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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.

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