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What are some good technical and non-technical books for a math lover to get in to quantitative analysis?
I want to start learning quantitative finance, where would you advise me to start? Books? Sites? Thank you
Where should a beginner start with quantitative finance?
How do you model concentration risk in credit portfolio in IRB framework?
I like the following book (though have only very briefly skimmed it): 1. [Optimization methods in finance][1] [1]: http://books.google.com/books?id=Z7MQvs9CsoYC&lpg=PP1&ots=gcdk6AVkvT&dq=optimization%20finance%20t%C3%BCt%C3%BCnc%C3%BC&pg=PP1#v=onepage&q&f=false
It seems that VIX futures could be a great hedge for a long-only stock portfolio since they rise when stocks fall. But how many VIX futures should I buy to hedge my portfolio, and which futures expiration should I use?
One that I found via google that seems promising (for beginners though) is. [Numerical methods in finance and Economics][1] [1]: http://books.google.com/books?id=litw2D3bLwMC&lpg=PP1&dq=optimization%20methods%20finance&pg=PP1#v=onepage&q=optimization%20methods%20finance&f=false
At my work I often see option prices or vols quoted in terms of deltas rather than strikes. For example for March 2013 Zinc options I might see 5 quotes as follows: ZINC MARCH 2013 OPTION DELTA -10 POINTS ZINC MARCH 2013 OPTION DELTA -25 POINTS ZINC MARCH 2013 OPTION DELTA +10 POINTS ZINC MARCH 2...
What is the "delta" option quoting convention about?
I want to start learning quantitative finance, what articles or blogs should I look at to start? Also see the Related Question on [Quantitative Finance Books][1] [1]: http://quant.stackexchange.com/questions/1/what-are-some-good-technical-and-non-technical-books-for-a-math-lover-to-get-in-t
What blogs or articles online should I read to get started with quantitative finance?
My type is "[An introduction to the mathematics of financial derivatives][1]" by *Salih N. Neftci*. Though it's definitely harder to digest than *Hull*. [1]: http://books.google.com/books?id=mWzMpAex1_kC
There are [three different commonly used Value at Risk (VaR) methods][1]: - Historical method - Variance-Covariance Method - Monte Carlo What is the difference between these approaches, and under what circumstances should each be used? [1]: http://www.investopedia.com/articles/04/092904.asp
What is the difference between the methods for calculating VaR?
When using time-series analysis to forecast some type of value, what types of error analysis are worth considering when trying to determine which models are appropriate. One of the big issues that may arise is that successive residuals between the 'forecast' and the 'realized' value of the variable may not be proper...
What type of analysis is appropriate for assessing the performance time-series forecasts?
At my work I often see option prices or vols quoted against deltas rather than against strikes. For example for March 2013 Zinc options I might see 5 quotes available for deltas as follows: ZINC MARCH 2013 OPTION DELTA -10 POINTS ZINC MARCH 2013 OPTION DELTA -25 POINTS ZINC MARCH 2013 OPTION DELTA +10...
According to the [Wikipedia article][1], > Contracts similar to options are believed to have been used since ancient times. > In London, puts and "refusals" (calls) first became well-known trading instruments in the 1690s during the reign of William and Mary. > *Privileges* were options sold over the counter ...
Are there any empirical observations or practices when to prefer Local Volatility Model for pricing over Stochastic Model or vice versa?
When looking at option chains, I often notice that the (**broker calculated) implied volatility has an inverse relation to the strike price**. This seems true both for calls and puts. As a current example, I could point at the SPY calls for MAR31'11 : the 117 strike has 19.62% implied volatility, which decreaseses ...
Why does implied volatility show an inverse relation with strike price when examining option chains?
There are few methods like Copeland-Antikarov, Herath-Park, Cobb-Charnes etc. to compute project volatility, however these methods compute upward biased volatility. What is the best method I could use to compute project volatility for real option valuation?
What is the best method to compute project volatility in Real Option Valuation?
To add on to what others have said: the formula still does not provide a price -- just a way to calculate "implied" volatility. The BSM calculates a hypothetical value (using binary branchings as the storytelling tool) and this hypothetical merely provides a reference for this common "what-if" question. The only...
Consider the following strategies: - a stat arb strategy with no overnight exposure, but significant market exposure intraday. - a market timing model which is always long or short the market. - etc is it meaningful to consider the betas of strategies like these? Or should we ignore beta when the portfolio...
is beta of a portfolio always meaningful?
Assume we decompose the daily (log) returns of a stock as beta times market movement plus an idiosyncratic part. If this is done ex-ante, what proportion of the variance is explained by the market component vs. the idiosyncratic part? I am looking more for rule of thumb/experience of others, based on, say, U.S. equitie...
Approximately what proportion of a stock’s volatility is explained by market movement?
I'm currently using IB's java api and getting feeds through them. However the realtime feed is updated only every 250ms and the historical feed only every second. I want a setup that allows me to get more accurate data. Tick by tick would be ideal, but probably prohibitively expensive. What good/economical setups...
what broker/feed/api setup allows for recording the most accurate data (cheaply)?
Are prices for [C]MBS and other structured finance products created purely by the market for them? Or is there a theoretical/mathematical basis for their valuation? If so, is the methodology mostly consistent across different products?
How are prices calculated for commercial/residential mortgage-backed securities?
What is the theoretical/mathematical basis for the valuation of [C]MBS and other structured finance products? Is the methodology mostly consistent across different products?
It appears that the log 'returns' of the VIX index have a (negative) correlation to the log 'returns' of _e.g._ the S&P 500 index. The r-squared is on the order of 0.7. I thought VIX was supposed to be a measure of volatility, both up *and* down. However, it appears to spike up when the market spikes down, and has a fa...
Why does the VIX index have *any* correlation to the market?
Is there a standard model for market impact? I am interested in the case of high-volume equities sold in the US, during market hours, but would be interested in any pointers.
Is there a standard model for market impact?
One of the main problems when trying to apply **mean-variance portfolio optimization** in practice is its high input sensitivity. As can be seen in (*Chopra*, 1993) using historical values to **estimate returns expected in the future** is a no-go, as the whole process tends to become **error maximization** rather than ...
What methods do you use to improve expected return estimates when constructing a portfolio in a mean-variance framework?
A potential issue with automated trading systems, that are based on Machine Learning (**ML**) and/or Artificial Intelligence (**AI**), is the difficulty of assessing the risk of a trade. An ML/AI algorithm may analyze thousands of parameters in order to come up with a trading decision and applying standard risk managem...
I want to create a lognormal distribution of future stock prices. Using a monte carlo simulation I came up with the standard deviation as being sqrt(days/252)*volatility*mean*log(mean) Is this correct?
How to calculate future distribution of price using volatility?
A potential issue with automated trading systems, that are based on Machine Learning (**ML**) and/or Artificial Intelligence (**AI**), is the difficulty of assessing the risk of a trade. An ML/AI algorithm may analyze thousands of parameters in order to come up with a trading decision and applying standard risk managem...
"My intuition would be that volatility is a property of the underlying, and should therefore be roughly the same regardless of strike price". I agree, but the market doesn't. People who buy out-of-money calls tend to be more optimistic than those who buy at-the-money calls, so out-of-money calls are "overp...
I would like to take advantage of a volatile market by selling highs and buying lows. As we all know the RSI indicator is very bad and I want to create a superior strategy for this purpose. I have tried to model the price using a time varying ARMA process, with no success for now. Any other ideas?
I may be off base here. But in terms of econometrics, when you calculate beta, you've assumed that the idiosyncratic portion is white noise. So the idiosyncratic portion is mean zero and normally distributed so it accounts for none of the return. So the ratio of market:idiosyncratic is 1:0. By definition the idiosyn...
How does pair trading work?
Ed Thorp is of the opinion that he could price options properly before Fischer and Myron: [link here (doc)][1] Sounds like he was using a risk-neutral approach [1]: http://www.google.ca/url?sa=t&source=web&cd=3&ved=0CCkQFjAC&url=http%3A%2F%2Fwww.edwardothorp.com%2Fsitebuildercontent%2Fsitebuilderfiles%2Fopti...
In response to your last question, "how do you use beta?" - I'd say try to as little as possible. Your use seems to be a bit out of the realm of what I'm used to, but whatever beta you get is so prone to observational error, that it may not be meaningful.
Short of having a 'reasonable' predictive model for expected returns and the covariance matrix, there are a couple lines of attack. 1. Shrinkage estimators (via Bayesian inference or Stein-class of estimators) 2. Robust portfolio optimization 3. Michaud's Resampled Efficient Frontier 5. Imposing norm constrai...
There is a missing link to early options pricing literature which had been overlooked. Put-call parity along with static delta hedging were understood in actionable detail well before BSM and trading and risk management were accomplished through heuristic methods which indeed continued to be used after BSM. Would po...
There is another reason why Stoc Vol Models should be usually prefered to Local vol Models, this reason is explained in the Hagan et al. paper ["Managing smile Risk"][1] about SABR process and is in simple terms the fact that "smile dynamics" is poorly predicted by local vol models leading to bad Hedging of exotic opti...
Naively, it seems that Bayesian modeling, structural models particularly, would be quite useful in finance because of their ability to incorporate market idiosyncrasies and produce accurate probabilistic estimates. The down-side of course, is model-brittleness and extremely slow computational speed. Has the Quant c...
Use of MCMC in Finance?
Are the prices of e-minis such as S&P 500, Russell 2000, EUROSTOXX, etc. manipulated? That is, are there traders who trade large enough positions to make the price go in the direction they want, taking unfair advantage of the rest of the traders in that market? If so, what implication does this have for designing an...
Are e-mini markets manipulated?
Mean-reversion and trend-following strategies have some kind of a theory behind them that explains why they might work, if implemented well. Pattern-recognition, on the other hand, seems like nothing more than data mining and overfitting. Could patterns possibly have any predictive value? In other words, is there any ...
Is there any theoretical basis for pattern-recognition strategies?
I heart so far about MetaTrader from http://www.metaquotes.net . Is there any other framework or program available. Do u use different software for backtracking and running your trading algorithmus?
What kind of basic framework or application you use to run your trading algorithmus?
I know the derivation of the Black Scholes differential equation and I understand (most) of the solution of the diffusion equation. What I am missing is the transformation from the Black Scholes differential equation to the diffusion equation (with all the conditions) and back to the original problem. All the transf...
Back in the mid 90's I used the Black-Scholes Model and the Cox-Ross-Rubenstein (Binomial) Model's to price Options. That was nearly 15 years ago and I was wondering if there are any new models being used to price Options?
Are there any new Option pricing models?
Weak form market efficiency says that you can't predict prices based on past prices. Or that technical analysis doesn't work. I think that the tests of weak form market efficiency are pretty conclusive and show that the US stock market is weak-form efficient; at least on a a timeline longer than a few minutes. That'...
Some of us see this as a data-driven, empirical problem. And for *Programming with Data*, you could do a lot worse than picking [R](http://www.r-project.org) which was made for the task. The [CRAN Task View on Finance](http://cran.r-project.org/web/views/Finance.html) lists a number of relevant packages. For trading...
A few pointers: - When I looked into this a few years ago, a good solution at the time was [LIM's XMIM][1], which also has an S-Plus/Matlab interface. This provides both the data and the software for analysis. - On the very high end (and expensive) side of the spectrum, [OneTick][2] and [KDB][3] are both being u...
What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in portfolio choice?
What is a "coherent" risk measure?
A few pointers: - When I looked into this a few years ago, a good solution at the time was [LIM's XMIM][1], which also has an S-Plus/Matlab interface. Whit Armstrong also provided [an R package][2] for this, although I don't know how complete it is. This provides both the data and the software for analysis. - O...
Some of us see this as a data-driven, empirical problem. And for *Programming with Data*, you could do a lot worse than picking [R](http://www.r-project.org) which was made for the task. The [CRAN Task View on Finance](http://cran.r-project.org/web/views/Finance.html) lists a number of relevant packages. For trading...
I ve struggled for a long time to understand this - What is this? And how does it affect you?
I'm currently using IB's java api and getting feeds through them. However the realtime feed is updated only every 250ms and the historical feed only every second. I'm primarily looking for ES data and other index futures and ETFs. I'm not looking at FX since that data is the most subjective since there is no exchang...
Any recommendations on the best schools and overall education choices for quantitative finance?
What are the best master programmes for someone interested in a career in quantitative finance?
Quantnet provided a [rankings of MS in Financial Engineering programs][1], which can be used for reference. More generally, this really depends on what area of quantitative finance that interests you: If you want to work in developing valuation and pricing models, than one of these programs will be very useful. If...
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 wou...
I ve struggled for a long time to understand this - What is this? And how does it affect you? Yes I mean risk neutral pricing - Paul Willmots forums was not clear about that
How do you model concentration risk of credit portfolio in IRB/Basel II framework?
[DTN's IQFeed][1] is really good, if a little expensive. I believe it starts at 80 dollars/month and then you add your exchange fees on top. To get access to the developer API you need to pay 300 dollars for a year's worth of access. Features: - Real-Time, TRUE Tick-by-Tick Data on US and Canadian Equities (NYSE...
One starts with the Black-Scholes equation $$\frac{\partial C}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2 C}{\partial S^2}+ rS\frac{\partial C}{\partial S}-rC=0,\qquad\qquad\qquad\qquad\qquad(1)$$ supplemented with the terminal and boundary conditions (in the case of a European call) $$C(S,T)=\max(S-K,0),\q...
_I am not very sure, if this question fits in here._ I have recently begun, reading and learning about machine learning. Can someone throw some light onto how to go about it or rather can anyone share their experience and few basic pointers about how to go about it or atleast start applying it to see some results fr...
How can I go about applying machine learning algorithms to stock markets?
How do I price OANDA box options without using their slow and machine-unfriendly user interface?: - fxtrade.oanda.com (free demo account) sells "box options": - If you already know what a box option is (or visit http://fxtrade.oanda.com/trade-forex/fxtrade/box-options or signup for a free ...
Since Mandelbrot, Fama and others have performed seminal work on the topic, it has been suspected that stock prices fluctuations can be more appropriately modeled using Lévy alpha-stable distrbutions other than the normal distribution law. Yet, the subject is somewhat controversial, there is a lot of literature in defe...
[DTN's IQFeed][1] is really good, if a little expensive. I believe it starts at 80 dollars/month and then you add your exchange fees on top. To get access to the developer API you need to pay 300 dollars for a year's worth of access. Details: - Real-Time, TRUE Tick-by-Tick Data on US and Canadian Equities (NYSE,...
There is a fairly recent (2010) [monograph][1] 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 m...
I heard so far about MetaTrader from [http://www.metaquotes.net][1]. Is there any other framework or program available. Do you use different software for backtracking and running your trading algorithms? [1]: http://www.metaquotes.net
What kind of basic framework or application you use to run your trading algorithms?
I heard so far about MetaTrader from [http://www.metaquotes.net][1]. Is there any other framework or program available. Do you use different software for backtracking and running your trading algorithms? Thank you guys for your great answers. I will check out the posted applications. [1]: http://www.metaquotes....
Suppose you have two sources of covariance forecasts on a fixed set of $n$ assets, method A and method B (you can think of them as black box forecasts, from two vendors, say), which are known to be based on data available at a given point in time. Suppose you also observe the returns on those $n$ assets for a following...
How do you evaluate a covariance forecast?
Since Mandelbrot, Fama and others have performed seminal work on the topic, it has been suspected that stock price fluctuations can be more appropriately modeled using Lévy alpha-stable distrbutions other than the normal distribution law. Yet, the subject is somewhat controversial, there is a lot of literature in defen...
Maybe you think about other model than a diffusion ? There is an article on [wilmott.com][1] about the Korn-Kreer-Lenssen Model. [1]: http://www.wilmott.com/detail.cfm?articleID=346
So my first answer was off base. For some reason I was thinking first moment (idiosyncratic returns), but he's looking for second moment (idiosyncratic volatility). There is a line of research on the returns to portfolios sorted on idiosyncratic volatility and I was hoping that there were descriptive statistics that sa...
So my first answer was off base. For some reason I was thinking first moment (idiosyncratic returns), but he's looking for second moment (idiosyncratic volatility). There is a line of research on the returns to portfolios sorted on idiosyncratic volatility and I was hoping that there were descriptive statistics that sa...
I heard about MetaTrader from [http://www.metaquotes.net][1]. Is there any other framework or program available. Do you use different software for backtracking and running your trading algorithms? Thank you guys for your great answers. I will check out the posted applications. [1]: http://www.metaquotes.net
What kind of basic framework or application do you use to run your trading algorithms?
I am currently trading futures products on some contracts that have low volumes. More accurately, the volumes of working orders in the book are fairly light. I am trying to execute a relatively large order that could move the market. I would like to break the order up to prevent this but I am unsure of the best algorit...
Does anyone common with Cubature on Wiener Spaces could explain why (i.e. with a detailed proof or a reference) some weak schemes such as those of Ninomiya-Victoir or Ninomiya-Ninomiya can be seen as a Cubature scheme over Wiener Spaces ? Those weak schemes are typicaly used for discretization of stochastic volatili...
The sensitivity of the option value $V$ to volatility $\sigma$ (a.k.a. vega) is different from the other greeks. It is a derivative with respect to a parameter and not a variable. To quote from *Paul Wilmott On Quantitative Finance* (Wiley, 2nd edition, p. 127): > It’s not even Greek. Among other things it is an Ame...