# Monte Carlo Simulation

• Straddles: Long position in call and put with same exercise price.
• Straddle is a non Linear derivative whose payoff increases with the increase in the volatility.
• Also delta normal VAR increases with the increase in the volatility.
• Going by the delta normal VAR for straddles, as the volatility increases, VAR should increase but in reality the payoff is becoming positive.

• The Monte Carlo approach assumes that there is a known probability distribution for the
• risk factors.
• The usual implementation of Monte Carlo assumes a stable, Joint-Normal distribution for the risk factors.
• This is the same assumption used for Parametric VaR.
• The analysis calculates the covariance matrix for the risk factors in the same way as
• Parametric VaR.
• Unlike Parametric VaR Monte Carlo Simulation:
• Decomposes the covariance matrix and ensures that the risk factors are correlated in each scenario.
• The scenarios start from today's market condition and go one day forward to give possible values at the end of the day.
• Full, nonlinear pricing models are then used to value the portfolio under each of the end-of-day scenarios.
• For bonds, nonlinear pricing means using the bond-pricing formula rather than duration.
• For options, it means using a pricing formula such as Black-Scholes rather than Greeks.