Positive Vega, Negative Vega

Vega is a price change in options theoretical pricing models value for each one-percentage-point change in volatility. Since in the theoretical pricing model a rise in volatility positively affects both call and put, they are marked as positive. Note the delta gamma and theta sensitivities have different effects in the theoretical pricing model over the time passage and strike price relations. Vega is also sensitive to the passage of time and price strike relations. Based on B&S theory of options pricing model, a one percent increase in volatility will lead to an increase of in the options value. Why is that?

The answer lays in the probability of options to produce profit for the financial instrument’s volatility. Let us say that an financial instrument’s volatility is 15% and the price is $75.00; a probable (68%) expectation is that it will range from $63.75 (-15%) to $86.25 (+15%) in a given time interval.

What if the alleged instruments volatility rises to 20%? The probability of ranging the wider prices rises, and for that, people are willing to pay.

For example, a stock trades in the $55.00 range, with 20% volatility in a given time. Buying a $55.00 strike, put option contract, the probability gaining from the stock's price range is in a relatively high range from $44.00 to $66.00. Looking at the best-case scenario, at the end of the given time, the maximum buyers profit is $11.00, or (55 – 44 = 11). If the volatility rises to 30% the range has widened (from 38.5 to 71.5) and the best-case scenario changes from $11.00 profit to $16.50, or (55 - 38.5). Because of the probability to gain more money, the theoretical option-pricing model is pricing this option to be more expensive than the option with the lower volatility. At an ATM 30 days to expiration, 46% implied volatility, interest rate 4% and dividend rate 2%, the vega equals 4 (0.0399). This value means that for each positive one percent change in volatility, options value will increase by $4.00. The opposite is also truea negative one percent change will lead to a decrease of $4.00 in the options value.

For an ATM 175 days to expiration, 46% implied volatility, interest rate 4% and dividend rate 2%, vega equals to 9.4 (0.0936). This value means that for each positive one percent change in volatility, the option’s value will increase by $9.40. The opposite is also true a negative one percent change will lead to a decrease of $9.40 in the option’s value.

As you can see, the vega’s denomination hardly changes with a financial instrument’s fluctuations. As far as an option gets from expiration and as close to ATM it gets a higher denomination. The farther out of the money and closer to expiration, the lower becomes the vegas denomination.

Traders who are very familiar with vegas differences and have a better understanding of the volatility behaviours achieve greater financial success. As you can see, ATM vegas denomination contains high values, and as the price goes either in the money or out of the money, the vega’s denomination reduces.