Understanding market, credit and operational risk : the value at risk approach / Linda Allen, Jacob Boudoukh and Anthony Saunders. 4 Extension of the VaR Approach to Non-tradable Loans 119 5 Extension of the VaR Approach to operational risks 158.
LIST OF TABLES
PREFACE
LIST OF ABBREVIATIONS
PCS Property and Claims Service PD probability of default PWC PricewaterhouseCoopers QIS quantitative impact study RAROC risk-adjusted return on capital RPI sales price index.
CHAPTER ONE
INTRODUCTION TO VALUE AT RISK (VaR)
This assumption is the key to the elegance and simplicity of the Black-Scholes option pricing formula. VaR calculations require assumptions about the possible future values of the portfolio sometime in the future.
CHAPTER TWO
QUANTIFYING VOLATILITY IN VaR MODELS
THE STOCHASTIC BEHAVIOR OF RETURNS .1 Revisiting the assumptions
- GARCH
This is the typical picture for common risk measurement systems: estimated volatility follows actual volatility. Here xt−i is the vector of variables describing the economic state at time t−i (e.g. the term structure), determining the appropriate weight ω(xt−i) to place on observation t −i, as a function of the.
IMPLIED VOLATILITY AS A PREDICTOR OF FUTURE VOLATILITY
The upper dashed line is the DM/GBP exchange rate, which represents our "event clock". The event is the collapse of the exchange rate. As was the case many times before this event, the most notable prediction of devaluation was already present - the GBP is visibly close to the intervention band. The second, rational markets, explanation for the phenomenon is that implied volatility is greater than realized volatility due to stochastic volatility.
Note the following facts: (i) volatility is stochastic; (ii) volatility is a price source of risk; and (iii) the underlying model (e.g. the Black–Scholes model) is therefore misspecified assuming constant volatility. The use of implied volatility is limited to highly concentrated portfolios where implied volatilities are present.
MEAN REVERSION AND LONG HORIZON VOLATILITY Modeling mean reversion in a stationary time series framework is called
When current volatility is above the long-term average, we can expect a decline in volatility over the longer term. Extrapolating long-horizon volatility based on today's volatility overestimates the actual expected long-horizon volatility. On the other hand, if current volatility is unusually low, extrapolating current volatility using the square root rule may underestimate true long-term volatility.
Expectations for the next period are the weighted sum of today's value of Xt and the long-term mean a/(1 −b). If b= 1, the process is a random walk - a non-stationary process with an undefined (infinite) long-term mean, so the expected value of the next period is equal to today's value.
CORRELATION MEASUREMENT
Convergence trades explicitly assume that the spread between two positions, a long and a short, means to reverse. Remember that the correlation between two assets is the ratio of their covariance divided by the product of their standard deviations. This method can result in a curious outcome, that the correlation is greater than one, a consequence of the assumptions.
This factor is transferred directly to the correlation parameter - the numerator of which increases by a factor of 2.66, while the denominator remains the same. The second alternative assumes, in addition to independence, that the intensity of the news flow is constant throughout the trading day.
SUMMARY
BACKTESTING METHODOLOGY AND RESULTS In Section 2.2, we discussed the MSE and regression methods for com-
To the extent that tail probability is cyclical, so will the occurrence of violations of the VaR estimate. The third property we examine is related to the first property – the bias of the VaR series, and the second property – the autocorrelation of tail events. The MAE is a conditional version of the previous statistic (percentage in the tail from table 2.4).
Specifically, we examine the first through fifth autocorrelations of the tail event series, with the null that all these autocorrelations must be zero. The test statistic is simply the sum of squared autocorrelations, appropriately adjusted for sample size.
CHAPTER THREE
STRUCTURED MONTE CARLO, STRESS TESTING, AND SCENARIO ANALYSIS
Second, the 100 basis point parallel shift scenario is a test of the effect of a single risk factor: the level of domestic interest rates. It is therefore the case that the 1 percent VaR according to the SMC is the first percentile of the distribution of the simulated scenario portfolio values. This is a simple extension of the fat tails effect for individual assets and risk factors.
In both cases, we need to estimate the effect of the scenarios on the firm's current portfolio position. Our analysis shows the importance of information in WCS over and above VaR.
SUMMARY
Consequently, the probability of exceeding the VAR and the 1 percent tail size of the WCS will be underestimated. Third, and related to model risk, there is the issue of the posterior behavior of the financial series. The full revaluation approach requires revaluation of the derivative at the VaR value of the underlying.
That is, to determine the risk in the derivative position, the derivatives must be revalued at an extreme value (eg the VaR value) of the underlying. We conclude with a discussion of the worst-case scenario measure of risk, an alternative to the standard VaR approach.
DURATION
What this means is that an increase in rates from 5 percent to 6 percent should generate a loss of $0.00907 in the value of the one-year zero, compared to a loss of $0.0373 in the value of the five-year zero coupon. connection. The expression for duration is actually an approximation.13 In contrast, the correct calculation would show that if interest rates rose 1 percent from 5 percent to 6 percent, then the new price of the one-year zero would be and. By comparing these new prices to the original prices before the interest rate increase (ie, $0.9524 for the one-year and $0.7835 for the five-year), we can get an accurate calculation of the price losses due to of the interest rate increase.
For example, suppose we are interested in the one-month VaR of the portfolio of one-year and five-year zeros, whose value is $1.7359 and duration is 2.18116. It is therefore the case that the VaR of the portfolio is just the sum of the VaRs of the two cash flows, the one-year zero and the five-year zero.
CHAPTER FOUR
TRADITIONAL APPROACHES TO CREDIT RISK MEASUREMENT
Historically, many bankers have relied on the 5 Cs of the credit expert system to assess credit quality. 5 Cycle (or economic) conditions – the state of the business cycle is an important element in determining exposure to credit risk. Due to the large number of possible connections, a neural network can grow very quickly.
This is most relevant in the context of interpreting external credit ratings that are designed to be "through-the-cycle" assessments of default probability over the life of the loan. Notes: Where possible, the explanatory variables are listed in order of statistical significance (eg the magnitude of the coefficient term) from highest to lowest.
THEORETICAL UNDERPINNINGS: TWO APPROACHES Modern methods of credit risk measurement can be traced to two altern-
The value of the option's underlying instrument: A, the market value (not the book value) of the firm's assets. 2 The volatility of the market value: σA, that is, the standard deviation of the firm's market value of assets. Equation (4.8′) expresses the yield on risky debt as the sum of the risk-free rate and the credit spread, consisting of PD × LGD.
Jarrow and Turnbull (1995) assume that the recovery rate is a known fraction of the bond's face value at maturity. Duffie and Singleton (1998) assume that the recovery rate is a known fraction of the bond's value just before default.
CREDITMETRICS
If the loan is downgraded, the required credit spread premium should increase (remember that the contractual lending rate is assumed to be 6 percent in our example), so the present value of the loan should fall. However, Table 4.3 shows that the loan value will drop to $83.64 million if the loan's credit quality deteriorates to CCC. The distribution of loan values at the one-year credit period date can be plotted using the transition probabilities in Table 4.2 and the loan valuations in Table 4.3.
If the loan had retained the BBB rating, the value of the loan would have been the same. The lower the (standardized) value of the company's assets, the greater the chance that the company will default; therefore, the creditworthiness of the loan deteriorates (improves) as the company's asset values decrease (increase).
ALGORITHMICS’ MARK-TO-FUTURE
What is the impact of the reduction in the risk manager proposed in Scenario S9 on the default risk of this BB-rated firm. If the results of the multi-factor model suggest that the debtor has a positive correlation with the risk driver, then it is expected that the swap transaction's credit quality will decrease (credit risk increase) under Scenario S9. The conditional cumulative default probability is calculated based on the results of the multi-factor model.
The results for Scenario S9 depend on the assumption that systemic risk explains 5 percent of the total variance of the CWI, while idiosyncratic risk explains the remaining 95 percent. In contrast, if systemic risk accounted for 80 percent of the variance, the five-year conditional default probability under Scenario S9 would have been 44.4 percent instead of 11.4 percent.
SUMMARY
For example, Russia's bankruptcy in August 1998 was foreshadowed by the devaluation of the ruble. Thus, integrating market risk factors into a credit risk measurement model can improve the quality of VaR estimates, especially during crisis periods. Therefore, dichotomizing credit risk and market risk undermines the accuracy of all risk measurement models.
The 1% VaR is interpolated based on the actual distribution of the loan value under different rating migrations. Using tables 4.4 and 4.5 we can calculate the VaR for the portfolio consisting of the two loans described in section 4.3.2.
CHAPTER FIVE
TOP-DOWN APPROACHES TO OPERATIONAL RISK MEASUREMENT
The top-down approach establishes an overall cost of operational risk for the entire firm (or for specific lines of business within the firm). In a top-down model, operational risk exposure is typically calculated as the variance in a target variable (such as revenue or costs) that is unexplained by external market and credit risk factors. Unlike top-down operational risk methodologies, more modern techniques use a "bottom-up" approach.
Furthermore, risk profiling can focus on the symptom (e.g. increased overtime), rather than the root cause of the operational risk problem. However, it is a matter of judgment as to which risk indicators are most relevant to the company's overall operational risk exposure.16.
BOTTOM-UP APPROACHES TO OPERATIONAL RISK MEASUREMENT
If the process map contains too much detail, it can become unwieldy and provide extraneous data, detracting from the main focus of the analysis. Therefore, the process map should identify the high-risk steps in the operational process that are the focus of management's concern. In contrast, the steps required to verify price and position are not considered by management to be particularly high in operational risk and are therefore summarized in the first box of the process map shown in Figure 5.3.
For example, data on the lead times for each phase of the process is collected and entered into the process map in Figure 5.3. In terms of the number of days required to complete each task, Figure 5.3 shows that most of the operational risk is mitigated in the last two steps of the process: settlement instructions and payment notification.
