Is stochastic cross-currency basis a better way to model IM?

Using Monte Carlo model extension for forward IM calculation avoids excessive outputs for MVA

Quantitative trading

The landscape for non-cleared over-the-counter derivatives transactions has undergone drastic regulatory changes over the past few years. Backing up derivatives transactions with collateral has become a central tenet in counterparty credit risk management, with rules and practices being consolidated on a more formal basis. In March 2017, the exchange of variation margin (VM) was made mandatory, and in September 2022, the last stage of the initial margin (IM) phase-in will finally be rolled out, completing the multi-year introduction of the global framework for minimum margin standards.

The exchange of IM inevitably creates funding costs for banks and other financial entities that are commonly quantified by margin valuation adjustment (MVA). When a counterparty defaults, VM provides protection against current exposure losses, while IM serves as a buffer against potential future exposure losses during close-out.

While estimating uncollateralised credit (CVA), debit (DVA), and funding (FVA) valuation adjustments can be straightforward using mark-to-market exposure simulations, MVA is more challenging as it involves the simulation of future IM requirements.

The benchmark methodology for IM estimates in non-cleared OTC markets is the International Swaps and Derivatives Association’s standard IM model (Isda Simm). This is based on a historically calibrated variance-covariance approach and takes portfolio sensitivities as inputs. Estimating MVA using the Isda Simm, therefore, typically requires a plethora of forward sensitivities, making the calculation even more complex.

Without more advanced methods, such as algorithmic differentiation or artificial neural nets, these sensitivities can be expensive to compute. As a case in point, Isda Simm requires 12 sensitivity inputs for each interest rate curve, time step and scenario, making fast and reasonably accurate MVA calculations in standard XVA simulation frameworks a non-trivial issue.

Diverging results

The Isda Simm methodology makes assumptions about the principal risk factors, volatilities and correlations based on a five-year historical calibration horizon that is updated annually.

Embedding an MVA calculation in a regular, risk-neutrally calibrated XVA Monte Carlo simulation, without computing portfolio sensitivities, can be done (and is often done). However, to produce outcomes that are comparable to those provided by Isda Simm requires an adjustment of the underlying XVA simulation model.

This is where an adequate model extension is vital. In fact, it seems that a relatively basic stochastic cross-currency basis model extension is indispensable when calculating the forward IM requirements for cross-currency instruments and cross-currency portfolios via standard IM estimation procedures.

Our research has shown that ignoring stochastic cross-currency basis dynamics is insufficient for certain trade types

To be more specific, a typical basic XVA simulation model consists of one stochastic interest rate driver per currency and one stochastic exchange rate driver per independent currency pair, and is calibrated to current market conditions. Ordinarily, all interest rate curves are constructed as deterministic spreads over the respective base interest rate drivers. As a result, all cross-currency basis spreads turn out to be deterministic.

To generate an expected IM profile that is suitable for MVA, a common approach is to estimate the relevant distributional moments of the portfolio profit and loss over the close-out period, conditional on the underlying risk factors, and to infer the corresponding 99th-percentile value-at-risk. Such values at risk can then be used to construct a raw expected IM profile forward in time that is uniformly scaled up or down to match the Isda Simm amount at time zero.

Matching the time-zero benchmark amount, however, does not guarantee that the resulting scaled IM profile resembles the corresponding Isda Simm profile in any way. Our research has shown that ignoring stochastic cross-currency basis dynamics is insufficient for certain trade types. For example, take the case of a forward-starting mark-to-market (resetting) cross-currency basis swap. Here, even though a simulate-and-scale approach using deterministic cross-currency basis dynamics and the Isda Simm tend to agree very well on the initial portion of the expected IM profile, the initial scale ratio typically ceases to apply after trade start. Consequently, the simulate-and-scale approach vastly overestimates the IM requirements over the lifetime of the swap, and leads to excessive MVAs, as illustrated in table A.

 

 

The cause for the discrepancy is that the mark-to-market cross-currency basis swap is largely dominated by cross-currency basis risk. As the basic XVA simulation model is unaware of cross-currency basis risk and only captures the residual interest and exchange rate risks of the swap – the latter of which is close to zero before trade start, but non-zero afterwards – uniform scaling of the raw expected IM profile by the time-zero scale factor is simply inconsistent and inadequate.

The way forward

For the simulate-and-scale approach to work, the XVA simulation model at a minimum must mirror the relevant risks and volatilities underlying Isda Simm. Augmenting the basic XVA simulation model by suitable stochastic cross-currency basis dynamics is a step in this direction that helps to alleviate IM discrepancies.

We used three different parameterisations for the cross-currency basis dynamics, representing distinct model-implied cross-currency basis risk weight term structures that range from moderately flat to intermediate to convex decaying. All result in dramatic improvements over the deterministic base case and track the Isda Simm expected IM benchmark much more accurately over the entire time horizon.

Among the three parameterisations, the best performer implies cross-currency basis risk weights that are closest to the flat, constant cross-currency basis risk weight term structure assumed by the Isda Simm. The improvement is also clearly seen in the corresponding MVAs, which are now roughly in the same ballpark as the Isda Simm MVAs (see table A).

In our research paper, we have undertaken a deeper analysis of the impact of stochastic cross-currency basis modelling on different interest rate swap types under different pricing conditions. In summary, it appears that identifying and accounting for the relevant risk factors is critical for any basic XVA simulation framework, particularly when computing IM and MVA for non-cleared OTC trades.

Moreover, a carefully chosen minimalistic stochastic cross-currency basis extension to a Hull-White-based XVA simulation model is effective and preserves, or, at most, mildly modifies, existing model characteristics and implementations.

Overall, for the swap cases studied, the resulting IM profiles and MVAs can be brought roughly in line with Isda Simm results relatively easily. Fine-tuning of the cross-currency basis dynamics may hold further potential to find scale factors that are appropriate for more diverse multi-trade portfolios.

Christoph M Puetter is a quantitative data and research analyst and Stefano Renzitti the head of financial engineering research in the Financial Risk Analytics Group at S&P Global in Vancouver

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