The current market price of a stock is 45.5. Over the next two quarters, this stock...

 

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The current market price of a stock is 45.5. Over the next two quarters, this stock is projected to either increase by 7% or decrease by 6% each period, as per a binomial lattice model. The risk-free interest rate is 6.1% per annum, with continuous compounding. (a) Calculate the price of a 6-month European call option on this non-dividend-paying stock with an exercise price of 46.5. (b) Calculate the price of a 6-month European put option on the same non-dividend-paying stock with an exercise price of 46.5. (c) Ensure that the calculated prices from (a) and (b) are consistent with the put-call parity relationship. (d) In the given market model, an investment bank has introduced an Asian call option that accounts for the full history of the stock's value. The payoff for this option is: ({S_n}^n=0,...,N) = max{ (1/(N+1)) * sum(S_n from n=0 to N) - K, 0}, where N is the total number of periods in the market model. Determine the initial price of the Asian call option with an exercise price of 46.5 at time t = 0. Hint: Apply a similar pricing strategy as used for the European call and put options, but with more precision. The value of the option at the final interval's midpoint (i.e., S_2(ud) or S_2(du)) will differ based on the stock's price path. Careful calculation is required to capture this distinction. The current market price of a stock is 45.5. Over the next two quarters, this stock is projected to either increase by 7% or decrease by 6% each period, as per a binomial lattice model. The risk-free interest rate is 6.1% per annum, with continuous compounding. (a) Calculate the price of a 6-month European call option on this non-dividend-paying stock with an exercise price of 46.5. (b) Calculate the price of a 6-month European put option on the same non-dividend-paying stock with an exercise price of 46.5. (c) Ensure that the calculated prices from (a) and (b) are consistent with the put-call parity relationship. (d) In the given market model, an investment bank has introduced an Asian call option that accounts for the full history of the stock's value. The payoff for this option is: ({S_n}^n=0,...,N) = max{ (1/(N+1)) * sum(S_n from n=0 to N) - K, 0}, where N is the total number of periods in the market model. Determine the initial price of the Asian call option with an exercise price of 46.5 at time t = 0. Hint: Apply a similar pricing strategy as used for the European call and put options, but with more precision. The value of the option at the final interval's midpoint (i.e., S_2(ud) or S_2(du)) will differ based on the stock's price path. Careful calculation is required to capture this distinction.