Doubt about greeks

Hi all,

I am Aneesh, relatively new this group. I have been reading about derivatives and their pricing. I had a question regarding the greeks. It is about the function "Vega" which is the ratio of change in the option price to the change in volatality of the underlying asset.

They say that "Vega of the underlying asset is zero". why ??

TO make a portfolio, "vega neutral", one needs to add a derivative to the portfolio so as to change the vega. Vega neutarl cannot be achieved by going long or short on the underlying asset.

Can someone explain this...Thanks a lot.

cheers,
Aneesh

The underlying asset's payoff doesn't vary depending on how its price moves (payoff is not contingent). Therefore, its price is not affected by price volatility (this is true only in a strict sense; in reality it may very well be affected).

To add on to the last response, think of it this way. During earnings season quite often we'll see option premiums start to rise in expectation of a big move based upon say a good earnings report. The underlying asset does not move just yet though. So the expectation (implied volatility rising) of an upcomming move means traders have to pay more for the option. If the move happens but Implied Volatility gets sucked out, you might see an underlying move but the option not move quite as much because the premiums came back down.

Vega neutral in my mind refers more to when your buying an option and your worried about paying high premiums due to Implied Vol higher, if one sells and option that also has a "inflated" premium, then if implied volatility crashes the trader both wins on the short position and losses on the long position thus more vega neutral.

As pointed out by maringhoul though, quite often a stock can move higher or lower in anticipation before returning- but just thinking about options...thats my take.

hope that helps

Thanks a lot guys for the reply...

I seem to understand that since the payoff of the underlying asset is not a contingent claim, it might not be affected by its own volatility and hence its vega is zero...

So stock options will be affected by volatility but not the underlying stock..

But if the underlying asset is not a stock and is maybe a bond or a futures..say we consider bond options or options on futures, then will the case be different ?? since now, the underlying asset's payoff becomes a contingent claim (I suppose ??)....

Look at it this way. Whatever you are thinking of, stock or option, would its value be affected if it were more volatile and why?

If I take a stock at a price of 100. It doesn't matter how volatile that stock is, its price is 100. You could have two stocks, one extremely volatile, and one extremely placid both at a price of 100. Volatility doesn't affect the value, and why should it?

But if I have a call option with strike 100, and the spot price now is 50, then volatility becomes important. Because if it is an option on a highly volatile stock, there is a chance it could move from 50 to above 100, and I could get a payoff. but if the volatility is next to nil, then there is very little chance of it getting above 100 and receiving a payoff, hence the value is near to zero.

aneesh.82 said:

Thanks a lot guys for the reply...

I seem to understand that since the payoff of the underlying asset is not a contingent claim, it might not be affected by its own volatility and hence its vega is zero...

So stock options will be affected by volatility but not the underlying stock..

But if the underlying asset is not a stock and is maybe a bond or a futures..say we consider bond options or options on futures, then will the case be different ?? since now, the underlying asset's payoff becomes a contingent claim (I suppose ??)....

Click to expand...

In practice, you would always assume that, for 'normal' options, the underlying, whatever it might be, is NOT a contingent claim. So in your case if it's a bond option or a futures option, it's going to assume that the prices for the underlying are independent of volatility.

Note that, in reality, this is a reasonable simplification to make things computationally tractable (pricing options on options is a real b1tch). Since bonds, in fact, have some convexity, their prices, strictly speaking, have some dependency on vol, but it's reasonably small. As a result, these phenomena are normally ignored for the sake of efficiency.

Also remember that Vega, like delta, needs to be dynamically hedged in order to maintain neutrality in an options portfolio. So to say a portfolio is vega neutral really usually means to say that a portfolio is vega neutral at the current point in space and time.