You observe two call options on the same stock that appear to be relatively mispriced. Call ABC sells for $3.50, has a strike price of X = 50, and an implied volatility from the Black-Scholes model of 30%. Call XYZ sells for $.75, has a strike price of X = 60, and an implied volatility of 25%. You wish to do a delta-neutral position on these options that will exploit the apparent inconsistency in implied volatilities.

a.

Suppose you believe that the Black-Scholes model is the correct model for valuing options. Which option will you buy? Which will you sell?

b.

If you buy and sell equal numbers of the two options, will your portfolio be delta neutral?

If not, which option will require a bigger position (i.e., a purchase or sale of a greater number of contracts) to establish a delta-neutral portfolio?