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 aboverainbow option.
- Bonus 2
Implement the inverse Cholesky method in Wang (2008) to price the above rainbowoption.
- Reference
Wang (2008), “Variance Reduction for Multivariate Monte Carlo Simulation,” Journal of Derivatives 16, pp. 7–28.
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