2. Consider a non-dividend-paying stock whose current price S(0) = S is $45. After each period...

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2. Consider a non-dividend-paying stock whose current price S(0) = S is $45. After each period there is a 25% chance that the stock price goes up by 25%, 35% chance that the stock price stays the same, and 40% chance that the stock price drops by 20%. Current risk-free interest rate is 7.2% per annum, compounded monthly. Count a month as one period. (a) Find risk-neutral probabilities q1. q2, and qs that make the expectation of any unit stock (a stock valued at $1) after one period (1+r) where r, is the risk-free rate per period, and the standard deviation 0.2. (In other words, find q, 2, and qs such that E[X] = (1+r,) and Var(X) = 0.04 where X is the random variable that represents the unit stock price after one period). (b) Use the above risk-neutral probabilities and a trinomial lattice tree to caleulate the current (t = 0) price of a Europenn call option on the above stock that has strike $49 and expires in four months. (e) Use any method you like to find the current price of a European put option that has the same conditions as the call option in part (b). 2. Consider a non-dividend-paying stock whose current price S(0) = S is $45. After each period there is a 25% chance that the stock price goes up by 25%, 35% chance that the stock price stays the same, and 40% chance that the stock price drops by 20%. Current risk-free interest rate is 7.2% per annum, compounded monthly. Count a month as one period. (a) Find risk-neutral probabilities q1. q2, and qs that make the expectation of any unit stock (a stock valued at $1) after one period (1+r) where r, is the risk-free rate per period, and the standard deviation 0.2. (In other words, find q, 2, and qs such that E[X] = (1+r,) and Var(X) = 0.04 where X is the random variable that represents the unit stock price after one period). (b) Use the above risk-neutral probabilities and a trinomial lattice tree to caleulate the current (t = 0) price of a Europenn call option on the above stock that has strike $49 and expires in four months. (e) Use any method you like to find the current price of a European put option that has the same conditions as the call option in part (b).

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