If a customer wishes to buy a 91-day call option, the market-maker ?lls this order by selling a call option. To be speci?c, suppose that S = $40, K = $40, ? = 0.30, r = 0.08 (continuously compounded), and dividend yield = 0. We will let T denote the expiration time of the option and t the present, so time to expiration is T ?t. Let T ?t = 91/365.

Daily pro?t calculation over 5 days for a market-maker who deltahedges a written option on 100 shares. To hedge this position, the market-maker can buy delta shares to delta-hedge the position. We now will consider the risk of a delta-hedged position by assuming that the market-maker delta-hedges and marks-to-market daily. Fill the blanks for Day 1 to Day 5.

Day 0Day Day 2 Day 3 Day 4 Day 5 40.00 40.5039.2538.75 40.0040.00 2.78043.0621 2.3282 2.0546 2.7104 2.6927 0.58240.6142 0.5311 0.49560.58060.5801 stock(S) Call price Cashflows from calls() 278.04 100 ? Cashflows from Shares() 2,329.62 investment($) interest(S) gains on stock (S) 58.24 2,051.58 gains on written calls (S daily profit(S) 0 Day 0Day Day 2 Day 3 Day 4 Day 5 40.00 40.5039.2538.75 40.0040.00 2.78043.0621 2.3282 2.0546 2.7104 2.6927 0.58240.6142 0.5311 0.49560.58060.5801 stock(S) Call price Cashflows from calls() 278.04 100 ? Cashflows from Shares() 2,329.62 investment($) interest(S) gains on stock (S) 58.24 2,051.58 gains on written calls (S daily profit(S) 0