Consider a put option written on an underlying security that has a current value of $100 and has a volatility of 25% (i.e. .25).  The put has a strike price of $100 and expires in 1 year.  The risk-free rate is 3% (.03).    If the time to expiration is changed from 1 to 2 to 3 years, what happens to the value of vega (the change in the put value given a percentage point change in the volatility – say from 25% to 26%)? (Note: vega is defined in note N16 on page 8; see ).  What is the comparison of the change in vega (given a change from 1 to 2 to 3 years to expiration) if the strike price is $105 (relative to if the strike is $100)?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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Consider a put option written on an underlying security that has a current value of $100 and has a volatility of 25% (i.e. .25).  The put has a strike price of $100 and expires in 1 year.  The risk-free rate is 3% (.03). 

 

If the time to expiration is changed from 1 to 2 to 3 years, what happens to the value of vega (the change in the put value given a percentage point change in the volatility – say from 25% to 26%)? (Note: vega is defined in note N16 on page 8; see ).  What is the comparison of the change in vega (given a change from 1 to 2 to 3 years to expiration) if the strike price is $105 (relative to if the strike is $100)?

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