Multivariate Risk Modeling 

Lecture Day

"Advances in Financial Mathematics"

January 19, 2011

Programme

Wednesday January 19

Abstracts

Umut Can (University of Tilburg, NL)

Goodness of Fit Testing with Empirical Copulas

We propose a sequential scanning innovation operation to transform the empirical copula process asymptotically into a standard Wiener process. This transformation paves the way to the development of a myriad of asymptotically distribution-free goodness-of-fit tests for copula-based models.

PRESENTATION

Roger Laeven (University of Tilburg, NL)

Entropy Coherent and Entropy Convex Measures of Risk

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences, respectively, upon requiring the certainty equivalents to be translation invariant. In addition, we study the properties of entropy coherent and entropy convex measures of risk, derive their dual conjugate function, and prove their distribution invariant representation. Some financial applications and examples of entropy coherent and entropy convex measures of risk are also investigated.

PRESENTATION

Dilip Madan

Capital Minimization as a Market Objective

The static two price economy of conic finance is fi…rst employed to defi…ne capital, profi…t, and subsequently return and leverage. Examples illustrate how profi…ts are negative on claims taking exposure to loss and positive on claims taking gain exposure. It is argued that though markets do not have preferences or objectives of their own, competitive pressures lead markets to become capital minimizers or leverage maximizers. Yet within a static context one observes that hedging strategies must then depart from delta hedging and incorporate gamma adjustments. Finally these ideas are generalized to a dynamic context where for dynamic conic …finance, the bid and ask price sequences are seen as nonlinear expectation operators associated with the solution of particular backward stochastic difference equations (BSDE) solved in discrete time at particular tenors leading to tenor specifi…c or equivalently liquidity contingent pricing. The drivers of the associated BSDEs are exhibited in complete detail.

PRESENTATION

Martijn Pistorius

On quantification of counter-party risk

We construct a dynamical credit model that can be calibrated exactly to CDS quotes. Modelling the default time as the first-passage time of a credit index process to the level zero, we show that the parameters of this credit index process can be chosen such that the risk-neutral (implied) distribution of the time of default is matched.
Employing this default model we develop a model for asset prices conditional on the occurrence of default at a given time.
We illustrate the use of the model in estimating the expected positive exposure of an oil swap traded with an airline as counterparty.
This is joint work with Mark Davis.

PRESENTATION

Wim Schoutens (KU Leuven)

Measuring Market Fear

- market fear ingredients: volatility, liquidity and herd behavior
- the concept of implied liquidity
- measuring herd behavior via the comonotonicity ratio
- how to extract the fear factors from option price data
- historical study and related trading strategies

PRESENTATION

Frederic Vrins (ING)

Analytical Pricing of Basket Default Swaps: A dynamic model with automatic calibration to CDS curves

In this talk, we will consider the model originally proposed by Hull & White in 2008 for the pricing of multiple-name credit derivatives. In this model, CDO tranches and related options can be priced in a semi-analytical way. It is therefore an interesting dynamic alternartive to the static Gaussian copula model. Unfortunately, in the original setup of Hull & White, the calibartion to the underlying CDSs cannot be achieved analytically: Monte Carlo simulations are needed to calibrate the model with respect to each underlying, and this is required at each step of the tranche calibration process. This is a major limitation of the model which becomes very quickly untractable unless some drastic assumptions (like pool homogeneity) are made.
In order to tackle that issue, we will consider some variants of the Hull White model for which those assumptions are not needed. In this framework, both calibration to underlying CDS and the pricing of nth to default swaps will be proved to be achievable in a fully analytical way. Further, the pricing of CDO tranches can be obtained in a similar way as in the original Hull-White method, using conditional independence.
Finally, if there is still time remaining, we shall briefly compare our method with that of Mai & Scherer. We will discuss how the "name-specific recovery rates" case, which is usually problematic in jump-based models due to simultaneous defaults, can be partly handled in our setup.

PRESENTATION

Last updated 21-jan-2011,
By PK

    P.O. Box 513, 5600 MB  Eindhoven, The Netherlands
tel. +31 40 2478100  fax +31 40 2478190  
  e-mail: office@eurandom.tue.nl