Roza Galeeva, Jiri Hoogland, and Alexander Eydeland
The importance of correlation as a measure of dependence has been often emphasized in the context of pricing derivatives whose payoffs depend on the joint distribution of underlying prices, indices, or rates. There is no doubt that at present these derivatives are getting noticeably more popular and numerous. For example, they include a vast class of basket options, i.e. options on linear combinations of various price indices from different markets. Another example can be found in commodity markets, where spread options, both standard and, increasingly, “multi-legged”, are omnipresent.
Obviously, there are limitations to the use of the correlation, especially in the case of complex joint distributions. However, even under these circumstances practical considerations often force one to use correlations as measure of dependence.
Once the correlation is used for pricing, an immediate question arises: namely, the question of estimating the sensitivity of derivative prices to the correlation parameters, and with it the question of corresponding correlation risk measure. In this chapter we discuss various ways to define and compute one such measure, the correlation VaR.
We start with a brief recap of the correlation and its properties. We discuss various approaches to parametrization of the correlation matrix. We then introduce different methods to generate distributions ...