Garman–Kohlhagen

(a) Starting from M08's Black–Scholes formula with a continuous dividend yield, derive (11.28) by identifying the "dividend yield" of holding one US dollar. State the replicating portfolio for the call: how many dollars are held, and how many rupees are borrowed. (b) Using $S = 94.47$, $K = 94.50$, $\tau = 54/365$, $r_d = 5.75\%$, $r_f = 3.90\%$ (continuous) and $\sigma = 5\%$ (assumed), price the call and the put, and check put–call parity. (c) The exporter of Worked example 11.10 instead buys 750 December puts at this strike. Compute the premium in rupees and the floor on its rupee receipts per dollar, including the cost of carrying the premium to expiry. (d) A market maker who wrote those 750 puts hedges with December futures. Compute the futures delta of one put and the number of futures lots needed, and say whether the market maker buys or sells futures.