Price an arithmetic average call with the following payoff using the binomial tree model.
Payoffτ = max(Save,τ − K,0),
where Save,τ is the arithmetic average of stock prices from the issue date until the current time point τ.
• Basic requirement
(iImplement the binomial tree model to price both European and American arithmeticaverage calls.
(ii) Implement the Monte Carlo simulation to price European arithmetic average calls.
(Inputs: St, K, r, q, σ, t, T−t, M, n, Save,t, number of simulations, number of repetitions. Outputs: Option values for both methods and 95% confidence interval for Monte Carlo simulation.)
• Bonus 1
Linearly vs. logarithmically equally-spaced placement method, i.e., compare the convergence rates for M = 50,100,150,...,400.
• Bonus 2
Compare the computational time of the following three methods to locate the positions of Au and Ad.
Sequential search (the traditional way)
Binary search
Linear interpolation method
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