Problem 6 Consider pricing a European call option on a stock which pays continuous dividends at a rate per annum (continuously compounded). For example, if the stock is paying dividends continuously and the amount of dividends paid in a year to its holders is 13.89 with the current stock price equal to 100, then n is given by n = In (1 + 100) = 13%. We call this rate n as a continuous) dividend yield. (a) We use the binomial lattice technique to price the option. Since the dividends provide a return of n to its holders, the stock price itself must, on average, provide a return of r-n in a risk-neutral world. Hence we have, with the risk-neutral probability 4. [Sat) = 95, + (1 q)5 d = Selva), 3 where So is the initial stock price, r is the risk-free rate (assuming continuous compounding). At is the time step length, Sat is the stock price at the end of the first time step, and u and d are the up and down parameters. denotes the expected value in a risk-neutral world. Using this equation, first obtain the value of q and then compute the option price with the following parameter setting: So = $100,u = 1.08, d = 0.92, K(strike price) = $90, r = 6% (per annum with continuous compounding). T(option maturity) = 7 months, At = 1 month and n = 13%. (b) Repeat the same calculation in the context of an American call option. Problem 6 Consider pricing a European call option on a stock which pays continuous dividends at a rate per annum (continuously compounded). For example, if the stock is paying dividends continuously and the amount of dividends paid in a year to its holders is 13.89 with the current stock price equal to 100, then n is given by n = In (1 + 100) = 13%. We call this rate n as a continuous) dividend yield. (a) We use the binomial lattice technique to price the option. Since the dividends provide a return of n to its holders, the stock price itself must, on average, provide a return of r-n in a risk-neutral world. Hence we have, with the risk-neutral probability 4. [Sat) = 95, + (1 q)5 d = Selva), 3 where So is the initial stock price, r is the risk-free rate (assuming continuous compounding). At is the time step length, Sat is the stock price at the end of the first time step, and u and d are the up and down parameters. denotes the expected value in a risk-neutral world. Using this equation, first obtain the value of q and then compute the option price with the following parameter setting: So = $100,u = 1.08, d = 0.92, K(strike price) = $90, r = 6% (per annum with continuous compounding). T(option maturity) = 7 months, At = 1 month and n = 13%. (b) Repeat the same calculation in the context of an American call option