X-Valuation Adjustment is a catch-all term for various adjustments made to derivative instruments. These kinds of calculations are computationally intensive: they require a modeller to calculate a larger number of default scenarios and the potential loss (Potential Future Exposure, or PFE) in each case. Agent-based simulation provides a framework to compute more accurate valuation adjustments for better risk management; let’s see why.
XVAs are needed to patch up the shortcomings of the Black-Scholes option pricing model, a risk-neutral pricing framework. To achieve this, XVA adjusts the Black-Scholes framework to account for risks which the model fails to capture. The most famous of the XVA family is CVA, or Credit Value Adjustment. This adjusts for the possibility that the party on the other side of a transaction could default, and is effectively the market value of counterparty credit risk. Derivative values, then, should be adjusted downwards to reflect this possibility of counterparty default and unrealised gains as a result of this default.
Back in 2014, EY detailed their most advanced method for simulating the drivers of the value of a derivative instrument:
“The most advanced approach for calculating credit adjustments used within the banking sector is the Expected Future Exposure (EFE) approach. Using this method, the market variables driving a derivative’s fair value are simulated. Expected exposure over the life of the derivative is calculated by revaluing the derivative for each simulated market scenario. These exposure profiles are then used to determine a CVA by applying counterparty PDs (i.e. probability of default).”
— Ernst & Young 2014
The issue with this approach is that it decouples the default probability (based on a counterparty’s credit spread) from the potential future exposure.
Instead, we need an approach which explicitly links counterparty default probabilities to market variables driving the derivative’s fair value. Enter, agent-based modelling (ABM), which allows us to do just this…
The ABM mindset embraces the complexity inherent in real-world derivative markets where counterparties are tangled in complex webs of interconnections.
A credit event in one part of the network can spread, or even be amplified, through the web of derivative contracts before impacting a bank. This network risk is currently not accounted for by most counterparty risk models, which only consider first-order connections.
There is an opportunity to better price risk here: agent-based models provide a natural framework for recreating network contagion processes. Agents can be linked into a network, or graph, where the nodes are financial institutions and edges are financial (derivative) contracts. Combining agent-based modelling with techniques from network theory allows the modeller to consider not only first-order counterparty credit risk, but also credit risk presented by second, third, and higher-order connections.
An agent-based counterparty risk model is a tool that can be used to generate millions of scenarios computationally. As a result, agent-based modelling provides a framework in which we can predict scenarios, many of which are likely to be default-free. Crucially, modelling the default process alongside the future exposure profiles allows for predicting scenarios in which defaults do occur. This allows us to capture the exposure at the point of default. Given enough computational power, it is possible to generate a full set of expected exposures at default (EEAD). Applications for agent-based simulations do not stop here; in our new era of post-crisis risk management, agent-based approaches to risk management are increasingly being recognised as the way to build resilient banks.