33 lines
1.8 KiB
Plaintext
33 lines
1.8 KiB
Plaintext
Chapter 37: How Volatility Affects Popular Strategies 751
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Stock Price July 50 call July 50 put Implied Volatility Put's Vega
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50 7.15 6.54 69% 0.10
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7.25 6.64 70% 0.10
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7.35 6.74 71% 0.10
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Thus, the put's vega is 0.10, too - the same as the call's vega was.
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In fact, it can be stated that a call and a put with the same terms have the same
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vega. To prove this, one need only refer to the arbitrage equation for a conversion. If
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the call increases in price and everything else remains equal - interest rates, stock
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price, and striking price - then the put price must increase by the same amount. A
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change in implied volatility will cause such a change in the call price, and a similar
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change in the put price. Hence, the vega of the put and the call must be the same.
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It is also important to know how the vega changes as other factors change, par
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ticularly as the stock price changes, or as time changes. The following examples con
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tain several tables that illustrate the behavior of vega in a typically fluctuating envi
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ronment.
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Example: In this case, let the stock price fluctuate while holding interest rate (5% ),
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implied volatility (70%), time (3 months), dividends (0), and the strike price (50) con
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stant. See Table 37-1.
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In these cases, vega drops when the stock price does, too, but it remains fairly
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constant if the stock rises. It is interesting to note, though, that in the real world,
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when the underlying drops in price especially if it does so quickly, in a panic mode
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- implied volatility can increase dramatically. Such an increase may be of great ben
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efit to a call holder, serving to mitigate his losses, perhaps. This concept will be dis
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cussed further later in this chapter.
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TABLE 37-1
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Implied Volatility Theoretical
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Stock Price July 50 Call Price Coll Price Vega
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30 70% 0.47 0.028
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40 2.62 0.073
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50 7.25 0.098
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60 14.07 0.092
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70 22.35 0.091 |