Actual Option Premiums
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There is a variety of mathematical models available that will indicate the theoretical “fair value” for an
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option, given specific information regarding the four factors detailed in the previous section. Theoret-
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ical values will approximate, but by no means coincide with, actual premiums.
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does the existence of
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such a discrepancy necessarily imply that the option is mispriced? definitely not. The model-implied
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premium will differ from the actual premium for two reasons:
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1. The model’s assumption regarding the mathematical relationship between option prices (premi-
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ums) and the factors that affect option prices may not accurately describe market behavior. This
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is always true because, to some extent, even the best option-pricing models are only theoretical
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approximations of true market behavior.
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2. The volatility figure used by an option-pricing model will normally differ somewhat from the
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market’s expectation of future volatility. This is a critical point that requires further elaboration.
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recall that although volatility is a crucial input in any option pricing formula, its value can
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only be estimated. The theoretical “fair value” of an option will depend on the specific choice of a
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volatility figure. Some of the factors that will influence the value of the volatility estimate are the
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length of the prior period used to estimate volatility, the time interval in which volatility is mea-
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sured, the weighting scheme (if any) used on the historical volatility data, and adjustments (if any)
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to reflect relevant influences (e.g., the recent trend in volatility). It should be clear that any specific
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volatility estimate will implicitly reflect a number of unavoidably arbitrary decisions.
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different
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assumptions regarding the best procedure for estimating future volatility from past volatility will
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yield different theoretical premium values. Thus, there is no such thing as a single, well-defined fair
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value for an option.
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All that any option pricing model can tell you is what the value of the option should be given
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the specific assumptions regarding expected volatility and the form of the mathematical relationship
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between option prices and the key factors affecting them. If a given mathematical model provides a
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close approximation of market behavior, a discrepancy between the theoretical value and the actual
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premium means the market expectation for volatility, called the implied volatility, differs from the
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historically based volatility estimate used in the model. The question of whether the volatility assump-
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tions of a specific pricing model provide more accurate estimates of actual volatility than the implied
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volatility figures (i.e., the future volatility suggested by actual premiums) can only be answered
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empirically. A bias toward buying “underpriced” options (relative to the theoretical model fair value) |