## Methodology

We provide services to risk managers with modeling credit and market risks of their portfolios. Our model ties these two major sources of risk for each portfolio exposure and calculates portfolio level risk measures at given time horizons. We also provide modeling for interest rate and operation risks in separate model and combine all risks together.

Our modeling methodology is based on the same modeling approach used by leading financial organizations around the world and accepted by developers of **Basel Standards**. Its engine uses structured credit or Merton modeling paradigm which is the cornerstone in methodologies used by other leading vendors such as RiskMetrics and KMV. This methodology is widely accepted in credit industry and **Basel Standards** recommendations are based on this modeling approach.

In its core principle, structural credit paradigm considers obligors asset/liability structure and assumes losses happen when liabilities exceed firms assets. Interested parties can learn more about it here: http://en.wikipedia.org/wiki/Merton_Model

# Investment Risk model

Our main objective is to provide advanced modeling for our client investment portfolios which satisfies most rigorous regulatory and internal risk management criteria. In our Investment Portfolio Model we use most advanced methodologies accepted by leading credit organizations, rating agencies and regulators.

Investment Risk Model consists of two components: **Credit and Market Risk**.

**Credit Risk**

In our credit model, we use structural finance or Merton paradigm, which is a foundation of most models used by leading credit organizations worldwide and which serves as a base for Basel regulatory criteria. For each exposure in the portfolio we supply the following data into the model:

__Probability of Default to Investment Horizon (PD)
__PD term structure is derived through a number of methods

- IRB (Internal Risk Based)
- Market implied (spread, cash or synthetic). It also might be called risk neutral PD
- Rating

__Recovery or Loss Given Default (LGD)
__Recovery assumptions are usually driven by exposure’s investment sector

__Correlation
__The critical part of the credit model is correlation assumptions between the exposures. Our model uses most widely used approach in the industry. First, it allocates all exposures into separate buckets based on their investment type (such as corporate industry, mortgage, sovereign etc) and assigns correlation parameter of the exposure to the bucket (so call R-squared). Second, the model inputs correlation assumptions between the buckets themselves.

__Coupon and other premiums cash flows__

The model accounts for all cash flows over the investment horizon, taking into account potential defaults that happen prior to it.

__Counterparty Info__

If investment portfolio contains hedges, the model will take into account potential defaults of a hedge counterparty.

__Final maturity
__Final maturity of a portfolio exposure is important to set up exposure’s PD structure

__EAD (Exposure at Default)
__Investment portfolio can contain cash and synthetic positions, as well as hedges. The model calculates the timing of default for each exposure at every simulation step. Users also provide amortization schedule for each exposure, so the model knows its balances at each time steps.

#### Market Risk

For market risk modeling purposes, our model uses GARCH (General Autoregressive conditional heteroskedasticity). To learn more about GARCH see: http://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity

We use GARCH because of a number of shortcomings that other techniques such as migration matrices have. GARCH addresses two main issues: clustering of market moves and correlations.

Most methodologies ignore prior period performances of a portfolio while GARCH allows capturing them. For example, if spreads were wide yesterday and two days ago, they are more likely to remain wide today. Also, we know that in times of stress market moves of all portfolio exposures are highly correlated. GARCH methodology is better than others in capturing these phenomena.

__Discount Curve__

We use Hull-White model to simulate discount (risk free) curve structure

__Simulation Process
__The model runs up to 1 million simulations to derive distribution of gains/losses at given time horizon.

__Horizon
__Financial organizations usual investment horizon targets are 1 month and 1 year.

__Other calculations
__The model also calculates for expenses, taxes and other cash flows

# Risk Measures Output

The model provides a number of risk measures as its output. Some of them are commonly used in the industry, and some are customized to meet client specific goals.

__VaR (Value at Risk)
__VaR is a widely used risk measure. It is defined as a threshold value such that the probability of a portfolio loss exceeds this value at a a given probability level (usually 99%). Although it is most common measure, there has been many complains about it as it fails to account for the shape of a loss distribution curve.

__Expected Shortfall
__Expected Shortfall (ES) is a risk measure alternative to VaR that is more sensitive to the shape of the loss distribution in the tail of the distribution. Effectively EL is a measure of an average value at the tail of a loss distribution.

Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), and expected tail loss (ETL).

EL received a lot of attention recently as shortcomings of commonly used VaR became apparent. Regulators have recently been asking credit organizations to pay more attention to Expected Shortfall together with VaR

__Individual Exposure Risk Contribution and Risk Weights
__Some names due to their size or highly correlated nature to the rest of the portfolio can contribute substantially more to the risk profile of the pool. Based on all simulation runs, the model will derive each exposure’s contribution to the loss distribution tail and calculate their risk weights.

__Other (Client Customized) Metrics
__The model output data can be customized to derive other risk measures suitable to clients. We can also provide the data dump of the model output.