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# Understanding Options Vega

Alan Grigoletto
October 19, 2017
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###### Prior to understanding Vega, we need to quickly review option-pricing models.

The options pricing models are mathematical formulas that help investors and traders remove the guesswork from determining an options price. The models make some assumptions, primarily that stock prices are random and that only one of the option Greeks changes at a given time. The Black Scholes model developed in 1973 is the most well known of the options pricing models. Subsequent models have been developed over time to correct for some of the earlier inaccuracies of the model such as, the assumption of constant volatility, log-normal distributions and not accounting for early exercise in American-Style options and dividends. While models such as these help traders and investors in determining prices, it is important to understand that no model can completely replicate all of the factors determining an options price in the real world.

Vega is one of the five Greeks and it measures the changes in option pricing relative to changes in volatility. Greek speakers throughout Canada will note that there is no Greek letter Vega. K or Kappa is the correct letter for this measurement; however, options traders chose to use the term Vega as the V in Vega reminded them of Volatility.

Vega is the expected change in an options value with a 1% change in implied volatility. It is a positive amount for both puts and calls and represents the change in the cash amount of an option and is expressed in decimal form. An option with a Vega amount of .10 will rise or fall by that amount for each percentage point move in implied volatility, remembering that all other factors are held constant.

Even novice traders who have limited experience in trading options will likely have concluded that implied volatility has the greatest impact on the price of an option. It is likely they have witnessed an increase in the price of a call or put option without any change in the underlying price. In other situations, investors may have experienced being long a call option and had the underlying move up or down in price only to see the put option decrease in value. This is due to a decrease in implied volatility and its downward impact on the price of that option.

###### Let’s look at an example:

XYZ is currently trading at C\$41.40 a share
The November 42 call is trading at \$2.70
Volatility is 29%
The Vega amount is .10

Volatility up 1% to 30% then Call price=\$2.80
Volatility down 1% to 28% then Call price=\$2.70
Percentage change=3%
Vega impact is greatest in dollar amounts for at-the-money options than either in-the-money or out-of-the-money options.

Vega impact is greatest in percentage amounts for out-of-the-money options.

November 50 call is trading at .45
Volatility is 27%
Vega amount is .06

Volatility up 1% to 28% then Call price=.51
Volatility down 1% to 26% then Call price=.39
Percentage change=13%

The changes in implied volatility and therefore the Vega amount can change at anytime and can often be significant. As we approach expiry, the impact of Vega for all options declines. If we think about this rationally, it makes sense that longer-term options are subject to a greater period in which volatility can affect prices.

Investors can often be long and short options at the same time.
Looking at the table below we see how we can net these Vega amounts.

 Position Vega Position Vega Total Position Vega (VEGA X 100) Long 20 November 42.00 calls 0.10 2.00 200 Short 20 November 50.00 calls -0.06 -1.20 120 Net position Vega +80.00

Should implied volatility for XYZ options increase 1 percentage point then this portfolio could expect to see a profit of \$80.00

If the implied volatility decreased 1 percentage point then expect a loss of \$80.00

###### Some final thoughts:

An investor with a forecast for increasing implied volatility could place positions
that get long Vega. A straddle is an options strategy composed of equal amounts of long calls and puts at the at-the-money strike. The straddle would also benefit from a sharp move either up or down in the underlying. The expectation in this case is that implied volatility is at a very low level and that any increase in implied volatility will overcome the time decay (Theta) from being long both call and put options.

Alan Grigoletto

CEO

Grigoletto Financial Consulting

Alan Grigoletto is CEO of Grigoletto Financial Consulting. He is a business development expert for elite individuals and financial groups. He has authored financial articles of interest for the Canadian exchanges, broker dealer and advisory communities as well as having written and published educational materials for audiences in U.S., Italy and Canada. In his prior role he served as Vice President of the Options Clearing Corporation and head of education for the Options Industry Council. Preceding OIC, Mr. Grigoletto served as the Senior Vice President of Business Development and Marketing for the Boston Options Exchange (BOX). Before his stint at BOX, Mr. Grigoletto was a founding partner at the investment advisory firm of Chicago Analytic Capital Management. He has more than 35 years of expertise in trading and investments as an options market maker, stock specialist, institutional trader, portfolio manager and educator. Mr. Grigoletto was formerly the portfolio manager for both the S&P 500 and MidCap 400 portfolios at Hull Transaction Services, a market-neutral arbitrage fund. He has considerable expertise in portfolio risk management as well as strong analytical skills in equity and equity-related (derivative) instruments. Mr. Grigoletto received his degree in Finance from the University of Miami and has served as Chairman of the STA Derivatives Committee. In addition, He is a steering committee member for the Futures Industry Association, a regular guest speaker at universities, the Securities Exchange Commission, CFTC, House Financial Services Committee and IRS.

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