The CESAM is pleased to announce that Professor Damiano Brigo (Imperial College) will give a PhD course on nonlinear valuation and XVA under credit risk, collateral margins and funding costs. To register, follow the link.
CESAM/ISBA PhD Course in Quantitative Finance
Nonlinear Valuation and XVA under Credit Risk, Collateral Margins and Funding Costs
Damiano Brigo (Imperial College)
November 19-20, 2015 at Louvain-la-Neuve, Belgium
Abstract
The market for financial products and derivatives reached an outstanding notional size of $708 trillions in 2011, amounting to ten times the planet gross domestic product. Even discounting double counting, derivatives appear to be an important part of the world economy and have played a role in the onset of the financial crisis in 2007.
After briefly reviewing the Nobel-awarded option pricing paradigm by Black Scholes and Merton, hinting at precursors such as Bachelier and de Finetti, we explain how the self-financing condition and Ito's formula lead to the Black Scholes Partial Differential Equation (PDE) for basic option payoffs. We hint at the Feynman Kac theorem that allows to interpret the Black Scholes PDE solution as the expected value under a risk neutral probability of the discounted future cash flows, and explain how no arbitrage theory follows, how it can be re-formulated, and discuss market incompleteness.
Following this quick introduction, we describe the changes triggered by post 2007 events. We re-discuss the valuation theory assumptions and introduce valuation under counterparty credit risk, collateral posting, initial and variation margins, and funding costs. We explain model dependence induced by credit effect, hybrid features, contagion, payout uncertainty, and nonlinear effects due to replacement closeout at default and possibly asymmetric borrowing and lending rates in the margin interest and in the funding strategy for the hedge of the relevant portfolio. Nonlinearity manifests itself in the valuation equations taking the form of semi-linear PDEs or Backward SDEs. We discuss existence and uniqueness of solutions for these equations. We also present a high level analysis of the consequences of nonlinearities, both from the point of view of methodology and from an operational angle. We discuss the Modigliani Miller theorem and whether this really implies that funding costs should be zero at overall institution level. We show assumptions under which the value of a portfolio can be decomposed in several valuation adjustments including CVA, DVA, LVA, FBA, FCA, FVA, CVAf and DVAf, usually denoted collectively with the acronym "XVA". We discuss possible overlaps, the possibly non-additive nature of the adjustments and ambiguities in their definitions.
Finally, we connect these developments to interest rate theory under multiple discount curves, thus building a consistent valuation framework encompassing most post-2007 effects.
Course Outline
Day 1
9:00 am - 10:30 am
Introduction to no-arbitrage valuation. Black Scholes, Harrison Kreps and Pliska, Attainable Claims, Self-financing Strategies, Feynman Kac Theorem, Risk Neutral Measure, No Arbitrage, Market Completeness. The Nobel award to Merton and Scholes.
10:30 am - 10:45 am
Coffee Break
10:45 am - 12:30 pm
The LTCM fund default. The CDO discussion. The current crisis. New and neglected risk factors and trading costs. Valuation adjustments? Introduction to Credit Risk Products and Models. CDS and Bonds. Market implied and Rating implied default probabilities.
12:30 pm - 1:30 pm
Lunch break
1:30 pm - 3:00 pm
Intensity models. Firm Value Models. Lehman Brothers case study. Interactive discussion, Q&A. CVA and DVA, Unilateral CVA and unilateral DVA, Bilateral Adjustment, Problems with DVA: Wrong incentives and hedging, First to default analysis, ISDA Closeout choices, Payout Risk. Examples of CVA and DVA with Wrong Way Risk: Rates, Commodities, Credit, Equity, Longevity. Interactive discussion, Q&A
3:00 pm - 3:15 pm
Coffee break
3:30 pm
Collateral: CSA and collateral, Thresholds and Minimum transfer amounts, Gap Risk, Collateral and residual CVA/DVA, numerical examples (swaps and CDS)
End Day 1
Day 2
9:00 am – 10:30 am
Summary of Day 1. Funding Costs: Treasury and different funding policies, Margining costs for collateral, Hedging and Funding, Total price, Recursive Nonlinear pricing problem.
10:30 am – 10:45 am
Coffee break
10:45 am – 10:30 pm
Funding Costs: Possible numerical techniques; Can we define FVA additively? Implications for the bank structure; Industry approximations; Interactive discussion, Q&A
12:30 pm – 1:30 pm
Lunch break
1:30 pm – 3:00 pm
Hints at CSA and CCPs. Standard CSA. Introduction to CCPs. Initial and Variation Margins. Costs of trading via CCPs. Valuation of trades traded via CCPs. Separability of adjustments. Hints at the multi-curve framework.
3:00 pm – 3:15 pm
Coffee break
3:15 pm
Interactive discussion, final Q&A and conclusions.
End Day 2
Fees and Registration
In order to participate, send a C.V. with this registration form to cesam.phd-course@uclouvain.be before 20/10/2015. The number of participants is limited. Participation costs are €100 for Ph.D. students, €200 for postdocs or academics and €800 for others. The course is free for the members of the organizing institutions. Registration costs only cover the 2-day course, the course material, breakfasts and lunches.
Venue
The course will be held in the premises of the Université catholique de Louvain in Louvain-la-Neuve. Further details will come soon.
Organizers
Frédéric Vrins, Leonardo Iania and Pierre Devolder.