A collect-on-delivery call (COD) costs zero initially, with the payoff at expiration being 0 if S < K, and S – K – P if S ≥ K. The problem in valuing the option is to determine P, the amount the option-holder pays if the option is in-the-money at expiration. The premium P is determined once and for all when the option is created. Let S = $100, K = $100, r = 5%, σ = 20%, T – t = 1 year, and δ = 0. Value a European COD call option with the above inputs. (Hint: Recognize that you can construct the COD payoff by combining an ordinary call option and a cash-or-nothing call.)Compute delta and gamma for a COD option. (You may do this by computing the value of the option at slightly different prices and calculating delta and gamma directly, rather than by using a formula.) Consider different stock prices and times to expiration, in particular setting t close to T. How hard is it to hedge a COD option?

A collect-on-delivery call (COD) costs zero initially, with the payoff at expiration being 0 if S < K, and S – K – P if S ≥ K. The problem in valuing the option is to determine P, the amount the option-holder pays if the option is in-the-money at expiration. The premium P is determined once and for all when the option is created. Let S = $100, K = $100, r = 5%, σ = 20%, T – t = 1 year, and δ = 0.

Value a European COD call option with the above inputs. (Hint: Recognize that you can construct the COD payoff by combining an ordinary call option and a cash-or-nothing call.)
Compute delta and gamma for a COD option. (You may do this by computing the value of the option at slightly different prices and calculating delta and gamma directly, rather than by using a formula.) Consider different stock prices and times to expiration, in particular setting t close to T. 
How hard is it to hedge a COD option?