26 lines
1.5 KiB
Plaintext
26 lines
1.5 KiB
Plaintext
Rho and Interest Rates
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Rho is a measurement of the sensitivity of an option’s value to a change in
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the interest rate. To understand how and why the interest rate is important to
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the value of an option, recall the formula for put-call parity stated in
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Chapter 6.
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Call + Strike − Interest = Put + Stock 1
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From this formula, it’s clear that as the interest rate rises, put prices must
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fall and call prices must rise to keep put-call parity balanced. With a little
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algebra, the equation can be restated to better illustrate this concept:
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and
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If interest rates fall,
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and
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Rho helps quantify this relationship. Calls have positive rho, and puts
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have negative rho. For example, a call with a rho of +0.08 will gain $0.08
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with each one-percentage-point rise in interest rates and fall $0.08 with
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each one-percentage-point fall in interest rates. A put with a rho of −0.08
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will lose $0.08 with each one-point rise and gain $0.08 in value with a one-
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point fall.
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The effect of changes in the interest variable of put-call parity on call and
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put values is contingent on three factors: the strike price, the interest rate,
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and the number of days until expiration.
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Interest = Strike×Interest Rate×(Days to Expiration/365) 2
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Interest, for our purposes, is a function of the strike price. The higher the
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strike price, the greater the interest and, consequently the more changes in
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the interest rate will affect the option. The higher the interest rate is, the
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higher the interest variable will be. Likewise, the more time to expiration, |