Workshop Financial and Actuarial Mathematics

5th workshop of the Freiburg-Strasbourg research group on Financial and Actuarial Mathematics

Abstracts:

Stephane Crépey

"XVA analysis from the balance sheet"

Since the 2008-09 financial crisis, derivative dealers charge to their clients various add-ons, dubbed XVAs, meant to account for counterparty risk and its capital and funding implications.

 
As banks cannot replicate jump-to-default related cash flows, deals trigger wealth transfers from bank shareholders to bondholders and shareholders need to set capital at risk. On this basis, we devise a theory of XVAs, whereby the so-called contra-liabilities and cost of capital are sourced from bank clients at trade inceptions, on top of the fair valuation of counterparty risk, in order to compensate shareholders for wealth transfer and risk on their capital.

 
The resulting all-inclusive XVA formula, meant incrementally at every new deal, reads (CVA+FVA+KVA), where C sits for credit, F for funding, and where the KVA is a cost of capital risk premium. All these XVAs are nonnegative and, even though we do crucially include the default of the bank itself in our modeling, unilateral in a certain sense. The corresponding XVA policy ensures to bank shareholders a submartingale wealth process corresponding to a target hurdle rate on their capital at risk, consistently between and throughout deals

Mitja Stadje

"On time-consistent and market-consistent evaluations"

Pricing insurance payoffs with an inherent financial risk in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market-consistent evaluation procedure which we call two step market evaluation. We give a complete axiomatic characterization for two step market evaluations and show that in a dynamic setting with continuous stock prices every evaluation which is time-consistent and market-consistent is a two step market evaluation. We also show many other appealing properties of two step market evaluations.

Programm:

10.00 Welcome

10.15 Stephane Crépey XVA analysis from the balance sheet

11.15 Anna Rita Bacinello The impact of longevity risk and contractural heterogeneity on the fail valuation of a life insurance portfolio

12.30 Lunch at FRIAS

14.00 Mitja Stadje On time-consistent and market-consistent evaluations

15.00 Coffee break at FRIAS lounge

15.30 Thorsten Schmidt A fundamental theorem of insurance valuation

16.30 Stefan Tappe Mortality-interest rate term structures

17.00 Closing discussion

19.30 Conference dinner