Price a lookback put with the binomial tree model. The payoff function of the lookback put is as follows.
Payoffτ = max(Smax,τ − Sτ,0), where Smax,τ = maxSu, for u = 0,∆t,2∆t,...,τ.
• Basic requirement
(i) Implement the binomial tree model to price both European and American lookbackputs.
(ii) Implement the Monte Carlo simulation to price European lookback puts.
(Inputs: St, r, q, σ, t, T, Smax,t, n, number of simulations, number of repetitions. Outputs: Option values for both methods and 95% confidence level for Monte Carlo simulation.)
• Bonus 1
Based on the same binomial tree framework, devise and implement a quick way to determine the Smax list for each node.
• Bonus 2
Implement the method in Cheuk and Vorst (1997) to price European and American lookback puts.and 1− in the CRR binomial tree, respectively.
• Reference
Cheuk and Vorst (1997), “Currency lookback options and observation frequency: a binomial approach,” Journal of International Money and Finance 16, pp. 173–187.
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