Quantitative Finance Collector

1. European Option Price with Excess Skewness and Kurtosis
   Stock returns however exhibit nonormal skewness and kurtosis as pointed out by Hull (1993) and Nattenburg (1994). Moreover, the volatility skews are a consequence of the empirical normality assumption violation. For this reason, Corrado and Su (1996) extend the Black-Scholes formula to account for nonnormal skewness and kurtosis in stock returns.
   
   This package calculates the European put and call option prices using the Corrado and Su (1996) model. This method explicitly allows for excess skewness and kurtosis in an expanded Black-Scholes option pricing formula. The approach adapts a Gram-Charlier series expansions of the standard normal density function to yield an option price formula that is the sum of a Black–Scholes option price plus adjustment terms for nonnormal skewness and kurtosis (Corrado and Su, 1997).
   For skewness = 0 and kurtosis = 3, the Corrado-Su option prices are equal to the prices obtained using the Black and Scholes (1973) model.
   
   You can download the Matlab code at Corrado and Su (1996) European Option Prices.
   
   References:
   Corrado, C.J., and Su T. Skewness and kurtosis in S&P 500 Index returns implied by option prices. Financial Research 19:175–92, 1996.
   
   Corrado, C.J., and Su T. Implied volatility skews and stock return skewness and kurtosis implied by stock option prices. European Journal of Finance 3:73–85, 1997.
   
   Hull, J.C., "Options, Futures, and Other Derivatives", Prentice Hall, 5th edition, 2003.
   
   Luenberger, D.G., "Investment Science", Oxford Press, 1998.
   Tags - black scholes , skewness , kurtosis , option
   Read the full post at European Option Price with Excess Skewness and Kurtosis.

   

   
2. Liquidity-Driven Dynamic Asset Allocation
   A paper published in The Journal of Portfolio Management, 2013, 39 (3), pp 102-111, by James X. Xiong, Rodney N. Sullivan, and Peng Wang.
   
   

   Quotation

   We propose a model of portfolio selection that adjusts an investors’ portfolio allocation in accordance with changing market liquidity environments and market conditions. We found that market liquidity provides a useful “leading indicator” in dynamic asset allocation. Specifically, market liquidity risk premium cycles anticipate economic and market cycles. Investors can therefore act to avoid markets with low liquidity premiums, waiting to extract liquidity risk premiums when the likelihood of extracting a liquidity premium improves. The result, meaningfully enhanced portfolio performance through economic and market cycles, and is robust to transactions costs and alternate specifications.

   
   
   Basically this article examines a portfolio strategy that buys stocks and sells bonds when the market is less liquid, thus enjoying a higher liquidity premium, this strategy outperforms a benchmark with equal weights on stocks and bonds by generating a higher sharpe ratio and positive alpha.
   
   Journal paper Working paper
   Tags - liquidity , portfolio , allocation
   Read the full post at Liquidity-Driven Dynamic Asset Allocation.

   

   
3. Mutual Funds R2 as Predictor of Performance
   Improving the accuracy of mutual funds' performance prediction is an interesting and endless topic. A paper published in Review of Financial Studies by Amihud and Goyenko (2013) No. 26 (3) investigates this issue at a new angle: Lower R2 indicates greater selectivity, and it significantly predicts better performance. Nice.
   
   

   Quotation

   We propose that fund performance can be predicted by its R2, obtained from a regression of its returns on a multifactor benchmark model. Lower R2 indicates greater selectivity, and it significantly predicts better performance. Stock funds sorted into lowest-quintile lagged R2 and highest-quintile lagged alpha produce significant annual alpha of 3.8%. Across funds, R2 is positively associated with fund size and negatively associated with its expenses and manager's tenure.

   
   
   Journal paper, Working paper.
   Tags - mutual-fund , prediction
   Read the full post at Mutual Funds R2 as Predictor of Performance.

   

   
4. A Constant-Volatility Framework for Managing Tail Risk
   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.
   
   

   Quotation

   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.
   
   
   Journal paper, Working paper.
   Tags - volatility , tail , risk , portfolio
   Read the full post at A Constant-Volatility Framework for Managing Tail Risk.

   

   
5. Worst-Case Value at Risk of Nonlinear Portfolios
   A paper published in Management Science written by Zymler, S., Kuhn, D., and Rustem, B. Nice & Practical.
   
   

   Quotation

   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.
   Tags - var , nonlinear , risk
   Read the full post at Worst-Case Value at Risk of Nonlinear Portfolios.

   

   
6. Fourth Set: Basel III counterparty credit risk - Frequently asked questions
   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.
   
   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
   Fourth set
   Tags - basel , faq , counterparty , credit
   Read the full post at Fourth Set: Basel III counterparty credit risk - Frequently asked questions.

   

   
7. How to Combine Long and Short Return Histories Efficiently
   Missing data imputation is a common technique many researchers have to apply for some certain situations, especially when we do some portfolio analysis that requires an equal length of historical returns of assets in the portfolio. Typically we assume a distribution of the underlying data and simulate missing data based on the assumption, MLE or EM algorithm is used for simulation. For example, a great R package I have introduced for missing data imputation was at here.
   
   "How to Combine Long and Short Return Histories Efficiently" is a good paper forthcoming in Financial Analysts Journal by Sébastien Page, as introduced
   

   Quotation

   A common challenge in portfolio risk analysis is that certain assets have shorter return histories than others. Unfortunately, many standard portfolio risk analysis techniques—including historical tail risk measurement, regime-dependent risk analysis, and bootstrapping simulations—require full return histories for all assets or risk factors. The author presents easy instructions on how to efficiently combine data for investments whose histories differ in length and offers a new model to better account for non-normal distributions.

   
   
   An important feature of this paper is instead of assuming that the uncertainty around the backfilled returns is normally distributed, the model samples empirical residuals from the short sample. Evidence shows this method is efficient. The author also provides Matlab code in the Appendix for us to play around.
   
   Paper
   Tags - missing , imputation , mle , em , distribution
   Read the full post at How to Combine Long and Short Return Histories Efficiently.

   

   
8. A CRO guide to deal with financial amnesia
   A guest post from Anton Kwaijtaal: A CRO guide to deal with financial amnesia.
   
   1. Don’t fear the risk of falling behind
   Whether it is the risk of falling behind, peer group pressure or ill-defined incentive schemes, there exists a tendency to choose direction based on the illusion of control when there is actually too much uncertainty. Instead, questions should be asked as to whether decisions based on more or less unfounded assumptions should be made at all. Unfounded and inappropriate assumptions are dangerous because of at least two well-known biases. First, we tend to be over-confident in our ability to make financial and economic probability models. The second bias is our tendency to favour information that confirms our beliefs or hypotheses. This is called the confirmation bias. Moreover, by using hyperbolic discounting we reveal a strong tendency to make choices that are inconsistent over time. In other words, we make choices today that our future self would prefer not to make, despite using the same reasoning. Therefore, CRO’s and all other professionals should minimize their bold assumptions about how the economy works. We know much less than we think we know. Warren Buffet, the highly successful investor, sets strict restraints on using assumptions. He nevertheless makes above average profits.
   
   2. Use real risk indicators
   The volatility is wrong when you really need it. When reading this sentence most risk managers immediately think about skewness, kurtosis or perhaps about extreme losses. However, it is necessary to take it one step further. Most of the risk indicators, also in a regulatory context, are based on statistics. In most circumstances this is a second moment, named "variance" or "volatility". The volatility is however an affect heuristic driven indicator. It has no real correlation with the actual risk. The affect heuristic leads people to have a low perception of risk when we feel positive about the economy (and the other way around). However, during long periods of bull markets – driven by debt accumulation – actual risk (e.g. the probability of a deep debt crisis) increases, but our perception of risk reduces.
   
   What you are really interested in is the consequence of market shocks when it actually goes terribly wrong. In this way you correlate risk with the probability of survival of your firm. The use of volatility is a good example of attribute substitution. A complex problem (what are the consequences of a serious meltdown) is replaced with a less complex problem (what is the observed volatility of the market over the last few months/years), at which point the answer to the less complex problem is seen as the solution to the original problem. Risk indicators should be correlated with actual risk, not with indicators such as (implied) volatility. A better risk indicator is the price to profit ratio of stocks, which reveals – in combination with debt levels – a lot about instability accumulating in an economy.
   
   3. Fit models to data, not data to models
   There is a combination of eagerness to use complex models and too high a dependence on (recent) data that makes the use of models tricky at the very least. The quantitative models used in the financial sector are not fit for their purpose. For the models to perform reasonably well they need more regime shifts and more chaos components. For example, when we add debt to macro-economic models, they become very unstable. The economy and the financial markets follow an almost chaotic process. This, however, makes models almost impossible to calibrate. Additions, such as jump diffusion, copulas and stochastic volatilities are well-intentioned attempts to bring the models closer to reality, but this is still not close enough. We know reality is much more unstable. But, we don't like ambiguity, so we replace this with clear models. However, in the end they are still based on the implausible assumption of a stable repeating data generating process. Complex models also challenge our biased cognitive abilities. This especially holds true for the interpretation of model results. It is better to use simple models and perform many back- and stress tests and to focus on the underlying data, including data from past debt crises.
   
   4. Listen to alternative stories
   According to Shiller, the human mind thinks in terms of stories, with internal logic and dynamics that appear as a unified whole. Taleb calls it "explanations (stories) bind facts together". There is a direct link between the content of stories, the collective confidence and the booms and busts of the financial markets. The spread of stories, and thus the collective confidence or pessimism, could be compared to an epidemic, which tends to spread extremely quickly and without warning. This is why the economy follows an almost chaotic process. Collective confidence does not necessary mean a strong economy; even worse, it can lead to growing instability. One should remember that it does not matter what something looks like, it's how it behaves that counts. What makes it even more confusing is that the models seem to prove the story. The estimations based on data seem to be statistically significant, but in reality this is false. The underlying process changes when an economy tips! The CRO should not blindly follow the herd. Thinking in advance about other stories will improve the chance of survival when the stories start to change. Directly related to this topic is the use of scenario thinking in risk management. With proper scenarios, which are at the very heart of risk management – the minimization of unbearable loss ­– will be more successful.
   
   5. Conduct behavioural self-assessments
   As we have already seen, the brain makes decisions based on simplifications or so-called rules of thumb. These heuristics and biases have a tendency to deviate our decision-making from rationality and are at the root of our structurally making the same mistakes over and over again. Even if models work correctly, the resulting decision can still be irrational, usually because of (unconscious) emotions. Emotions and behaviour play a large role in decision-making. Seemingly rational decisions are actually driven by fear, loss aversion and affective forecasting. For example, people act completely differently when they are confronted with a loss than when they find themselves in a profit situation. This is a well-known and important aspect of Prospect Theory that is known as "aversion to a sure loss". Many more of these emotional aspects, that make us decide depending on the emotional state we're in, are known. Understanding all of this, it seems strange that no one in financial institutions is formally given the role of monitoring the behaviour and emotions of the senior management. Perhaps supervisory boards should consider hiring behavioural specialists. At the very least, the senior management and thus the CRO, should start conducting behavioural self-assessments.
   
   Anton is the chief editor/publisher of Quant Magazine, aiming to be the personification of a new culture in finance
   Tags - quant , magazine
   Read the full post at A CRO guide to deal with financial amnesia.

   

   
9. Thanksgiving 2012: A Famous Temple in China
   Time flies, another thanksgiving day of a year.
   
   I would like to express utmost thanks to my supervisor, Professor David Newton, for his continued encouragement, support and guidance throughout the course of my PhD research. I am grateful for his patience, interest and willingness to accept my PhD research topics. Not only does he provide me with research guidance but also his advice for my career drives the whole course of research and makes the three-year PhD study in Nottingham much more interesting.
   
   I thank my parents for their unconditional love and understanding. My life wouldn’t be as it is now without their selfless support. I also want to thank Ms. Haoyu Ma, who has always been at my side supporting me throughout this whole research. Your love and support make every mission possible.
   
   I also take this opportunity to show my thanks to my PhD colleagues and friends at the Nottingham University Business School for their encouragement and help. Spending three fantastic years with you is memorable for the rest of my life. In particular, I would like to thank Dr. Huainan Zhao, Dr. Kai Dai, Ms. Ting Qiu and Mr. Ding Chen, who have always provided me with invaluable advice and suggestions, and helped me in the many ways they can.
   
   Importantly, I thank my co-authors, Dr. Qian Han, Dr. Doojin Ryu, Dr. SongTao Wang, and Prof. David Newton. Our publications and working papers would not be so great without your collaboration. I also appreciate the fly-out opportunities given by University of Otago (New Zealand), Renmin University (China), and KAIST (Korea Advanced Institute of Science and Technology), I had very good time and the experience is memorable no matter an offer will be given or not.
   
   Finally, thanks for your continue reading my blog despite my infrequent posts this year. A photo taken few weeks ago when I visit a famous temple in HangZhou, China, wish you all healthy and successful in the coming year.
   
   Tags - thanksgiving
   Read the full post at Thanksgiving 2012: A Famous Temple in China.

   

   
10. Basel III counterparty credit risk - Frequently asked questions
    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.
    
    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
    Tags - risk , counterparty , basel , credit , cva
    Read the full post at Basel III counterparty credit risk - Frequently asked questions.