Tuesday, July 14, 2009

Vega Part Deux

In our first installment on Vega I reviewed the basics of implied volatility and its effects on option premiums. The key take away was:

As implied volatility rises, options become more expensive.
As implied volatility falls, options become less expensive.

Gaming volatility necessitates a basic understanding of how to measure implied volatility's effect on option premiums. The greek vega allows us to do just that, so today's post will focus on reviewing its basic nuances.

Here are links to other relevant posts on the greeks:

Vega is used to quantify or measure an option's sensitivity to a one point change in implied volatility.

Consider the affect of Vega on the following two positions on XYZ which is trading at $60 and has an implied volatility of 50%.

Long 60 Straddle
Long 60 call @ $3.00; Vega = +.20
Long 60 put @ $3.00; Vega = +.20
Net Debit = $6.00
Net Vega = +.40

Suppose IV increases from 50 to 55%. How much will our position increase in value? With a position Vega of +.40, we can expect our position to increase by $2.00 (.40 x 5).

Short 70-50 Strangle
Short 70 call @ $1.00; Vega = -.10
Short 50 put @ $1.00; Vega = -.10
Net Credit = $2.00
Net Vega = -.20

Suppose IV decreases from 50 to 45%. How much will our position increase in value? With a position vega of -.20, we can expect our position will increase by $1.00 (.20 x 5).

Vega is positive for long options and negative for short options

When you buy an option, you are essentially buying or going long volatility. A long option position is one that seeks volatility (both realized and implied). Think about the last time you bought a call option. Were you thinking, “Man, I hope this stock stays stagnant!” Or was it more along the lines of, “Boy, I hope this stock busts a move so I can make some money!” Odds are it was the latter. Why? Remember when you’re long an option you want it to be worth as much as possible at expiration. Thus, the more a stock moves the higher your chances for raking in profits. As option owners (long vega) we not only like to see a stock’s realized volatility pick up, we also like to see implied volatility increase because it increases the value of an option.

When you sell an option, you are essentially selling or going short volatility. A short option position is one that shuns volatility. As an option sellers (short vega) we usually want the option to expire worthless. What were your thoughts last time you shorted an OTM call or put option? You were probably hoping the stock would remain relatively quiet (i.e. exhibit low realized volatility). As realized and implied volatility diminish, the option value becomes worthless much quicker.

Vega is highest for long term options and lowest for short term options

If implied volatility doubles, which do you think it will affect more- an option that expires tomorrow or one that expires in a year? In other words, do you think implied volatility doubling has more ramifications for the underlying stock in the next day or over the next year? The obvious answer is over the next year. As such, long term options are more sensitive to changes in implied volatility than short term options.

Take a look at Goldman Sachs options below, focusing on the vega of each option. Currently GS is trading around $145 and we’re looking at the 145 strike call for 5 different expiration months (click to enlarge).


July is .05, Aug is .18, Oct is .28, Jan 2010 is .40, Jan 2011 is .67. A 1% increase in IV would increase the July option by $.05 and the Jan 2011 option by $.67- quite a difference!

Vega is highest for At-The-Money options and lowest for In-The-Money or Out-of-The-Money

Like Theta and Gamma, Vega also peaks in ATM options. Take a look at August options on GS below:

Vega peaks at .18 in the 145 strike which is ATM

So based on the previous two principles, buying a long term, ATM straddle (long call + long put) would be the purest long volatility bet. Conversely, shorting a long term, ATM straddle (short call + short put) would be the purest short volatility bet. Now, that's not to say it's the best way to play volatility, only the purest.

Vega is the same for calls and puts

For the same strike-same month call and put you’ll typically find that vega is the same for both options.

Tyler-

8 comments:

Jignesh said...

why vega theta and gamma highest at at the money ?

Tyler Craig said...

Jignesh,

Extrinsic Value peaks in ATM options (as far as I'm aware that's just the way it is). as such, ATM options have the most extrinsic value to lose due to time decay as well as changes in volatility (hence the higher Vega and Theta).

Gamma is the highest for ATM options because they possess a delta around 50. Delta ranges between 0 & 100, so options that are already close to 0 or 100 won't have a delta that changes as quickly as one that's right in the middle (50).

There may be other explanations out there, but those seem the most intuitive to me.

Jignesh said...

thanks but there is internsic value i have heard first time Extrinsic Value so please tell me which one is correct
bye

Tyler Craig said...

An options premium is comprised of 2 parts: Extrinsic & Intrinsic Value.
Intrinsic value is the amount an option is In the money. Extrinsic Value, sometimes called time value, is the amount you pay over and above intrinsic value.

For example, suppose stock XYZ is at $50 and the 45 strike call option is trading at $7.

Because the 45 call is $5 in the money, there is $5 (50-45) of intrinsic value. Because it is worth $7, it also has $2 of extrinsic value (7 - 5).

Jignesh said...

thanks

Jignesh said...

i have made one Excel files on Delat Gamma Vega and Theta on the basis of Nifty Option(Indian Stock Market Index) so i want to send u that file and some conclusion or suggestion on that small projects
can u help me?
for that i required your mail Address
bye

Tyler Craig said...

rtylercraig@comcast.net

Jignesh said...

hi
please check your mail and open the file in microsoft excel2007


thanks