Monte Carlo European Pricer

Junior Quant · Numerical Implementation

Question

Implement a Monte Carlo pricer for a European call (

S_0 = 100

K = 100

r = 5\%

\sigma = 20\%

T = 1

) using GBM simulation. Report a 95% confidence interval for the price. What is the convergence rate in terms of number of paths

N

? Express the required

N

as a function of the payoff standard deviation

\sigma_{\text{pay}}

and target standard error

\varepsilon

. For this call, estimate

\sigma_{\text{pay}}

from your simulation and compute the

N

needed to achieve

\varepsilon < 0.01

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