Value At Risk and Simulations Flashcards
What are the three steps in VaR calculations?
Specify the probability at loss.
Decide the holding period.
Identify the probability distribution.
What is the advantage of the student-t distribution over the normal distribution in a financial context?
The probability distribution of returns have fat tails compared with the normal distribution, just like the student-t distribution.
What happens to the student-t distribution if its degrees of freedom go to infinity?
The student-t distribution becomes the normal distribution.
What are the advantages and disadvantage of Historical Simulations for forecasting risk?
HS is not subject to estimation error.
It directly captures nonlinear dependence.
The model doesn’t react to structural changes very fast because every observation has the same weight.
What are the disadvantages of using parametric methods to forecast VaR?
You need to estimate the distribution of the data first. This can be either impossible or subject to a large estimation error and model risk.
This makes the choice of model more difficult.
What are the limitations of the Monte Carlo approach for calculating prices and VaR?
First, a good simulation requires a lot of computer time. Some simulations aren’t even possible within the given time. Second, a simulation is only as good as the model behind it. The limits of model specification thus also apply to the simulation.
What is the difference between pure simulation and bootstrapping?
Pure simulation involves the construction of an entirely new dataset from artificially constructed data, while bootstrapping involves resampling with replacement from a set of actual data.
What are the merits of pure simulation? Name a situation where it is more beneficial than bootstrapping.
Simulation is more controlled. Every variable is controlled. It is thus very suitable for testing models.
What are the merits of bootstrapping? Name a situation where bootstrapping is more beneficial than pure simulation.
Bootstrapping is useful when you want to mimic certain data without knowing its distributional properties. This can be used when you want to simulate future paths for stock prices when checking risk management models.
What are variance reduction techniques? Name two.
Antithetic variates and control variates. These are two techniques to reduce Monte Carlo sampling error.
What are antithetic variates?
A variance reduction technique where the opposite of a set of random draws is used as the random draws for another simulation.
What are control variates?
A variance reduction technique where the analytical solution for a similar problem is used to improve the accuracy of this simulation.
How are random numbers generated by a computer?
A number is chosen, and then updated using modular arithmetic. The algorithms used for this can be very close to random, but not truly. Thus it is called pseudo random.
What are the drawbacks of simulation methods compared to analytical approaches?
They can take a lot of power and time. If this time isn’t taken and too little simulations are done, the estimation will be inaccurate. They also can’t be replicated without setting a seed beforehand.
Because a simulation is specific to the particular set of parameters investigated, it can be too specific. Analytical methods are mostly more generally applicable.
