Agostino Capponi

Arbitrage-free bilateral counterparty risk valuation under collateralization and application to Credit Default Swaps

We develop an arbitrage‐free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on‐default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation‐induced contagion is illustrated with numerical examples.

Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment Including Re-Hypotecation and Netting

This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize our analysis to interest-rate swaps as underlying portfolio, and allow for mutual dependences between the default times of the investor and the counterparty and the underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models, including also the effect of interest rate and credit spread volatilities. The impact of re-hypotecation, of collateral margining frequency and of dependencies on the bilateral counterparty risk adjustment is illustrated with a numerical example.

Bilateral Counterparty Risk Valuation with Stochastic Dynamical Models and Application to Credit Default Swaps

We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis (2008) [5] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [5], we find that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Differently from [5], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.

Dynamic Portfolio Optimization with a Defaultable Security and Regime Switching

We consider a portfolio optimization problem in a defaultable market with finitely-many economical regimes, where the investor can dynamically allocate her wealth among a defaultable bond, a stock, and a money market account. The market coefficients are assumed to depend on the market regime in place, which is modeled by a finite state continuous time Markov process. We rigorously deduce the dynamics of the defaultable bond price process in terms of a Markov modulated stochastic differential equation. Then, by separating the utility maximization problem into the pre-default and post-default scenarios, we deduce two coupled Hamilton-Jacobi-Bellman equations for the post and pre-default optimal value functions and show a novel verification theorem for their solutions. We obtain explicit optimal investment strategies and value functions for an investor with logarithmic utility. We finish with an economic analysis in the case of a market with two regimes and homogenous transition rates, and show the impact of the default intensities and loss rates on the optimal strategies and value functions.

Surveillance by means of a random sensor network: a heterogeneous sensor approach

A distributed approach to the surveillance is presented. A clustering architecture is modelled and the behavior of the corresponding heterogeneous random network with self-organizing capability is investigated. Two types of sensors, simple and complex, spread out over the surveillance area. Simple sensors can only compute binary information (yes or no detection); complex sensors, instead, are able to form a target track. A two-way efficient local communication among sensors is hypothesized. From it, a global coherent behaviour of the network emerges, and the resulting network is able to track the moving objects. Benefits and drawbacks of our solution are analysed by means of Monte Carlo simulations.

Systemic Risk in Interbanking Networks

We develop a mean field model of interbanking borrowing and lending activities. Each bank borrows from or lends to other counterparties at an idiosyncratic rate and is exposed to sudden shocks affe...

Optimal Investment in Credit Derivatives Portfolio Under Contagion Risk

We consider the optimal portfolio problem of a power investor who wishes to allocate her wealth between several credit default swaps (CDSs) and a money market account. We model contagion risk among the reference entities in the portfolio using a reduced form Markovian model with interacting default intensities. Using the dynamic programming principle, we establish a lattice dependence structure between the Hamiltonian-Jacobi-Bellman equations associated with the default states of the portfolio. We show existence and uniqueness of a classical solution to each equation and characterize them in terms of solutions to inhomogeneous Bernoullis type ODEs. We provide a precise characterization for the directionality of the CDS investment strategy and perform a numerical analysis to assess the impact of default contagion. We find that the increased intensity triggered by default of a very risky entity strongly impacts size and directionality of the investor strategy. Such findings outline the key role played by default contagion when investing in portfolios subject to multiple sources of default risk.

A New Algorithm for On-line Coloring Bipartite Graphs

We first show that for any bipartite graph

Pricing and Mitigation of Counterparty Credit Exposures

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PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK

with at most five vertices there exists an on-line competitive algorithm for the class of