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Commercial risk models (e.g., [Barra][1], [Axioma][2], [Barclays][3], [Northfield][4]) have evolved to a very high level of sophistication. However, all of these models attempt to solve a very broad set of problems. The optimal risk model for, say, risk attribution in a fundamental portfolio may differ substantially ... |
When should you build your own equity risk model? |
I have been trading (mostly equity and equity index) options for a while now and I want to apply a slightly more quantitative approach to my trading - specifically, by calculating IV and incorporating it into my decision making process. BTW, I am referring to a "bog standard" BS model for exchange traded european and a... |
Can anyone give me a practical example of pricing and calculating IV on equity index options? (i.e. using real market data) |
Yahoo finance confidently provides [historic ratings][1] from a number of analysts. Unfortunately, each analyst seems to use a different scale: buy/hold/sell, perform/outperform/neutral, overweight/equal weight/underweight, etc.
I've already [written a function][2] to scrape this data into R, and I would like to ex... |
I am in the process of building zero coupon curves for some countries in the Eurozone.
I have the following data sets:
1. Euribor and EONIA
2. Swap rates
3. Bond price and yields
The bond prices (and thus yields) reflect the relative credit worthiness of the sovereign issuer (a point that has come to the for... |
The "industry standard" for calculating implied volatility is OptionMetrics. Chapter 3 of their [reference document][1] contains details of how they calculate all the inputs to the standard Black-Scholes model. They also have a [white paper][2] just on dividend yield forecasting, which can potentially be a major issu... |
How to assign analyst ratings to a common, numeric scale? |
I am in the process of building zero coupon curves for some countries in the Eurozone.
I have the following data sets:
1. Euribor and EONIA
2. Swap rates
3. Bond price and yields
The bond prices (and thus yields) reflect the relative credit worthiness of the sovereign issuer (a point that has come to the for... |
How to build the short end of a zero coupon curve for non-core Eurozone countries? |
How to assign equity analyst recommendations to a common, numeric scale? |
My objective is to measure the modified-CVAR for a portfolio given it's weights and matrix of security returns. Luckily the wonderful package PerformanceAnalytics has an ES() function that does just this.
Issue I am having is that modified-CVAR takes minutes to compute when according to this [paper][1] (by the same... |
Community Wiki question --
What are some quant theoretical or empirical insights that have shaped your thinking or provided a deeper conceptual basis for explaining returns and risk? |
Empirical or theoretical quant insights that have shaped your thinking? |
What are some quant theoretical or empirical insights that have shaped your thinking or provided a deeper conceptual basis for explaining returns and risk? |
Is there a free way to download the current prices (and possibly other data) for stocks for various companies?
Context: This is for a data source for a group programming project for a class. We weren't assigned this project or even a list of projects to pick from. If there isn't a way to do this for free, we'll do... |
Way to download current stock information (for free)? |
> **Possible Duplicate:**
> [What data sources are available online?](http://quant.stackexchange.com/questions/141/what-data-sources-are-available-online)
<!-- End of automatically inserted text -->
Is there a free way to download the current prices (and possibly other data) for stocks for various companies?
C... |
Wondering if anyone can recommend book on math, that explains the math symbology used in quantitative finance academic papers? |
Recommendation for a book to understand the math symbology in quant finance papers? |
How do you handle daily noise of daily price variations?
For example you may not care about 1% deviations from day to day in one stock vs 3% another day.
|
How do you handle noise? |
Can anyone recommend books that explain the math used in quantitative finance academic papers? |
Recommendations for books to understand the math in quantitative finance papers? |
I doubt you will find one book that covers everything you need, but here are a few that I continually come back to whenever I have some questions on the mathematics.
- [Analysis of Financial Time Series][1]
- [An Introduction to High-Frequency Finance][2]
- [Probability and Statistics][3]
- [Statistical Infer... |
I am currently trying to understand the in's and out's of options and more specifically hedging. I came across a document that was talking about Delta Hedging which is just making sure the delta of your overall position will be 0. But how do you hedge Omega(Time)? |
How do you distinguish between losses that are withing the normal range for day-to-day shifts and situations with a real potential for loss? The specific application I have in mind is pattern recognition-based algorithmic trading. |
How do you distinguish "significant" moves from noise? |
Deutsche Bank's Quantitative Strategy (US) team put together the [following piece][1] on this topic (note: their research is available for clients, but I found that somebody uploaded the piece to a sketchy web site). In case the link dies, some of the academic papers they site are:
- [Akbras, F., E. Kocatulum, and... |
Any research on how neuro-linguistic programming can be used to forecast stocks? |
This phenomenon is known as the "leverage effect." It was first pointed out by Black (1976) ["Studies of Stock Price Volatility Changes"]. It was studied in slightly greater detail by [Schwert (1989)][1]. A (relatively) more recent reference is [Figlewski and Wang (2000)][2].
[1]: http://www.jstor.org/pss/232... |
Have you considered a Monte Carlo simulation on your returns? Then you could look at the distribution of Maximum Drawdowns. |
When returns are auto-correlated, calculating a Sharpe ratio := $\frac {mean(x)}{\sqrt{var(x)}}$, (where $x$ are the returns) is complicated, but basically solved (see, e.g. [Lo (2005)][1]). Without the correction, the Sharpe ratio is too large, b/c auto-correlation reduces the variance of the returns.
However calcu... |
How do you correct Max Draw-Down for auto-correlation? |
Is it better to grade hedging strategies based on the sum of absolute or squared hedging errors? |
How can an ETF outperform its benchmark index? |
* Are there any other mechanisms at play here which might explain this kind of tracking error?
Dirk is right, you often lend the titles internally or not, etc.
You can also write calls for your index, this is not orthodox, but it's ETF, there is no orthodoxy there...
* Why the discrepancy between the fund's NAV ... |
* Are there any other mechanisms at play here which might explain this kind of tracking error?
Dirk is right, you often lend the titles internally or not, etc.
You can also write calls for your index, this is not orthodox, but it's ETF, there is no orthodoxy there...
Edit : With the graph and given the outperfor... |
Forewarning: this is a complete newbie question :-)
I am starting to learn about ETFs by trying to do the numbers. When learning about the compounding effect in leveraged ETFs, I wanted to simulate the return for a simple ETF. Here is what I wanted to do: a hypothetical index ETF gains 1% every day for a 10-day rang... |
You want to construct an optimal portfolio.
Let's say you have an alpha signal that arrives with some period (say quarterly). The alpha signal predicts arithmetic returns one-year ahead. You have risk estimates that are updated daily.
The optimizer your utility function is maximizing is expected returns from the... |
You want to construct an optimal portfolio.
Let's say you have an alpha signal that arrives with some period (say quarterly). The alpha signal predicts arithmetic returns one-year ahead. You have risk estimates that are updated daily.
The optimizer your utility function is maximizing is expected returns from the... |
When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve.
Is this completely accurate? It looks to me that the slope of the curve would be measured in dollars per yield, whereas duration is percentage change in price per yield? Hence they ac... |
In my mind, there are two questions here:
1) How does DB make money given a zero expense ratio?
This is covered by Dirk and Lliane. Basically, DB gets cheap funding and stock loan fees in return for paying marketing / index / hedging costs. The ETF investor gets zero expense ratio in return for taking DB credit... |
When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve.
Is this completely accurate? It looks to me that the slope of the curve would be measured in dollars per yield, whereas duration is percentage change in price per yield? Hence they ac... |
How to calculate compound returns of leveraged ETFs? |
When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right?
Duration is (change in price) divided by (price times change in yield). That's hardly the slope of the curve which would be (change in price) divided by (cha... |
Is Duration really the slope of the Price-Yield curve? |
How do you distinguish between losses that are within the normal range for day-to-day shifts and situations with a real potential for loss? The specific application I have in mind is pattern recognition-based algorithmic trading. |
Recently I was trying to reproduce the results of ["Intraday Patterns in the Cross-Section of Stock Returns"][2]. The authors used cross-sectional regression to determine which intraday lags have predictive power.
From my understanding when doing cross-sectional regression all variables have to be from the same tim... |
How do I reproduce the cross-sectional regression in "Intraday Patterns in the Cross-Section of Stock Returns"? |
Recently I was trying to reproduce the results of ["Intraday Patterns in the Cross-section of Stock Returns"][2]. The authors used cross-sectional regression to determine which intraday lags have predictive power.
From my understanding when doing cross-sectional regression all variables have to be from the same tim... |
How do I reproduce the cross-sectional regression in "Intraday Patterns in the Cross-section of Stock Returns"? |
Honstly, I have to disagree. I would almost always prefer sum of errors instead of squared sum of errors unless my holding periods were very short.
There is a good amount of vol in (especially closing) prices that would be real hedging errors . Imagine a trading strategy that is a near perfect hedge. Say trade SP... |
If you need a primer covering various domains of math, then [Dan Stefanica's text][2] will do the job.
Hull's [Options Futures, and Derivatives][1] is a classic.
[1]: http://www.amazon.com/Options-Futures-Other-Derivatives-6th/dp/0131499084
[2]: http://www.amazon.com/Primer-Mathematics-Financial-Engineerin... |
If you need a primer covering various domains of math, then [Dan Stefanica's text][1] will do the job.
Hull's [Options Futures, and Derivatives][2] is a classic that includes stochastic calculus.
Rene Carmona's "Statistical Analysis of Financial Data in S-Plus" covers a lot of ground with examples compatible with... |
If you need a primer covering various domains of math, then [Dan Stefanica's text][1] will do the job.
Hull's [Options, Futures, and Derivatives][2] is a classic that includes stochastic calculus and the topics in the title.
Here are the best applied statistics books:
Rene Carmona's "Statistical Analysis of Fi... |
If you need a primer covering various domains of math, then [Dan Stefanica's text][1] will do the job.
Hull's [Options, Futures, and Derivatives][2] is a classic that includes stochastic calculus and the topics in the title.
Here are the best applied statistics books:
Rene Carmona's "[Statistical Analysis of ... |
In their 1990 book, [A Non-Random Walk Down Wall Street][1], Andrew Lo and Craig MacKinlay document a number of persistent predictable patterns in stock prices. One of these "anomalies" is variously known as lead-lag or serial cross-correlation, and it says that the returns of larger, more liquid stocks tend to lead t... |
If you need a primer covering various domains of math then [Dan Stefanica's text][1] will do the job. The text covers multivariable calculus, lagrange multipliers, black scholes PDF, greeks & hedging, newton's method, boot strapping, taylor series, numerical integration, and risk neutral valuation. It also includes a m... |
I plan to develop a neural network to trade commodities futures, but while messing around with some code, a question came up. If I understand correctly, people use various technical indicators with their networks (moving average, MACD, etc.). However, how do these come into play in a machine learning context? Should I ... |
How to incorporate technical indicators into neural networks? |
Measuring expected shortfall (also known as conditional value-at-risk) answers the simpler question of "what is my average expected loss at the i-th quantile?" given the empirical distribution of returns. A variation is [value-at-risk][1] which measures the loss at the i-th quantile.
Arguably you could leave at this... |
Measuring expected shortfall (also known as conditional value-at-risk) answers the simpler question of "what is my average expected loss at the i-th quantile?" given the empirical distribution of returns. A variation is [value-at-risk][1] which measures the loss at the i-th quantile.
Arguably you could leave at this... |
If you asked me for a single book as a starting point I'd probably go for:
- [Frequently Asked Questions in Quantitative Finance][1] by Paul Wilmott
[1]: http://books.google.de/books?id=HtfetswOX30C&printsec=frontcover&source=gbs_atb#v=onepage&q&f=false |
I did check the related posts, like this one [here][1].
However, given if one already has knowledge in finance, machine learning and statistics, and wants to know something more advanced on machine learning based trading rather than the introductory. What would you recommend?
I am looking for anything related: e... |
Excellent information source on advanced machine learning / data mining based trading? |
I did check the related posts, like this one [here][1].
However, given if one already has knowledge in finance, machine learning and statistics, and wants to know something more advanced on machine learning based trading rather than the introductory. What would you recommend?
I am looking for anything related: e... |
If you need a primer covering various domains of math then [Dan Stefanica's text][1] will do the job. The text covers multivariable calculus, lagrange multipliers, black scholes PDF, greeks & hedging, newton's method, boot strapping, taylor series, numerical integration, and risk neutral valuation. It also includes a m... |
My question is much more an academic one as I am still a student but should prepare for interviews.
I have heard that SABR model was not good at pricing CMS. How is that?
Many thanks |
I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that? |
Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)? |
Are there ways to measure the risk aversion of a representative investor, based on publicly available market data? Public available data could include asset price, volume, and flow data, and may be aggregated according to some criterion (asset class and contract type being the most obvious). Pointers to any existing l... |
**This answer is my ongoing attempt to consolidate some recent commentary on this hot topic.**
A good place to start for anyone thinking about this question is the Economists's [Buttonwood: Not So Fast][1], which mentions recent research by [Biais and Woolley (2011)][2] and [Dichev, Huang, and Zhou (2011)][3].
[D... |
Suppose that you have a model of returns, and a representative agent whose form of utility function you have specified right off the bat. This RA can be constructed, under conditions, from a population that is defined to have heterogeneous utility objectives. This is the problem of aggregation, and it's treated in any ... |
Suppose that you have a model of returns, and a representative agent whose form of utility function you have specified right off the bat. This RA can be constructed, under conditions, from a population that is defined to have heterogeneous utility objectives. This is the problem of aggregation, and it's treated in ever... |
In the Quantitative Finance there are a lot of models which are formulated in terms of partial differential equations. For example the Black–Scholes model. I wonder what is a standard approach in Quantitative Finance to solve these equations? Do people use some general packages for solving differential equations (like ... |
What tools are used to numerically solve differential equations in Qunatitative Finance? |
What tools are used to numerically solve differential equations in Quantitative Finance? |
Deutsche Bank's Quantitative Strategy (US) team put together the [following piece][1] on this topic (note: their research is available for clients, but I found that somebody uploaded the piece to a sketchy web site). In case the link dies, some of the academic papers they site are:
- [Akbras, F., E. Kocatulum, and... |
Measuring expected shortfall (also known as conditional value-at-risk) answers the simpler question of "what is my average expected loss at the i-th quantile?" given the empirical distribution of returns. A variation is [value-at-risk][1] which measures the loss at the i-th quantile.
Arguably you could leave at this... |
There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these equations? Do people use some general packages for solving differential equations (like Maple, MATLAB or Mathematica)? O... |
How does Volatility affect the price of a Binary Option, in theory. A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now lets say you have a binary option priced at .30 as people do not believe it will be worth 1.00 at expiration. How much does Volat... |
- [Average net worth][1] of people at bogleheads forum is very strong argument.
- Also, [Dogs of the Dow][2] is interesting approach for long term investing.
[1]: http://www.bogleheads.org/forum/viewtopic.php?t=69175&sid=aba236c544030593768957b39df3913c
[2]: http://www.dogsofthedow.com/ |
Joel Greenblatt's "magic formula" is similar in spirit to classic value styles. He has a discussion of why he thinks it will continue to work (despite it's simplicity and public knowledge) around p. 73 in his Little Book that Beats the Market (see http://books.google.com/books?id=M5HxYZaNQEQC&lpg=PA68&dq=continue%20to... |
I did some digging and found the following papers - most of them offering quite a distinct perspective compared to classical option pricing theory!
- [Stock Options as Lotteries by Brian H. Boyer et al. (2011)][1]
- [The Efficiency of the Buy-Write Strategy: Evidence from Australia by Tafadzwa Mugwagwa et al. (2... |
I have a process that estimates the parameters for the following function using the [NL2SOL algorithm](http://people.sc.fsu.edu/~jburkardt/f77_src/nl2sol/nl2sol.html).
$C-[\alpha+\frac{\beta-\alpha}{1+e^-\theta(y_t-\delta)} \delta y_t]$
The process currently holds $\alpha$ and $\beta$ constant, so only $C$, $\the... |
I have a process that estimates the parameters for the following function using the [NL2SOL algorithm](http://people.sc.fsu.edu/~jburkardt/f77_src/nl2sol/nl2sol.html).
$C-[\alpha+\frac{\beta-\alpha}{1+e^-\theta(y_t-\delta)} \vartriangle y_t]$
The process currently holds $\alpha$ and $\beta$ constant, so only $C$,... |
To my ladies and gents in the credit space (or not), how do you use bond prices/yields to infer probabilities of default? I would think of it as follows:
Create a relationship between default free (ex: Germany) and defaultable (ex: Greece) bond prices and solve for p:
\tilde{B}(0,T) = B(0,T)rp + B(0,T)(1-p)
... |
To my ladies and gents in the credit space (or not), how do you use bond prices/yields to infer probabilities of default? I would think of it as follows:
Create a relationship between default free (ex: Germany) and defaultable (ex: Greece) bond prices and solve for p:
$$\begin{eqnarray}
\tilde{B}(0,T) = B(0,... |
I have a covariance matrix of security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise in the matrix).
I am performing some operations on the covariance matrix and the the input matrix must be positive semi-definite. What is the best way to "fix" the covariance matrix? (Fo... |
What is the best way to "fix" a covariance matrix that is not positive semi-definite? |
I have a covariance matrix of security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise in the matrix).
I am performing some operations on the covariance matrix and the input matrix must be positive semi-definite. What is the best way to "fix" the covariance matrix? (For wh... |
I have a covariance matrix of security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise in the matrix).
I am performing some operations on the covariance matrix and the input matrix must be positive semi-definite. What is the best way to "fix" the covariance matrix? (For wh... |
I have a covariance matrix of security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise in the matrix).
I am performing some operations on the covariance matrix and the input matrix must be positive semi-definite. What is the best way to "fix" the covariance matrix? (For wh... |
I have a covariance matrix of security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise in the matrix).
I am performing some operations on the covariance matrix and the input matrix must be positive semi-definite. What is the best way to "fix" the covariance matrix? (For wh... |
I have a covariance matrix of security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise in the matrix).
I am performing some operations on the covariance matrix and the input matrix must be positive semi-definite. What is the best way to "fix" the covariance matrix? (For wh... |
I have a covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix).
I am performing some operations on the covariance matrix and the input matrix must be positive semi-definite. What is the best way to "... |
I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix).
I am performing some operations on the covariance matrix and this matrix must be positive definite. What is the best way to "fix... |
I run a Johansen Cointegration test on 3 instruments, A B and C.
The result that I'm getting are:
R<=x | Test Stat | 90% | 95% | 99%
0 --> 36.7 | 18.9 | 21.1 | 25.8
1 --> 8.4 | 12.29 | 14.26 | 18.52
2 --> 0.21 | 2.7 | 3.8 | 6.6
----------------------------------... |
How do you use bond prices/yields to infer probabilities of default? I would think of it as follows:
Create a relationship between default free (e.g., Germany) and defaultable (e.g., Greece) bond prices and solve for $p$:
$$\begin{eqnarray}
\tilde{B}(0,T) = B(0,T)rp + B(0,T)(1-p) \\
\frac{1}{1+\tild... |
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