Options on a dividend paying stock. Suppose that the stock index is currently at S0 = $100. The stock follows the process: dSt = Stdt + StdBt, where = 10% and = 20%. The risk free rate (continuously compounded) is r = 5% and this is constant. Suppose that the stock pays dividends continuously at the annualized rate of y = 4%.

Consider the call struck at K = $110 expiring in T = 1 year.

a) Find d1 and d2 in the appropriate version of Black Scholes equation?

b) ) Find the price of a call struck at K = $110 expiring in T = 1 year.

c) True or false, In this scenario the total expected return (due to capital gain and dividend) for investing in the stock will be approximately = 10%.

d) True or False: the risk-neutral expected stock price percent increase (i.e. the expected return due to capital gains: (EQ[S1] S0)/S0) will be approximately equal to rrf = 5%.

e)True or False: Say the current futures price for December 2023 Oil is F 12 4 = $60.80. Assuming the convergence of spot and futures prices, this means E Q 4 [S12] = $60.80.

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