We explore how the joint modeling of financial assets can utilize methodologies from geostatistical modeling. The considered approach is essentially based on modeling data as realizations of a (Gaussian) random field. This allows for a parsimonious representation of the dependence structure by means of a covariance function taken to be a function of the distance between observations. A key beneft of this ansatz is the possibility to include new data points, i.e. to consider new companies in financial applications. Consequently, geostatistical modeling has appealing benefits in the contexts of covariance matrix estimation and missing data imputation. We thoroughly discuss the necessary adjustments when applying geostatistical methods to the high-dimensional framework that entails the modeling of financial data, instead of the 2D/3D coordinate space encountered in original applications of the method. We illustrate the two use cases of covariance matrix estimation and missing data imputation on a data set of CDS spreads of constituents of the iTraxx universe.
Assuming the absence of arbitrage in a single-name credit risk model, it is shown how to replicate the risk-free bank account until a credit event by a static portfolio of a bond and infinitely many credit default swaps (CDS). From the viewpoint of classical arbitrage pricing theory this static portfolio can be viewed as the solution of a credit risk hedging problem whose dual problem is to price the bond consistently with the CDS. This duality is maintained when the risk-free rate is shifted parallelly. In practice, there is a unique parallel shift that is consistent with observed market prices for bond and credit default swaps. The resulting, risk-free trading strategy in case of a positive shift earns more than the risk-free rate, is referred to as negative basis arbitrage in the market, and the parallel shift defined in this way is a scientifically well-justified definition for what the market calls negative basis. In economic terms, it is a premium for taking the un-modeled residual risks of a bond investment after interest rate risk and credit risk are hedged away, predominantly these are liquidity risk and legal risk.
The major part of observed correlation matrices in financial applications exhibits the Perron-Frobenius property, namely a dominant eigenvector with only positive entries. We present a simulation algorithm for random correlation matrices satisfying this property, which can be augmented to take into account a realistic eigenvalue structure. From the construction principle applied in our algorithm, and the fact that it is able to generate all such correlation matrices, we are further able to compute explicitly the proportion of Perron-Frobenius correlation matrices in the set of all correlation matrices in a fixed dimension.
A current market-practice to incorporate multivariate defaults in global risk-factor simulations is the iteration of (multiplicative) i.i.d. survival indicator increments along a given time-grid, where the indicator distribution is based on a copula ansatz. The underlying assumption is that the behavior of the resulting iterated default distribution is similar to the one-shot distribution. It is shown that in most cases this assumption is not fulfilled and furthermore numerical analysis is presented that shows sizable differences in probabilities assigned to both “survival-of-all” and “mixed default/survival” events. We furthermore present a survey of those copula families that make the aforementioned methodology work.
We discuss some critical aspects when evaluating convertible bonds whose underlying equity trades in a currency different from the bond currency.