Comparing Vega of options across strikes and time

Quantitative Finance Level 1

When the stock is trading at 100, which of the following options have the largest vega?

Call on the 100 strike with 1 month to expiry Call on the 80 strike with 1 months to expiry Call on the 80 strike with 3 months to expiry Call on the 100 strike with 3 months to expiry

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Calvin Lin by Calvin Lin

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1 solution

Vega ν = ∂ V ∂ σ \nu = \dfrac {\partial V} {\partial \sigma} measures the sensitivity to volatility. Therefore, the higher the strike price and and further away from the expiry date, the higher the vega. Therefore, the answer is: Call on the 100 strike with 3 months to expire. \boxed{\text{Call on the 100 strike with 3 months to expire.}}

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How did you arrive at the conclusions of "Therefore, ..."?

Are you sure sure "the higher the strike price, the higher the vega"? IE Does the call on the 1000 strike with 3 months to expiry have a higher vega?

Calvin Lin Staff - 6 years, 3 months ago

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I am assuming higher strike price has a larger range to swing.

Chew-Seong Cheong - 6 years, 3 months ago

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That is a false assumption. For a strike that is very far away, there is hardly an extrinsic value to it. Vega, which is the rate of change of option price with respect to volatility, would thus not be high, if the option price itself isn't high.

Calvin Lin Staff - 6 years, 3 months ago

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@Calvin Lin – Thanks, Calvin. I have much to learn. As far as I know there isn't option trading in Asia. Well, I haven't been active in financial market.

Chew-Seong Cheong - 6 years, 3 months ago

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@Chew-Seong Cheong – Check out the Vega wiki page. I've been spending time writing up these pages, and hence reduced the number of questions.

Singapore wants to build up the options trading market, but there isn't enough liquidity / trading activity to make it worthwhile as yet. It will take them a while to get there, but that have already been attracting firms in for the past few years.

Calvin Lin Staff - 6 years, 3 months ago

In fact : first we know that as the strike is close to the stock price (100$) the vega gets more value in the ATM zone , so to get large vega we choose the strike the most close the stock price. secondly, as vega is large when time to expiry is large: we choose the largest time to expiry ( 3 months) in order to get the largest vega

Ferhati Tahar - 1 year, 8 months ago

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