a) On p. 50 of Options, Futures and Other Derivatives by Hull the presence of competitors that do not hedge is stated as one of the arguments against hedging. Based on the literature on corporate risk management in the presence of product market interactions present a simple model which illustrates that a firm will indeed be better off by not hedging when its competitors do not hedge either.
(30 marks)
b) Based on the same stream of literature evaluate critically the above argument. What assumptions are required to obtain such an outcome (i.e., that hedging is not optimal if competitors do not hedge)? Are there any models that demonstrate that hedging actually is optimal in the presence of competitive interactions? If so, reconcile the findings of those models with the answer to part (a).
(20 marks)

Question 2
a) The Black-Scholes-Merton (BSM) formula for pricing European call options on a non- dividend paying stock is given by equation (14.20) in Options, Futures and Other Deriva- tives by Hull. Provide an interpretation (as precise as possible) of its first and the second component (i.e., S0N(d1) and Ke rTN(d2), respectively). How can we interpret coef- ficients N(d1) and N(d2)? Calculate the limits of the formula in four special cases: i) S0 ! 1, ii) S0 ! 0, iii) ! 1, and iv) ! 0. Verify whether your interpretations of S0N(d1), Ke rT N(d2), N(d1) and N(d2) still make sense in each of the cases i)–iv).
(30 marks)
b) One of the early firm value-based models of credit risk, Merton model, is based on the BSM option pricing formula. In Merton model, the value of the firm’s equity E is a call option on the firm’s assets V with the exercise price equal to the face value of debt F. In other words, E, V and F correspond to c, S0, and K in the notation of equation (14.20). The value of corporate debt, D = V E, is therefore equal to V N( d1) + Fe rT N(d2). Using the insights from your answer to part (a), interpret both components of the formula for the debt value (i.e., VN( d1) and Fe rTN(d2)) as well as (re-)interpret coefficients N( d1) and N(d2). Next to providing interpretations in a general case, consider the same four special cases as in part (a).