puting VaR to work Flashcards
Explain and give examples of non-linear derivatives
the notion of linearity or nonlinearity is a function o f the definition of the underlying risk factor
Call option is an example of non-linear derivative. The risk of call option depends on the risk of the underlying asset, as well as the probability of being exercise
the change in the value of the call option is not constant when the stock price change, indicating the relationship is not linear
Describe and calculate VaR for linear derivatives
calculate the VaR for non-linear derivative(the delta-normal approach)
The Var for the non-linear derivative can be approximated using the local delta, the mean percentage change of the derivative for the 1% change of the value of the underlying asset
the problem of calculate the VaR from non-linear derivative using linear approximation
for call option, the biggest problem is delta change when the price of the underlying factor change. For small change in value the approximation won’t deviate too much, but for large change in value the approximation will result in large error
one way to compare is first to calculate the Var using local delta method, and then calculate the decline in option value when the asset value change, and compare the decline in option value to the prediction from Var
How the Taylor approximation can reduce the problem of calculating the VaR for non-linear derivative
the Taylor approximation provides both the delta and gamma, the rate of change in delta. so it actually capture the curvature of the curve.
that is, using linear approximation only assume the relation is linear, when the relation is non-linear, the Taylor approximation provides the non-linear terms, the second derivative, which makes the rate of change more accurate
advantage of delta normal approach over the full revaluation approach
full revaluation approach is computationally expensive
structured Monte Carlo approach
correlation breakdown
During the crisis, the market tends to move in the same direction. This means it is difficult to seek the benefit of diversification because no opposite correlation exists. In fact, during the crisis the demand for the diversification is highest. The increase of volatility will require much higher correlation effect, which is rare in the crisis. Change in correlation will change the distribution of the asset return
A simulation using the SMC approach is not capable of predicting scenarios during times of crisis if the covariance matrix was estimated during normal times. Unfortunately, increasing the number of simulations does not improve predictability in any way.
how to model the correlation breakdown scenario?
Stress testing the covariance matrix that generates the structure Monte Carlo scenario. It is an attempt to model the contango effect when the market break down and model the associated effect on volatility and correlation
but stressing the covariance matrix may affect a certain property of it, such as invertibility
Stress test approach
one approach is to identify the historical crisis, and determined the impact on the current portfolio
the another approach is historical simulation. it identify “extreme stress” situations for different asset classes and determined the impact on the current portfolio. this approach looks extreme valuation instead of extreme movement in the underlying risk factor. the biggest adv is it identified the scenario that may not be a crisis across all asset class but is important to one specific asset class.
an alternative approach is to identified the stress scenario, such as a sudden rise of the short term rate by 200bp and the effect on today’s portfolio
problem of stress scenario approach in stress testing
The effect of asset class specific risk. The specific risk is not well understood and modeled. if the portfolio cannot fully diversify, then such risk will affect the precision of the stress test as this risk is not included or fully included in the stress testing scenario.
(i.e., the scenario may overlook the asset specific risk, which not even identified but does exist and have influence if the portfolio is not fully diversified. therefore the stress scenario such as extreme movement in short term rate may capture a fraction of the underlying risk and therefore limit the accuracy of stress test)
Worst case scenario (general idea)
Worst case scenario is the distribution of the tail event. It provides the first and second moment of the tail event. Var tells the probability of exceeding the certain value during the extreme event but does not provide the exact number. Worst case scenario provides the estimated number given the distribution of the tail event.
so var gives the probability, while wcs gives the magnitude
the key point is worst period will occur for certain, but the problem is how bad it is
A Comparison of VaR to WCS(numerically)
