Monte Carlo for European Options Implement a Monte Carlo method for single-asset European options, based on the Black–Scholes model. Perform experiments with various values of N and a random number generator of your choice. Compare results obtained by using the analytic solution formula for St with results obtained by using Euler’s discretization. For

c) B is the barrier such that the option expires worthless when St ≥ B for some t. input: S0, number of simulations (trajectories) N, payoff function Ψ(S), riskneutral interest rate r, volatility σ, time to maturity T , strike K. payoffs:

a) vanilla put, with Ψ(S)=(K − S)+, S0 = 5, K = 10, r = 0.06, σ = 0.3, T = 1.

b) binary call, with Ψ(S) = 1S>K, S0 = K = σ = T = 0.5, r = 0.1

c) up-and-out barrier: call with S0 = 5, K = 6, r = 0.05, σ = 0.3, T = 1, B = 8. Hint: Correct values are:

a) 4.43046

b) 0.46220 [Que07]

c) 0.0983 [Hig04]