Fixed Income

Market Risk


market risk

  1. Market Risk Data

Effective market risk management requires all markets risks to be appropriately identified, measured and controlled. Market risk itself is defined as the potential (adverse) change in portfolio value from changes in the market inputs. A well-functioning risk control process reflects the foundational role of valuation and the direct linkage with risk from end-to-end with appropriate control points and feedback loops.

ResearchGate data construction pdf

ResearchGate curve construction

Zenodo repo curve

2. Profit and Loss

Risk measurement will create a strong linkage between pricing models used for profit and loss (P&L) and pricing models used for risk measurement. All market inputs are available for incorporation to risk management systems though some require alternative historical data for calibration procedures. Consistent valuation models will facilitate the identification of market factors driving valuation.

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ResearchGate rho pdf

ResearchGate rho

3. Backtest Exception

Backtest exceptions occur when Clean P&L and/or Model P&L exceed Model VaR on an absolute basis. The use of both model P&L and clean P&L for exception reporting gives granularity in the drivers of the exception

Cases where the market move is the only cause of the exception, no further validations are required. The conclusion can be further proved by a comparison of the market data change with its historical trend, showing that the move is in a greater magnitude than the historical data, as well as what’s captured in the VaR window.

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ResearchGate fair pdf

ResearchGate fair

4. Independent Price Verification

At each month-end, the Valuation Product Control Group (VPC) performs an independent fair valuation of all portfolios within Trading Products. This process results in independent price verification adjustments (IPV) and valuation adjustments (VA). IPV reflect the valuation difference between the line of business (LOB) view of valuation and the independent VPC view. VA’s are adjustments used to achieve fair value and include Close-Out, Uncertainty, Liquidity, Model Risk, and Administrative.

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ResearchGate bet pdf

ResearchGate bet

5. Gamma Shocks

In the Commodity framework, risk factors for NG pipelines are currently defined with respect to base and spread (over NYM_NG).  The delta sensitivities in RDR are given for the base and spread, but the gamma is an “all-in”, meaning it calculated with respect to base plus spread curve.  Because we do not have separate risk factors for the all-in curves, we modify shocks generated for the base and spread curves to construct those for the all-in curves. 

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6. Commodity Simulation Translation

Market instruments may be daily, for instance, but simulated risk factors may be monthly. Therefore, we need to convert monthly simulated risk factors into daily market instruments. Here we use linear interpolation within the range of risk factors and extrapolation beyond the range.

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7. Commodity Volatility Closing Rate Calculation

To populate the closing rate for implied volatility skew risk factors, it will be necessary to implement the forward-delta based Omega skew models and use the Brent root finding algorithm to solve for the closing rate.  This function spec will outline this procedure.

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ResearchGate binary pdf

ResearchGate binary

8. Precious Metal Futures

Futures contracts are typically valued as a spread to the forwards curves.  This spread is the EFP (Exchange of Futures for Physical).  This function spec outlines the introduction of this spread as a basis risk factor into system and the transformation of sensitivities with respect to futures contracts to those with respect the spot contract, forward offered rates, and basis.

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ResearchGate futures pdf

ResearchGate futures

9. Dividend Risk

Due to the difference between stock dividend risk factor model and stock price risk factor model, it is more natural to carry out the simulation of these two types of risk factors separately. Currently, stock price risk factor is simulated in Simulation 3 based on beta and idiosyncratic volatility assigned to it. The derived risk factor for price of stock basket or index is simulated in Simulation 4 based on closing rate and weights of components of the basket or index.

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ResearchGate dividend pdf

ResearchGate dividend

10. Dividend Exposure Measurement and Management

We model dividend risk by introducing a new risk factor – the innovation in dividend expectation. It is to describe the day-to-day relative changes to the expected dividend amount of the underlying stock, basket of stocks, or equity index. The new risk factor facilitates the calculation of the market expected dividend when pricing an equity derivative at future time.

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ResearchGate forward dividend pdf

ResearchGate forward dividend

11. Dividend Risk Modeling and Methodology

Pricing of equity derivatives on single stock usually takes expected dividend amount as input. Sensitivity with respect to expected dividend amount is readily available. Directly modeling changes to dividend expectation is a very convenient way to capture risk via DGV approach.

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12. Dividend Risk Model Calibration

As described in model description and calibration of the model, the daily innovation to expected dividend of an index is simulated from double exponential distribution with specified correlation with all other risk factors. The daily innovation to expected dividend of a single stock is simulated on the fly without correlation with other risk factors.

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ResearchGate model pdf

ResearchGate model