Question

In time 0, an investor takes a calendar spread by selling two-year European call option and buying three-year European call option. These two options have the same strike price of $80 and are for the same stock that pays no dividends. The two-year option sells for $5 and the three-year option sells for $7. Two years later, the stock price turns out to be $90. The risk-free rate is 2% per annum. What is the minimum of the profit from this strategy? (We assume that we sell the longer-term option in year two)

Answer 1

Enswer page:01 Given details strike price of two-year European call option=480 1 (selling) strike po price of Three-year European call option = $80 (beying) Two year option Sells - 45 Three year option sells - ¢ + stock price twins to = $90 risk free state = 20% (per annum given information, we have to calculate From the Required minimum from this strategy. of the profit total inflow and outflow First we have to calculate at t=0 and t= 2. For To from the given information we know strike police - $ 80 Sell one two yeary European call option = $5. Buy one three year european call option

page: 02 net cash So, at t=0, cash flow = & 2. flow = $2. that's From problem Strike parice = $ 90. $90 ts gureater than $ 80 Ewopean call option will be exercised and investor will suffer a loss $ 90- $ 80 - $10. one ewropean call option total loss = $10 investor is long in 3 year european call option the expfse one Чао мост поиз. now, we can find the value of option; {mor Co, st = (x{1+r)), st] where st stock price x → exercise parice ry risk free rate to time left for expiry = lyr. Substituting values

page-03 80 value of option = Max 0, 90- 18.) - Max Co, 90- 78.43134] value & option = 44.5686. if investor sell the 3 year european call option at the end of a years. he will receive - $11.5686 - Total cash flow at end of and year =) Gain from selling the 3 year european call option - loss from exercise the a year european call option 11,5686 -40 1,5686. Therefore, the total cash flows at t= o and t-a is - loss in t=0 t. Gain in t=2 = -2 + 1.5686 24-0.4314 > minimum porofit from this strategy No profit from this strategy i.e, Zero..