Vega of an option definition

Mathematically, vega is the first derivative of option price with respect to change in volatility. Since first derivatives are theoretically instantaneous rates of change, and since vega estimates the impact of a one percentage point change, there frequently will be rounding errors.

Vega answers this question:

Option greeks in LAVA

How option greeks look in option chain

Another result of the put-call parity concept is that vegas of calls and puts with the same underlying, strike, and expiration are equal.

According to put-call parity, there is a quantifiable relationship between the price of the underlying instrument and the prices of calls and puts with the same strike and same expiration.

Suppose, that we observe that the volatility of a certain security trades in a range between 20 percent and 34 percent. Furthermore, suppose that volatility is currently 32 percent, and we are considering selling the volatility.

Assume that we establish a position that has a position vega of -5.00; that is, for each one point increase in volatility (i.e., from 32 percent to 33 percent), we would lose $500. This assumes that -5.00 vega is worth $500, which it would be for any option whose unit of trading was $100 per point. If it were a futures option, however, with a larger unit of trading, then the volatility risk would be -5.00 times whatever the unit of trading was.

Vega is stated as a negative number here, indicating that a falling volatility would be profitable for the position, while a rising volatility would be harmful.

If we truly believe in our volatility trading range having a top of 34 percent, then our risk due to volatility is two points (from 32 percent to 34 percent), or $1,000.

If we are looking for volatility to decrease back to 27 percent, for example, which is the center of the volatility's past trading range, then we could make $2,500 ($500 times 5 points of volatility decrease, from 32 percent to 27 percent) if that happened.

Overall, then, this is a position that has $1,000 of risk and $2,500 of profit potential, as measured by the vega. Of course, as we know, other factors could influence the position, including the fact that implied volatility could trade to higher levels than previously seen. Nevertheless, this example shows that by using vega, we can measure the volatility risk of a position.

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