8008 Exam Dumps : PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition

The index option is affected by the spot value for the underlying index, as also the risk free interest rate, or the zero rate for the duration of the option. It is also affected by the volatility of the underlying. The 'strike price' is set and is fixed at the time the option is purchased, and therefore is not a risk factor.

Therefore other than IV, all other choices are valid risk factors that underlie an equity index option.

Other instruments may have other risk factors - for example, a long forex position will have the spot exchange rate as the only risk factor.

Survivorship bias is the tendency for failed companies, funds, investments and even entire markets (eg Russian stock market returns after the Communist revolution) to be excluded from performance studies because they no longer exist. Survivorship bias results in past results looking better than they actually were as data points relating to failures are not included.

A risk manager needs to be aware of survivorship bias when basing risk analysis on historical data and should question if failures (eg failed funds, delisted companies etc) have been included in the data he or she is relying upon.

In the univariate Gaussian model, each risk factor is modeled separately independent of the others, and the dependence between the risk factors is captured by the covariance matrix (or its equivalent combination of the correlation matrix and the variance matrix). Risk factors could include interest rates of different tenors, different equity market levels etc.

While this is a simple enough model, it has a number of limitations.

First, it fails to fit to the empirical distributions of risk factors, notably their fat tails and skewness. Second, a single covariance matrix is insufficient to describe the fine codependence structure among risk factors as non-linear dependencies or tail correlations are not captured. Third, determining the covariance matrix becomes an extremely difficult task as the number of risk factors increases. The number of covariances increases by the square of the number of variables.

But an inability to capture linear relationships between the factors is not one of the limitations of the univariate Gaussian approach - in fact it is able to do that quite nicely with covariances.

A way to address these limitations is to consider joint distributions of the risk factors that capture the dynamic relationships between the risk factors, and that correlation is not a static number across an entire range of outcomes, but the risk factors can behave differently with each other at different intersection points.