35 lines
2.6 KiB
Plaintext
35 lines
2.6 KiB
Plaintext
750 Part VI: Measuring and Trading Volatility
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of how volatility affects option positions will be in plain English as well as in the more
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mathematical realm of vega. Having said that, let's define vega so that it is understood
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for later use in the chapter.
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Simply stated, vega is the amount by which an option's price changes when
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volatility changes by one percentage point.
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Example: XYZ is selling at 50, and the July 50 call is trading at 7.25. Assume that
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there is no dividend, that short-term interest rates are 5%, and that July expiration is
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exactly three months away. With this information, one can determine that the implied
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volatility of the July 50 call is 70%. That's a fairly high number, so one can surmise
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that XYZ is a volatile stock. What would the option price be if implied volatility were
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rise to 71 %? Using a model, one can determine that the July 50 call would theoreti
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cally be worth 7.35 if that happened. Hence, the vega of this option is 0.10 (to two
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decimal places). That is, the option price increased by 10 cents, from 7.25 to 7.35,
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when volatility rose by one percentage point. (Note that "percentage point" here
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means a full point increase in volatility, from 70% to 71 %.)
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What if implied volatility had decreased instead? Once again, one can use the
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model to determine the change in the option price. In this case, using an implied
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volatility of 69% and keeping everything else the same, the option would then theo
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retically be worth 7.15- again, a 0.10 change in price (this time, a decrease in price).
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This example points out an interesting and important aspect of how volatility
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affects a call option: If implied volatility increases, the price of the option will
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increase, and if implied volatility decreases, the price of the option will decrease.
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Thus, there is a direct relationship between an option's price and its implied volatili-
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ty.
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Mathematically speaking, vega is the partial derivative of the Black-Scholes
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model (or whatever model you're using to price options) with respect to volatility. In
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the above example, the vega of the July 50 call, with XYZ at 50, can be computed to
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be 0.098 - very near the value of 0.10 that one arrived at by inspection.
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Vega also has a direct relationship with the price of a put. That is, as implied
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volatility rises, the price of a put will rise as well.
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Example: Using the same criteria as in the last example, suppose that XYZ is trading
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at 50, that July is three months away, that short-term interest rates are 5%, and that
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there is no dividend. In that case, the following theoretical put and call prices would
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apply at the stated implied volatilities: |