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