36 lines
2.4 KiB
Plaintext
36 lines
2.4 KiB
Plaintext
864 Part VI: Measuring and Trading Volatility
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Example: With XYZ at 49, the strategist has the following position in February, so
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that the April calls are nearer to expiration than the July calls. This position is similar
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to a large calendar spread position.
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Option Position
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Position Theta Theta
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Short 4,000 XYZ 0.00 0
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Short 150 XYZ April 50 calls -0.04 +600
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Long 150 XYZ April 30 calls -0.02 -300
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Short 78 XYZ July 30 puts -0.02 +156
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Total Theta: +456
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This position is expected to make $456 per day due to time decay. Note that
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short options, whether puts or calls, have a positive position theta, while long options
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have a negative position theta. A negative position theta means the position has risk
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due to time, while a positive position theta means time is working for the position.
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RHO
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Rho is the name given to the price change of an option's value due to a change in
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interest rates. Recall that one of the components that contributes to an option's price
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is interest rates. As interest rates rise, call prices will rise, but put prices will fall. The
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opposite is true as well: As interest rates fall, call prices decline and put prices rise.
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Rho measures the amount by which these prices rise or fall.
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This behavior of puts and calls with respect to interest rates may not be imme
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diately obvious, but recall that the arbitrage that can be established with in-the
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money calls (the "interest play," discussed in Chapter 27 on arbitrage) demonstrates
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that arbitrageurs are willing to pay more for an in-the-money call as interest rates rise
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because they will be earning more interest on the stock that they sell short against
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that in-the-money call. Thus, rising interest rates cause call prices to increase.
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The opposite is true for puts: Rising interest rates cause put prices to decline.
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Again, an arbitrage can be used to demonstrate the point. Recall that in a reversal
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arbitrage, the arbitrageur is selling the stock and the put while buying the call. We
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have just demonstrated that, as interest rates rise, he is willing to pay more for the
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call since he can earn extra interest on the short sale of his stock. This automatically
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means that he will be willing to sell the put for less.
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Rho is expressed as a positive number for calls and a negative one for puts. Rho
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is smallest for deeply out-of-the-money options and is large for deeply-in-the-money
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options. It is larger for longer-tenn options and is nearly zero for very short-tenn |