# Quantitative Finance Collector is a blog on Quantitative finance analysis, financial engineering methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management. Random thoughts on financial markets and personal staff are posted at the sub personal blog.

Dec 7

#### Predicting Heavy and Extreme Losses in Real-Time for Portfolio Holders

Posted by abiao at 00:57 | Code » Other | Comments(10) | Reads(7736)
Pawel wrote a great article on predicting heavy and extreme losses in real-time for portfolio holders, the goal is to calculate the probability of a very rare event (e.g. a heavy and/or extreme loss) in the trading market (e.g. of a stock plummeting 5% or much more) in a specified time-horizon (e.g. on the next day, in one week, in one month, etc.). The probability. Not the certainty of that event.

In this Part 1, first, we look at the tail of an asset return distribution and compress our knowledge on Value-at-Risk (VaR) to extract the essence required to understand why VaR-stuff is not the best card in our deck. Next, we move to a classical Bayes’ theorem which helps us to derive a conditional probability of a rare event given… yep, another event that (hypothetically) will take place. Eventually, in Part 2, we will hit the bull between its eyes with an advanced concept taken from the Bayesian approach to statistics and map, in real-time, for any return-series its loss probabilities. Again, the probabilities, not certainties.

Read this excellent post and accompanying Pathon codes at http://www.quantatrisk.com/2015/06/14/predicting-heavy-extreme-losses-portfolio-1/
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Jan 21

#### Worst-Case Value at Risk of Nonlinear Portfolios

Posted by abiao at 18:50 | Paper Review | Comments(1) | Reads(7330)
A paper published in Management Science written by Zymler, S., Kuhn, D., and Rustem, B. Nice & Practical.

Portfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR over all return distributions of the derivative underliers with given first- and second-order moments. The derivative returns are modelled as convex piecewise linear or—by using a delta–gamma approximation—as (possibly nonconvex) quadratic functions of the returns of the derivative underliers. These models lead to new worst-case polyhedral VaR (WPVaR) and worst-case quadratic VaR (WQVaR) approximations, respectively. WPVaR serves as a VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon, whereas WQVaR is suitable for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon. We prove that—unlike VaR that may discourage diversification—WPVaR and WQVaR are in fact coherent risk measures. We also reveal connections to robust portfolio optimization.

Journal, Working paper in PDF.
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Oct 29

#### A Fully Integrated Liquidity and Market Risk Model

Posted by abiao at 08:40 | Paper Review | Comments(1) | Reads(8175)
An excellent and practical paper by Attilio Meucci, "A Fully Integrated Liquidity and Market Risk Model" forthcoming in Financial Analysts Journal.

Going beyond the simple bid–ask spread overlay for a particular Value at Risk, the author introduces an innovative framework that integrates liquidity risk, funding risk, and market risk. He overlaid a whole distribution of liquidity uncertainty on future market risk scenarios and allowed the liquidity uncertainty to vary from one scenario to another, depending on the liquidation or funding policy implemented. The result is one easy-to-interpret, easy-to-implement formula for the total liquidity-plus-market-risk profit and loss distribution.

Journal paper, Working paper
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May 21

#### New Illiquidity Measure Week in Review

Posted by abiao at 09:17 | Paper Review | Comments(1) | Reads(6912)
Noise as Information for Illiquidity: We propose a measure of liquidity for the overall financial market by exploiting its connection with the amount of arbitrage capital in the market and observed price deviations in US Treasuries.

The Risk Map: A New Tool for Validating Risk Models: This paper presents a new method to validate risk models: the Risk Map. This method jointly accounts for the number and the magnitude of extreme losses and graphically summarizes all information about the performance of a risk model. We show that the Risk Map can be used to validate market, credit, operational, or systemic risk estimates (VaR, stressed VaR, expected shortfall, and CoVaR) or to assess the performance of the margin system of a clearing house.

Deviations from Put-Call Parity and Stock Return Predictability: Deviations from put-call parity contain information about future returns. Using the difference in implied volatility between pairs of call and put options to measure these deviations we find that stocks with relatively expensive calls outperform stocks with relatively expensive puts by 51 basis points per week.

Nassim Taleb on the J.P.Morgan Trading Loss: Nassim Taleb interviewed on the J.P.Morgan Trading Loss (May 2012).
Mar 1

#### 2011 Risk Manager of the Year Week in Review 010312

LABORSTA Internet: View and download data for over 200 countries or territories from LABORSTA, an International Labour Office database on labour statistics operated by the ILO Department of Statistics, excellent!

Estimating the Value-at-Risk: A Comparative Study of the Extreme Value Theory and Transformed Kernel Density Approach: peak-over-threshold (POT) method outperforms the transformed kernel density and the generalized extreme value block-maxima approaches to estimate Value-at-Risk.

Volatility timing and portfolio selection: How best to forecast volatility: the frequency of data used to construct volatility estimates, and the loss function used to estimate the parameters of a volatility model.

Interview: Donald R. van Deventer Risk Management: interview Donald, the Chairman and Chief Executive Officer of Kamakura Corporation, one of the 50 members RISK Magazine Hall of Fame in 2002.

The "Out of Sample" Performance of Long-run Risk Models: This paper studies the ability of long-run risk models to explain out-of-sample asset returns during 1931-2009.

GARP, 2011 Risk Manager of the Year Awarded to Aaron Brown: the 2011 Risk Manager of the Year Award to Aaron Brown, Head of Risk Management at AQR Capital Management, author of the book Red-Blooded Risk: The Secret History of Wall Street

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