Consider a stock, the current price (So) of which is $30. We model stock-price evolution using...

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Consider a stock, the current price (So) of which is $30. We model stock-price evolution using a Binomial model. In every three-month period, u = 1.1052 and d = 0.9048. The risk free rate of interest is 5% per annum continuously compounded. The four-step Binomial tree is shown below: 30 Node Time: 0.0000 33.16 Payoff= 27.15 0.2500 36.64 30.00 24.56 0.5000 40.50 33.16 [max(S₂, S.)-min (S₁,S,) max(S₁, S₂, S.,)-S, 27.15 22.22 0.7500 44.75 36.64 if S, 230 if S₁ < 30 30.00 24.56 A European-style exotic derivative has been written on this stock. The derivative has one year to expiry. Denote by S, S₂, S, and S, the stock price after three, six, nine and twelve months respectively. The payoff to the derivative is specified as follows: 20.11 1.0000 Required: Using a four-step Binomial framework and the risk-neutral approach, calculate the current value of this exotic derivative. Use continuous compounding for all present value calculations. Show all working. Consider a stock, the current price (So) of which is $30. We model stock-price evolution using a Binomial model. In every three-month period, u = 1.1052 and d = 0.9048. The risk free rate of interest is 5% per annum continuously compounded. The four-step Binomial tree is shown below: 30 Node Time: 0.0000 33.16 Payoff= 27.15 0.2500 36.64 30.00 24.56 0.5000 40.50 33.16 [max(S₂, S.)-min (S₁,S,) max(S₁, S₂, S.,)-S, 27.15 22.22 0.7500 44.75 36.64 if S, 230 if S₁ < 30 30.00 24.56 A European-style exotic derivative has been written on this stock. The derivative has one year to expiry. Denote by S, S₂, S, and S, the stock price after three, six, nine and twelve months respectively. The payoff to the derivative is specified as follows: 20.11 1.0000 Required: Using a four-step Binomial framework and the risk-neutral approach, calculate the current value of this exotic derivative. Use continuous compounding for all present value calculations. Show all working.

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To calculate the current value of the exotic derivative using the fourstep Binomial framework and the riskneutral approach we need to work backward th... View the full answer