Discuss the limitations of the Monte Carlo approach for calculating prices and VaR.

Define the period of a random number generator and explain its importance.

Why is it important to set the seed in most applications?

Consider a stock with a current price of \(P=150\) and daily volatility \(\sigma_{\text{daily}}=0.02\). Assume a risk free rate of \(r=3\%\)

Use \(S=10^6\) simulations to calculate the one-day \(VaR(0.01)\) of the stock.

Now assume you also own a European put option on the stock with strike price \(X=155\), annual volatility \(\sigma_{\text{annual}}=\sqrt{250\times\sigma^2_{\text{daily}}}\) and an expiration date in 3 monthsâ€™ time. Calculate the MC one-day \(VaR(0.01)\) again.

What is the main difference between simulating returns of one asset (and option/s on the same asset) and the multivariate case?

Explain why it is important to choose the number of simulations correctly and discuss how this can be done.