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766 Part VI: Measuring and Trading Volatility
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(2) Put TVP = Put price - Strike price + Stock price
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The arbitrage equation, (1), can be rewritten as:
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(3) Put price - Strike price+ Stock price= Call price+ Dividends - Carrying cost
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and substituting equation (2) for the terms in equation (3), one arrives at:
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( 4) Put TVP = Call price + Dividends - Carrying cost
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In other words, the time value premium of an in-the-money put is the same as the
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(out-of-the-money) call price, plus any dividends to be ea med until expiration, less
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any carrying costs over that same time period.
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Assuming that the dividend is small or zero (as it is for most stocks), one can see
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that an in-the-money put would lose its time value premium whenever carrying costs
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exceed the value of the out-of-the-money call. Since these carrying costs can be rel
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atively large ( the carrying cost is the interest being paid on the entire debit of the
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position - and that debit is approximately equal to the strike price), they can quickly
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dominate the price of an out-of-the-money call. Hence, the time value premium of
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an in-the-money put disappears rather quickly.
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This is important information for put option buyers, because they must under
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stand that a put won't appreciate in value as much as one might expect, even when
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the stock drops, since the put loses its time value premium quickly. It's even more
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important information for put sellers: A short put is at risk of assignment as soon as
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there is no time value premium left in the put. Thus, a put can be assigned well in
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advance of expiration even a LEAPS put!
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Now, returning to the main topic of how implied volatility affects a position, one
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can ask himself how an increase or decrease in implied volatility would affect equa
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tion ( 4) above. If implied volatility increases, the call price would increase, and if the
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increase were great enough, might impart some time value premium to the put.
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Hence, an increase in implied volatility also may increase the price of a put, but if the
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put is too far in-the-nwney, a modest increase in implied volatility still won't budge
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the put. That is, an increase in implied volatility would increase the value of the call,
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but until it increases enough to be greater than the carrying costs, an in-the-money
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put will remain at parity, and thus a short put would still remain at risk of assignment.
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STRADDLE OR STRANGLE BUYING AND SELLING
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Since owning a straddle involves owning both a put and a call with the same terms,
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it is fairly evident that an increase in implied volatility will be very beneficial for a
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straddle buyer. A sort of double benefit occurs if implied volatility rises, for it will
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