By Moorad Choudhry
The value-at-risk dimension method is a widely-used software in monetary marketplace possibility administration. The fourth variation of Professor Moorad Choudhry's benchmark reference textual content An advent to Value-at-Risk bargains an available and reader-friendly examine the concept that of VaR and its varied estimation tools, and is aimed in particular at rookies to the marketplace or these surprising with glossy threat administration practices. the writer capitalises on his event within the monetary markets to provide this concise but in-depth insurance of VaR, set within the context of possibility administration as a complete.
Topics lined comprise:
- Defining value-at-risk
- Variance-covariance method
- Monte Carlo simulation
- Portfolio VaR
- Credit danger and credits VaR
themes are illustrated with Bloomberg monitors, labored examples, workouts and case stories. similar matters akin to records, volatility and correlation also are brought as worthy history for college students and practitioners. this can be crucial examining for all those that require an creation to monetary marketplace threat administration and value-at-risk.
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Additional info for An Introduction to Value-at-Risk
To investors risk usually is the probability of loss. Standard deviation is a traditional measure often used by investment professionals. It measures an investment’s variability of returns; that is, its volatility in relation to its average return. While standard deviation has the cachet of science it is a narrow measure and may not provide sufficient information by itself. It is simply a measure of volatility and as a measure of the probability of loss is of limited use. However, its usefulness is increased if one pairs 10 AN INTRODUCTION TO VALUE-AT-RISK it with returns, as in the Sharpe Ratio or the Van Ratio.
Arithmetic mean We say that the random variable is X, so the mean is EðXÞ. In a time series of observations of historical data, the probability values are the frequencies of the observed values. The mean is: P xi ð2:1Þ EðXÞ ¼ i n where 1=n ¼ Assigned probability to a single value among n; and n ¼ Number of observations. The standard deviation of the set of values is: X 1 rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðXÞ ¼ ½xi À EðXÞ2 n i ð2:2Þ The probability assigned to a set of values is given by the type of distribution and, in fact, from a distribution we can determine mean and standard deviation depending on the probabilities pi assigned to VOLATILITY AND CORRELATION 15 each value xi of the random variable X.
24 AN INTRODUCTION TO VALUE-AT-RISK Implied volatility is a necessary tool to obtain the predicted value of an option which has been obtained from the present value of that option by entering different levels of volatility into an option pricing model, until the current market price is reached. This iterative process effectively reduces the margin of error. In a working situation, most option pricing models allow the calculation of implied volatility by entering the present market price for an option.
An Introduction to Value-at-Risk by Moorad Choudhry