27 lines
1.7 KiB
Plaintext
27 lines
1.7 KiB
Plaintext
the greater the effect of interest. Rho measures an option’s sensitivity to the
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end results of these three influences.
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To understand how changes in interest affect option prices, consider a
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typical at-the-money (ATM) conversion on a non-dividend-paying stock.
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Short 1 May 50 call at 1.92
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Long 1 May 50 put at 1.63
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Long 100 shares at $50
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With 43 days until expiration at a 5 percent interest rate, the interest on
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the 50 strike will be about $0.29. Put-call parity ensures that this $0.29
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shows up in option prices. After rearranging the equation, we get
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In this example, both options are exactly ATM. There is no intrinsic value.
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Therefore, the difference between the extrinsic values of the call and the put
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must equal interest. If one option were in-the-money (ITM), the intrinsic
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value on the left side of the equation would be offset by the Stock − Strike
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on the right side. Still, it would be the difference in the time value of the
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call and put that equals the interest variable.
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This is shown by the fact that the synthetic stock portion of the
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conversion is short at $50.29 (call − put + strike). This is $0.29 above the
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stock price. The synthetic stock equals the Stock + Interest, or
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Certainly, if the interest rate were higher, the interest on the synthetic
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stock would be a higher number. At a 6 percent interest rate, the effective
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short price of the synthetic stock would be about $50.35. The call would be
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valued at about 1.95, and the put would be 1.60—a net of $0.35.
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A one-percentage-point rise in the interest rate causes the synthetic stock
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position to be revalued by $0.06—a $0.03 gain in the call value and a $0.03
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decline in the put. Therefore, by definition, the call has a +0.03 rho and the
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put has a −0.03 rho. |