a)Youdecide to protect your futures position by buying call options on the Index at a strike price of 3,700. Using the level of the S&P 500 Index as the X-axis and your profit or loss as theY-axis,graph (i) the payout profile of that callat expirationand (ii) the combination of the short position and the call. Indicate the point along the X-axis at which you would break even with this combination. (10points)

b)In order to subsidize the cost of the call option struck at 3,700, you decide to sell a call at 3,760. Graph the payout profileat expirationof this new combination of (i) short position plus (ii) call purchased at 3,700, and (iii) call sold at 3,760. Indicate the point along the X- axis at which you would break even with this combination. (8points)

c)Briefly describe the pattern of implied volatility assumptions being used by traders to price these Index options.Wouldyou characterize this pattern as a "smile", a "frown", or a "sneer" (and, yes, traders do use these monikers as descriptions of implied volatility curves)? Why might this pattern of implied volatilites exist? (5points)