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Greek Lessons: Vega Explained

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Wrangling Vega and the Impact of Volatility on an Option

Greek V for Vega | Swan BlogThe volatil­i­ty of an option’s under­ly­ing asset is one of the major fac­tors in deter­min­ing the val­ue of that option. An option’s sen­si­tiv­i­ty to volatil­i­ty is known as “vega” and is one of the so-called “Greeks” that are used to deter­mine an option’s val­ue. Oth­er Greeks include delta, gam­ma, theta, and rho.
A sim­ple trick to remem­ber: “V” is for Volatil­i­ty and Vega.

 

In a recent blog post, we exam­ined how the impact of volatil­i­ty drag, or vari­ance drain, is the detri­men­tal impact that volatil­i­ty has upon a a buy-and-hold invest­ment and an investor’s long-term wealth. Gen­er­al­ly speak­ing, the more volatile the invest­ment and the longer the hold­ing peri­od, the more an investor’s wealth is adverse­ly impact­ed by volatil­i­ty.

But what impact does volatil­i­ty have on options?

In option pric­ing, volatil­i­ty takes on an entire­ly dif­fer­ent mean­ing. In fact, when it comes to under­stand­ing the impact that volatil­i­ty has on the price of an option, it might be use­ful to com­plete­ly set aside what one knows about volatility’s impact upon long-term, buy-and-hold invest­ing. The two are actu­al­ly sep­a­rate con­ver­sa­tions.

Impact of Volatil­i­ty on Option Pric­ing

Gen­er­al­ly speak­ing, the more volatile the under­ly­ing asset the more valu­able the option will be. Why? In most tra­di­tion­al schools of finance, volatil­i­ty is treat­ed as risk and some­thing to be avoid­ed.

Why is high­er volatil­i­ty asso­ci­at­ed with high­er option prices?

It is impor­tant to remem­ber that option pric­ing is all based upon prob­a­bil­i­ties.

Beyond ‘death and tax­es’, noth­ing is cer­tain to hap­pen; but the prob­a­bil­i­ty of some­thing hap­pen­ing or not will dri­ve an option’s val­ue.

In the fol­low­ing graph we see the return dis­tri­b­u­tion for three dif­fer­ent assets.

  • The red curve rep­re­sents an asset with a nor­mal dis­tri­b­u­tion.
  • The blue curve is an asset with low volatil­i­ty — the prob­a­bil­i­ty is that most of the prices will be rather close to the mean price.
  • Alter­na­tive­ly, the green curve rep­re­sents a high­ly volatile asset, where the price is quite unpre­dictable.

There is a rather large range of plau­si­ble out­comes.

Greek-Lesson-Vega-Explained-Different-Standard-Deviation-Curves-Swan-Blog

Source: www.lisashea.com, Swan Global Investments

Super­im­posed over these three dis­tri­b­u­tions is an orange straight line rep­re­sent­ing the strike price of an out-of-the-mon­ey call option. If the asset price exceeds the option’s call price, the option goes in-the-mon­ey and becomes worth some­thing. It could poten­tial­ly be worth a lot.

In the graph above we see how more volatile assets have a greater pos­si­bil­i­ty of their options going in-the-mon­ey. Nat­u­ral­ly it fol­lows that such options would be worth more. Of course volatil­i­ty will also impact the val­ue of put options in the same way; a more volatile asset’s put options will also be more valu­able.

So how does this then work out in the mar­ket­place? How do the prices that investors pay for options rec­on­cile against actu­al volatil­i­ty con­di­tions?

These ques­tions get to the crux of what is known as ‘volatil­i­ty har­vest­ing’ or pre­mi­um col­lec­tion strate­gies. These strate­gies seek to cap­i­tal­ize on the dif­fer­ence between implied volatil­i­ty (i.e., what mar­ket par­tic­i­pants are will­ing to pay for options) and real­ized volatil­i­ty (i.e., how mar­kets actu­al­ly fare after the fact).

In the fol­low­ing graph we see the his­toric rela­tion­ship between the two. More often than not mar­kets tend to over­es­ti­mate the amount of volatil­i­ty that will be in the mar­ket.

  • The blue line is the VIX, which is the implied volatil­i­ty of the mar­ket.
  • The red line is the actu­al, real­ized, after-the-fact volatil­i­ty.

The gap between implied and real­ized volatil­i­ty can be a source of prof­it if one sys­tem­at­i­cal­ly sells over­priced options and col­lects the pre­mi­um, and then buys them back at a low­er price at a lat­er date.

Greek-Lesson-Vega-Volatility-Spreads-Swan-Blog

Source: Bloomberg and SG Financial Engineering

Of course, this trade won’t always be prof­itable. There will be times when the mar­gin between implied and real­ized volatil­i­ty is small, lim­it­ing the prof­itabil­i­ty of the trade. Worse, there are times when the rela­tion­ship inverts and the real­ized volatil­i­ty is high­er than the implied volatil­i­ty, in which case a volatil­i­ty har­vest­ing strat­e­gy will most like­ly be unprof­itable. Those times are seen in the red, “neg­a­tive spread” areas of the above graph. But more often than not volatil­i­ty is over­priced and can be exploit­ed for prof­it.

Sys­tem­at­i­cal­ly col­lect­ing option pre­mi­um from the sale of short-term puts and calls is one of the three pri­ma­ry dri­vers of the Defined Risk Strat­e­gy. Along with a buy-and-hold equi­ty posi­tion and the down­side hedge, the pre­mi­um col­lec­tion piece rep­re­sents the mar­ket-neu­tral return com­po­nent of the DRS.

In a future blog post we will exam­ine the chal­lenges faced by those who try to prof­it from volatil­i­ty by uti­liz­ing VIX futures.

 

Marc Odo, Marc Odo, CFA®, CAIA®, CIPM®, CFP®, Director of Investment Solutions - Swan Global InvestmentsAbout the author: Marc Odo, CFA®, CAIA®, CIPM®, CFP®, Direc­tor of Invest­ment Solu­tions, is respon­si­ble for help­ing clients and prospects gain a detailed under­stand­ing of Swan’s Defined Risk Strat­e­gy, includ­ing how it fits into an over­all invest­ment strat­e­gy. For­mer­ly Marc was the Direc­tor of Research for 11 years at Zephyr Asso­ciates.

 

 

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By | 2017-08-17T17:15:36+00:00 February 2nd, 2017|Blog|Comments Off on Greek Lessons: Vega Explained