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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.

Jan 31
A paper published in the Journal of Portfolio Management, 2013, Vol. 39, No. 2: pp. 28-40, by Alexandre Hocquard, Sunny Ng, and Nicolas Papageorgiou.

Since Lehman Brothers collapsed in 2008, tail-risk hedging has become an increasingly important concern for investors. Traditional approaches, such as purchasing options or variance swaps as insurance, are often expensive, illiquid, and result in a substantial drag on performance. A more prudent, cost-effective way to maintain a constant risk exposure is to actively manage portfolio exposure according to the prevailing volatility level within underlying assets. The authors implement a robust methodology based on Dybvig’s payoff distribution model to target a constant level of volatility and normalize monthly returns. This approach to portfolio and risk management can help investors obtain their desired risk exposures over both short and longer time frames, reduce exposure to tail risk, and in general increase portfolios’ risk-adjusted performance.


The idea is simple, easy to implement, has a good performance based on the authors' results.
constant volatility tail risk

Journal paper, Working paper.
Jan 21
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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Nov 21
The Basel Committee on Banking Supervision has received a number of interpretation questions related to the December 2010 publication of the Basel III regulatory frameworks for capital and liquidity and the 13 January 2011 press release on the loss absorbency of capital at the point of non-viability.
basel banking
Below are three sets of frequently asked questions (FAQs) that relate to counterparty credit risk, including the default counterparty credit risk charge, the credit valuation adjustment (CVA) capital charge and asset value correlations. More sets may be forthcoming, stay tuned.

First set
Second set
Third set
Oct 29
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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Aug 16
A very nice paper by Knaup and Wagner (2012) published in Management Science. Enjoy it.

We propose a new method for measuring the quality of banks' credit portfolios. This method makes use of information embedded in bank share prices by exploiting differences in their sensitivity to credit default swap spreads of borrowers of varying quality. The method allows us to derive a credit risk indicator (CRI). This indicator represents the perceived share of high-risk exposures in a bank's portfolio and can be used as a risk weight for computing regulatory capital requirements. We estimate CRIs for the 150 largest U.S. bank holding companies. We find that their CRIs are able to forecast bank failures and share price performances during the crisis of 2007–2009, even after controlling for a variety of traditional asset quality and general risk proxies.


Article, Working paper
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