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Market risk is the risk of losses in a portfolio due to adverse movements in market variables such as interest rates, exchange rates, equity prices, and volatilities of equities and exchange rates.

The standard approach is to base the calculation of the empirical distribution of daily shifts in market variables over some period, typically the most recent year of the data or data from a particularly stressed historical period. Each set of daily shifts are applied to the inputs of the pricing models for each asset in the bank’s portfolio. Assuming, say, 250 business days worth of shift data, this gives rise to 250 possible valuation changes in the portfolio. Market risk capital is often taken to be a certain quantile of this empirical distribution, say the 99% quantile or worst move out of 100 . This is called VaR (value at risk). However, there is an alterative approach called expected shortfall.

A significant amount of the work involved in market risk management therefore goes into developing, validating and revalidating the asset pricing models. This typically includes:

- Spot, forward and futures trades
- Fixed income products and interest rate products like bonds, inflation bonds, FRNs and swaps.
- Derivatives on equities, FX and interest rates, including European/American exercise and features such as barriers.

For some asset classes, accurate models may be computationally prohibitive. This is the case for barrier options for example, whose sensitivity to volatility term structure requires the use of a local volatility or stochastic volatility model. This may necessitate pricing barrier options using a constant volatility assumption, and then developing an auxillary model to calculate and compensate for the capital error. In many cases, historical volatility data may have to be processed through a cleaning algorithm to remove arbitrage and unusual data from volatility surfaces.

In addition to the building asset pricing models, developing or validating a market risk system involves correctly calculating shifts in market data. There are many subtle pitfalls in this process, including dealing with interpolation between curve pillars. Cubic spline interpolation can lead to strange behaviour which must be carefully considered. Some market risk systems will switch from cubic spline to linear interpolation to increase valuation speed, which introduces an error that must be quantified and shown to be acceptable.

Furthermore, when calculating market risk for bonds, it’s necessary to calculate shifts in both the underlying interest rate curve and the zspread on top of it (alternatively, some systems prefer to work in terms of survival curves). When validating zspread shifts for bonds, we’ve found that there are some subtle issues in calculating these which need to be handled carefully. Since zspread shifts are calibrated primarily to the bond maturity, once must be careful to shift all historical curves forward to today’s date before calculating the zspread shift. One must also be careful about whether one is using absolute or relative shifts for the interest rate, if the interest rate shift is to be consistent with the zspread shift.

The Fundamental review of the trading book (FRTB) is a new international for market risk measurement. Developed by the Basel Committee, it’s designed to improve upon deficiencies in market risk management that came to light during the GFC. Most larger banks would aim to implement the Internal Modelling Approach (IMA), as the alternative Standardized Approach is typically far more punitive in terms of the amount of market risk capital that must be held. The implementation of the FRTB regulation is generally expected to increase market risk capital, particularly around products that are illiquid or hard to model.

Because of its importance to regulators, the requirement to implement and comply with new FRTB regulation, and the complexity involved in calculating market risk for a large and diverse portfolio, market risk management is currently a highly active field. We offer a wide range of market risk consulting services including:

- Development of VaR and expected shortfall calculations
- Development and validation of asset pricing models
- Development and validation of market data shift calculations including interest rate curves, FX curves and zspreads / survival curves.

To discuss how our sophisticated cloud-based quant consulting business can supercharge your financial services firm, contact us today.