# Tag Info

18

I recently read "Modeling financial data with stable distributions" (Nolan 2005) which gives a survey of this area and might be of interest (I believe it was contained in "Handbook of Heavy Tailed Distributions in Finance"). Another more recent reference is "Alpha-Stable Paradigm in Financial Markets" (2008). I'm not aware of anything covering "risk of ...

16

There are several application of Lévy alpha-stable distributions to finance, especially in insurance and reinsurance. I believe that Embrechts-Kluppelberg-Mikosh's "Modelling Extremal Events for Insurance and Finance" is still an excellent reference. However, in the modeling of stock prices, this line of research is essentially inactive. The reason is that ...

15

ML/AI systems are susceptible to a number of risks not traditionally discussed in risk management: What I call 'backtest arbitrage'. In the process of automated model generation and testing, your machine learner may discover, exploit, and concentrate on irregularities in your backtesting system which do not exist in the real world. If, for example, your ...

12

There are many advantages and flaws to each quoted method by Shane(presuming that I understand them properly), the first one has the big main advantage that it doesn't need any evaluation of probability law, it is just some kind of evolved scenario re-playing "as of" today using the history of (usually) one day market evolutions over one or two year. So ...

11

I assume you mean risk neutral pricing? Think of it this way (beware, oversimplification ahead ;-) You want to price a derivative on gold, a gold certificate. The product just pays the current price of an ounce in $. Now, how would you price it? Would you think about your risk preferences? No, you won't, you would just take the current gold price and ... 10 I am still a beginner to this topic, and have been working through Cont and Tankov's textbook Financial Modelling With Jump Processes (2003), which is a fairly elementary treatment of the subject. I think a revised second edition is to come out later this year. One interesting area of applications that has become more prominent with a recent wave of papers ... 10 The text of your question doesn't actually match the question title. The answer to your title is of course yes binary options make sense. And as others have pointed out with binary options your reward is limited, and conversely the risk involved in writing them is less. To answer your additional question you can replicate a binary option with a tight call ... 9 Suppose that you and other bettors participate in a lottery with$N$possible outcomes; event will occur with probability$\pi_n$. There are$N$basic contracts available for purchase. Contract$n$costs$p_n$and entitles you to one dollar if outcome$n$occurs, zero otherwise. Now, imagine that you have a contingent claim that pays a complex payoff based ... 9 We bet on a fair coin toss -- heads you get$\$100$, tails you get $\$0$. So the expected value is$\$50$. But it is unlikely that you'll pay $\$50$to play this game because most people are risk averse. If you were risk neutral, then you WOULD pay$\$50$ for an expected value of $\$50$for an expected net payoff of$\$0$. A risk neutral player will accept ...

9

There is a fairly recent (2010) monograph by Martin Hibbeln entirely devoted to this very question. He starts with the standard Asymptotic Single Risk Factor model and shows how it can be modified in order to be consistent with the Basel II framework. He also compares the accuracy and runtime of several modern models which have been developed to measure ...

9

I am implementing a method in Java to calculate the variance, covariance, and value at risk for a portfolio, which should be flexible for use with any number of assets in a portfolio. I am struggling with how to calculate the covariance of the assets as I can only find formulae to do so for two or three sets of values. Are you sure you ...

9

I'm not sure about the "CAPM formula" that you are referring to. I assume you are referring to the estimated coefficient of a regression of a security on a market portfolio. That is to say $$\beta_{security,market} = \frac{\sigma_{security,market}}{\sigma^2_{market}}$$ The idiosyncratic risk is the portion of risk unexplained ...

8

The risks involved in trading is everywhere and always a multifaceted thing: it includes the volatility of the selected asset, the leverage and concentration of the porfolio, whether there is a stop loss, a hedge, etc. Also, risk management is frequently not tied to the "alpha model" directly (e.g. VaR, shortfall, and scenario testing). For instance, one ...

8

I just ran across an interesting presentation comparing the effectiveness of Normal, Cauchy, and Student's-t distributions in modeling the S&P. It concludes that the normal distribution underestimates extreme movements, the Cauchy overestimates them (although a comment on the presentation points out that Mandelbrot used different parameters than the ...

8

Perhaps you may want to consider article by D. Levine - Modeling Tail Behavior with Extreme Value Theory who gives practicale example on how EVT can be used to calculate probabilities on returns in tails with use of the Pickands-Balkema-de Haan Theorem and generalized Pareto distribution. It also contains some criterias and points on other methods that can ...

8

One approach is Conditional Value at Risk (CVaR) a.k.a. Expected Shortfall (ES). It does, as you suggest, take into account the whole set of returns. However, instead of traditional VaR which asks "what is the worst 1% or 5% loss I can expect" in a given time frame, conditional VaR asks "assuming I sustain losses of at least 95% or 99% (and perhaps am ...

7

Well all that you have cited seems quite all you can do with scenario maybe I can add another one which is portfolio dependent. Instead of looking to arbitrary scenarios you first decompose the factor to which you portfolio is the most sensitive to, and then look for scenarios that are specifically impacting this combination of risk factors. ...

7

You mention "daily" risk, so I'm assuming you're looking at a daily frequency. Yang-Zhang Volatility (Drift-independent Volatility Estimation Based on High, Low, Open and Close Prices) fits the bill for what you're asking, it takes into account intraday fluctuations as well.

7

About a year ago I saw a presentation by Attilio Meucci in London. The twist of his work is a little bit different compared to yours but the general approach is similar and there is lot to be learned from his accompanying paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1358533 Here he is also using PCA for dimensionality reduction constructing ...

7

I found this paper: Conditional value-at-risk for general loss distributions by Rockafellar and Uraysev http://dx.doi.org/10.1016/S0378-4266(02)00271-6 which says CVaR is coherent for general loss distributions, including discrete distributions. I think that I was confused by other authors who were also confused with the definitions of CVaR. In particular, ...

7

Yes. Check out the Lower Partial Moments literature. In my view the best introduction to this is Narwrocki - A Brief History of Downside Risk Measures. Uryasev established equivalence between CVaR approach and low partial moments. If Markowitz had the tools at the time time, LPM utility functions would be the introductory optimization model as opposed to ...

7

The "Component ES" section of ?ES says: For the decomposition of Gaussian ES, the estimated mean and covariance matrix are needed. For the decomposition of modified ES, also estimates of the coskewness and cokurtosis matrices are needed. The estimate of the coskewness and cokurtosis matrices are what take such a long time. You can calculate them ...

7

Nick Higham happens to have given a talk on this very subject this summer; he continues to actively work to improve nearest correlation matrix algorithms. You can see his talk and notes here: http://mxm.mxmfb.com/rsps/ct/c/629/r/90368/l/48110

6

To give an example of a source of risk that isn't one of the ones you mentioned but still broadly on-topic for a Quant Finance site: operational risk - for which there are many references for contigency plans. This is the domain of the back office. Trades are created (priced and analysed) by quants, executed by traders and approved by preferably at least one ...

6

Here's a partial answer: This partly depends on the return characteristics. One way to look at this is to analyze the skewness and kurtosis of the returns. Most strategies have a negative skewness, which roughly means that they have mostly consistent small positive returns, with the occasional large negative return. Alternatively, some strategies have ...

6

Each shop will differ - there is no widely used, unified framework shared across firms. Competitive advantages vary across shops, which ultimately reflect the biases/characteristics of the particular shop. Some will be far more mathematically sophisticated/inclined than others. Some maintain strong aversion to quantiative techniques such as risk models. ...

6

You could use something like the interquartile or semi-interquartile range, which is somewhat more insensitive to extremes. This is a better measure to use if your data is skewed, however if your data is normally distributed it is still better to use the standard deviation. http://en.wikipedia.org/wiki/Interquartile_range

6

$VaR^\alpha$ is not a coherent risk measure because it fails sub-additivity (a coherent risk measure is monotonic, sub-additive, positive homogenous, and translation invariant). The expectation operator $E[\cdot]$ is linear, so it meets sub-additivity, as well as the other three properties, so $CVaR$ is a coherent risk measure.

6

Glad people are reading. Simple with more history in terms of time and indexes is better in my book. I have spent 13 years reading over 200 research papers, incorporating complicated and advanced techniques, and studying very reputable buy side research with no improvement in results. Readers are on their own to extend to lots of markets including Nikkei ...

6

The short answer is that I don't know, but your question gives some hints about how to find out. The key thing for me is that you want a minimum variance portfolio. I don't think you should be thinking about some abstract mathematical operation that is "best", but rather look over a few mathematical operations and see which seems to work best for your ...

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