## Risk Management

One of the central tenets of financial economics is the necessity of some trade off between risk and expected return. Because high risk is associated with high reward, investor may potentially obtain higher profits only if he is willing to accept a higher chance of losses. Risk-return trade-off is one trading principal in financial markets.

Risk management is a process to identify and measure risk. The goal of risk management solution is to ensure that risk is under limit and there is no surprise in future. In capital markets, risk management is accountable for oversighting and monitoring the profit and loss, market risk, credit risk, liquidity risk and valuation risk activities of a firm.

Capital market risk management system is an information technology platform that helps people in financial markets balance risk appetite with performance to ultimately optimize capital efficiency, identify probblems, mitigate threats, control risk, avoid unexpected loss, and enhance opportunities.

Market risk is the risk of losses in positions due to market movements, whereas counterparty credit risk refers to the risk that a counterparty to a bilateral financial derivative contract may fail to fulfill its contractual obligation causing financial loss to the non-defaulting party. FinPricing offers capital market risk management products and services to help your organization effectively identify and address the risk you face in financial markets.

### Counterparty Credit Risk

Counterparty risk is the risk that the counterparty to a financial transaction may fail to meet its contractual payments, causing financial loss for the bank. Counterparty risk is represented via exposure profiles. Exposure is the cost of replacing or hedging a contract at the time of default. Other measures include Potential future exposure (PFE), Expected exposure (EE), Expected Positive Exposure (EPE), Effective expected exposure (EEE), Effective EPE, Exposure at default or EAD.

Counterparty risk is much less specific for pricing models than it is for simulating the market prices. The only requirement here is that pricing supports “mark to future” or the path dependent value and events of a trade at any point across the simulation time bucket. This involves storing and accessing reset rates, exercise status, realized stochastic events that will affect our exposure in the future.

### Credit Risk Simulation

To calculate credit exposure or replacement cost in future times, one needs to simulate market evolutions. Simulation must be conducted under the real-world measure. One could use a simple but inaccurate solution, or accurate but complex approach. Some vendors and institutions use this simplified approach. Only a couple of stochastic processes are used to simulate all market risk factors. They use Vasicek model for all mean reverting factors dr=k(θ-r)dt+σdW where r – risk factor; k – drift; θ – mean reverse; σ – volatility; W – Wiener process. And use Geometric Brownian Motion (GBM) for all non-mean reverting risk factors: dS=μSdt+σSdW. The calibration results for different risk factors are different from each other.

Simulation models have the objective to forecast within a reasonable range and horizon market factors such as equity prices, interest and FX rates, and so on. In order to capture a realistic view of our exposure going forward, and because CCR is not directly hedgeable, those models are typically calibrated using historical data (~3 years) and are not systematically implied from today’s market prices.

Counterparty Credit Risk Monte Carlo Simulation

### Collateral Management

In the derivatives world, collateral posting is a risk reduction tool that mitigates risk by reducing credit exposure. It allows financial institutions to reduce economic capital and credit risk, free up lines of credit, and expand the range of counterparties. All of these factors contribute to the growth of financial markets. The benefits are broadly acknowledged and affect dealers and end users, as well as the financial system generally.

When the Bank determines that the counterparty is in default, it will start to negotiate new trades to replace exist derivative portfolio. At the same time, it will take hold the collateral asset and try to sell these assets in the market. The value fluctuations of the portfolio and the collateral asset during their liquidation periods create risk to the Bank.

### CVA

CVA, by definition, is the difference between the risk-free portfolio value and the true (or risky or defaultable) portfolio value that takes into account the possibility of a counterparty’s default. The risk-free portfolio value is what brokers quote or what trading systems or models normally report. The risky portfolio value, however, is a relatively less explored and less transparent area, which is the main challenge and core theme for CVA. In other words, central to CVA is risky valuation.

### FVA

FVA is the cost of funding that is considered in the valuation of uncollateralized derivatives. It is introduced to quantify the adjustment to the value of derivatives in order to ensure that a trader recovers funding costs that are consistent with the market’s view of the funding costs associated with the same trade. This presentation elaborates an integrated framework for calculating both CVA and FVA. We also discuss the pros and cons of comparing the popular credit exposure approach and the more accurate least square Monte Carlo approach.

### FRTB

FRTB provides a clear definition of the boundary between the trading book and the banking book. It consists of an overhaul of the internal model approach (IMA) to focus on tail risk and an overhaul of the standardized approach (SA) to make it more risk sensitive. Each approach also explicitly captures default risk and other residual risks. Liquidity risk is explicitly included for different asset classes via liquidity horizons.

### Historical VaR

Market risk itself is defined as the potential (adverse) change in portfolio value from changes in the market inputs. A distribution analysis of historical returns against simulated returns will be performed in cases where material adverse effects are observed. This includes the evaluation of important spreads (such as libor-OIS) as well as outright prices.

The historical VaR approach follows the following procedures: First, obtain one year historical value time series of all market factors, such as a stock
price time series is ■(x ̅*1&⋯&x ̅_251 ). Assuming today’s value is x_0, generate 250 historical scenarios. The i-th is x_i=(x ̅_i⁄x ̅*(i-1) -1)x_0.
Compute base PV at today t as P(x_o), Compute 250 scenario PVs: P(x_i). Then derive 250 scenario P&L: P(x_i )-P(x_0). Finally sort 250 scenario P&L.
The VaR is the average between 2nd and 3rd lowest (negative) numbers.

### SIMM

Initial margin calculation is counterparty-portfolio-based. It applies to non-cleared OTC derivatives only. Derivative trades belonging to a counterparty will be divided into cleared-trade portfolio and non-cleared-trade portfolio. The initial margin is computed for the non-cleared portfolio.

Margin is collateral that one party needs to deposit with a broker or an exchange to cover some or all of market risk or credit risk. There are several types of margin. Initial Margin is the amount of collateral required to open a position. Maintenance Margin is the minimum amount of collateral required to keep the position open after inception. If (Margin balance) < (Maintenance margin), the broker issues a margin call that requires the investor to bring the margin balance back to initial margin.

### IRC

To caluclate IRC, one needs to simulate default and migration for one-year horizon. Also, one needs to take concentration into account, that measures the degree of a portfolio diversification. For example, if a significant number of issuers belong to a certain category, the portfolio is a concentrated one.

### Market

One of the central tenets of financial economics is the necessity of some trade off between risk and expected return. This presentation gives an overview of financial market basics. Click the links below for details. People in financial market care about returns. Financial return is the measure of profit or loss on an investment. Return is more important than value itself.

### Economic Capital

Economic capital falls into the category of Value at Risk (VaR) measures as both try to capture value change due to market movement. Most institutions use the existing VaR system to compute economic capital. VaR captures the market risk of 1-day time period at 99% confidence level whereas Economic capital measures the market risk of 1-year time period at 99.95 confidence level. Therefore, scaling methodology is the key to compute economic capital, i.e., scaling 1-day to 1-year and 99% to 99.95%. This presentation is intended to answer several fundamental economic capital questions: what is economic capital? What is the difference between economic capital and regulatory capital? How to compute economic capital?

### Parametric VaR

Value at Risk (VaR) is the regulatory measurement for assessing market risk. It reports the maximum likely loss on a portfolio for a given probability defined as x% confidence level over N days. VaR is vital in market risk management and control. Also regulatory and economic capital computation is based on VaR results. Although VaR measure is objective and intuitive, it doesn’t capture tail risk. There are three commonly used methodologies to calculate VaR – parametric, historical simulation and Monte Carlo simulation. This presentation focuses on parametric VaR.

### Sensitivity

Risk sensitivities or Greeks are vital for risk management. They can help financial market participants isolating risk, hedging risk and explaining profit & loss. This presentation gives certain practical insights onto this topic.

Delta is a first-order Greek that measures the value change of a financial instrument with respect to changes in the underlying asset price. Vega is a first-order Greek that measures the value change of a financial instrument with respect to changes in the underlying implied volatility. Gamma is a second order Greek that measures the value change of a financial instrument with respect to changes in the underlying price. Theta is a first order Greek that measures the value change of a financial instrument with respect to time.

### Monte Carlo VaR

Monte Carlo VaR assumes market factors follow certain stochastic processes. It has easy back and stress test and is good for high confidence level and tail risk. The drawbacks are dependent on distribution assumption and calibration is required. Most importantly it requires extensive computation.

The only way to verify a VaR system is backtest. At a certain day, compute hypothetic P&L (valuation date and portfolio unchanged). If (hypothetic P&L > VaR), then breaches. For one year, if number of breaches is 0-4, the VaR system is in Green zone. If number of breaches is 5-9, the VaR system is in Yellow zone If number of breaches is 10 or more, the VaR system is in Red zone.