[SOLVED] NTUIB Assignment 4

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),whereSmax,τ =maxSu,foru=0,∆t,2∆t,…,τ.

• Basic requirement :

  (i) Implement the binomial tree model to price both European and American lookback puts.

  (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 deter-

  mine the Smax list for each node.

• Bonus 2

  Implement the method in Cheuk and Vorst (1997) to price European and American lookback puts.




u3 max(u3 1,0) u2 max(u2 1,0) u m a x ( u  1 , 0 )

1 max(11,0)

u

1

u2




 u











1



1

※ Note that


and 1 −
in the CRR binomial tree, respectively.

and


are not exactly to be the branching probabilities

• Reference
Cheuk and Vorst (1997), “Currency lookback options and observation frequency: a bino-

mial approach,” Journal of International Money and Finance 16, pp. 173–187. 1