August 11th, 2007, 9:58 pm
Depends where your spot reference is. If your spot reference is close to the barrier, then the vega is higher for the shorter dated OT (the gamma is higher for this). The price of a OT is the discounted probability of hitting a certain level, and vega is the change in price for a change in vol. So with spot near the barrier, say the price of the 1mth OT is 30% and the 1yr OT is 75%. An increase in vol will increase both prices, but moreso for the shorter dated one as that has more spot convexity. If the price of the 1yr OT is already 75% (i.e. probability of hitting barrier = 75%), relatively how much more probable will an increase in vol make this? Not that much more. Whereas an increase in vol for the shorter dated OT could change the picture from a scenario that wasn't looking that probable to one where it is much more likely. With spot further away the longer dated OT has more vega than the shorter dated one using the same kind of intuition.