--- title: Chapter 7 Simulation methods for VaR for options and bonds layout: default ---

# Simulation methods for VaR for options and bonds

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

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

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

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

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

2. 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.

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

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