Price a maximum rainbow option with the payoff max(max(S1T,S2T,...,SnT)−K,0) using the Monte Carlo simulatiton.
(Inputs: K, r, T, number of simulations, number of repetitions, n, S10, S20, ..., Sn0, q1, q2,..., qn, σ1, σ2,..., σn, ρij. Outputs: Option value and 95% confidence interval.)
• The basic requirment
Apply the Cholesky decomposition method to pricing the above rainbow option.
• Bonus 1
Combine the antithetic variate approach and moment matching method to price the above rainbow option.
• Bonus 2
Implement the inverse Cholesky method in Wang (2008) to price the above rainbow option.
• Reference
Wang (2008), “Variance Reduction for Multivariate Monte Carlo Simulation,” Journal of Derivatives 16, pp. 7–28.
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