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since the underlying of spx is SP500, while SPY is the ETF which tracks sp500, i think there should be an obvious connection of the two implied vol curves from SPX market and SPY market. A very simple idea would be : with the same expiration date (while one is AM and other is PM), for the strike has the same log moneyn... |
What's the connection between implied vol curve of SPX and SPY? |
Since the underlying of SPX is SP500, while SPY is the ETF which tracks sp500, I think there should be an obvious connection of the two implied vol curves from the SPX and SPY markets.
A very simple explanation would be : with the same expiration date (while one is AM and the other one is PM), for the strike at the ... |
I think there should be an obvious connection of the two implied vol curves from the SPX and SPY markets since the underlying of SPX is SP500, while the underlying of SPY is a ETF which tracks sp500 index
A very simple idea would be : with the same expiration date (while one is AM and the other one is PM), for the ... |
Can social media sites, like Twitter, be used to analyze financial markets for algorithmic trading? How much research has been done on this topic? |
Can social media be applied to algorithmic trading? |
Is there any measure being non-trivial combination of VWAP and TWAP ?
Trivial is for example VTWAP=(VWAP+TWAP)/2.
I'm thinking about something like this:
VTWAPexp(alfa,T)=sum ( Pi * Vi * exp(-i * alfa) )/sum(Vi * exp(-i * alfa))
where Pi is price at time t=T-i+1 and Vi is volume at time t=T-i.
Influence ... |
Is there any measure being non-trivial combination of VWAP and TWAP? |
Is there any measure that is a non-trivial combination of VWAP and TWAP? For example:
\begin{equation}
VTWAP = \frac{VWAP+TWAP}{2}
\end{equation}
I'm thinking about something like this:
\begin{equation}
VTWAPexp(\alpha,T) = \frac{\sum{P_i * V_i * e^{-i*\alpha}}}{\sum{V_i * e^{-i*\alpha}}}
\end{equation}
... |
Is there any measure that is a non-trivial combination of VWAP and TWAP? |
Is there any measure that is a non-trivial combination of VWAP and TWAP? For example:
\begin{equation}
VTWAP = \frac{VWAP+TWAP}{2}
\end{equation}
I'm thinking about something like this:
\begin{equation}
VTWAPexp(\alpha,T) = \frac{\sum{P_i * V_i * e^{-i*\alpha}}}{\sum{V_i * e^{-i*\alpha}}}
\end{equation}
... |
Is there any measure that is a non-trivial combination of VWAP and TWAP? For example:
\begin{equation}
\textrm{VTWAP} = \frac{\textrm{VWAP}+\textrm{TWAP}}{2}
\end{equation}
I'm thinking about something like this:
\begin{equation}
\textrm{VTWAP}_{\textrm{exp}}(\alpha,T) = \frac{\sum{P_i * V_i * e^{-i*\alpha}... |
I have a future on a two-year UK government bond that I wish to price. The bond future expires in 3 months. I was thinking of building a portfolio of 3-month deposit futures (1 x 3 month deposit starting in 3 months, 1 x 3 month deposit starting in 6 months and so on out to 2 years + 3 months). My intuition leads me... |
Is there any measure that is a non-trivial combination of VWAP and TWAP? For example:
\begin{equation}
\textrm{VTWAP} = \frac{\textrm{VWAP}+\textrm{TWAP}}{2}
\end{equation}
I'm thinking about something like this:
\begin{equation}
\textrm{VTWAP}_{\textrm{exp}}(\alpha,T) = \frac{\sum{P_i * V_i * e^{-i*\alpha}... |
Is there any measure that is a non-trivial combination of VWAP and TWAP? For example:
\begin{equation}
\textrm{VTWAP} = \frac{\textrm{VWAP}+\textrm{TWAP}}{2}
\end{equation}
I'm thinking about something like this:
\begin{equation}
\textrm{VTWAP}_{\textrm{exp}}(\alpha,T) = \frac{\sum{P_i * V_i * e^{-i*\alpha}... |
(Original Post - http://math.stackexchange.com/questions/107879/portfolio-optimization-problem-without-correlation-info)
I received this interesting problem from a friend today:
Assume that you are a portfolio manager with $10 million to allocate to hedge funds. The due diligence team has identified the following i... |
I am able to retrieve prices for IVV using this code
library(quantmod)
getSymbols("IVV")
names(IVV)
[1] "IVV.Open" "IVV.High" "IVV.Low" "IVV.Close" "IVV.Volume"
[6] "IVV.Adjusted"
Is it possible to use other libraries/sources/functions to get a price at 10am, noon, and 2pm?
... |
How can I get intra-day prices via API into R? |
You dont pay anything for IB's API (they charge some for Fix through). It is a very simple and straightforward way to pull IVV through the IB API, either IVs directly (I dont recommend it because you inherently accept IB's dividend curves, model, what have you...). Better yet, pull in the prices of the options under co... |
(Here is a link to the [original post][1])
I received this interesting problem from a friend today:
Assume that you are a portfolio manager with $10 million to allocate to hedge funds. The due diligence team has identified the following investment opportunities (here Expected Return and Expected StdDev stand fo... |
Can I perform an asset allocation optimization if assets are perfectly uncorrelated? |
There's no problem at all using mean-variance optimization when correlations are zero. Any Quadratic Program solver will give you optimal weights. The problem is that the optimal weight a QP will give you will not, in general, result in dollar allocations that are integer multiples of the Price. To enforce that cons... |
I have a future on a two-year UK government bond that I wish to price. The bond future expires in 3 months. I was thinking of building a portfolio of 3-month deposit futures (1 x 3 month deposit starting in 3 months, 1 x 3 month deposit starting in 6 months and so on out to 2 years + 3 months). My intuition leads me... |
I would like to know how Expected Shortfall $SF_\alpha$ and variance $\sigma^2$ are related.
If I follow what [Aaron Brown][1] answered in [this post][2], when the underlying distribution is Normal with standard deviation $\sigma$, then:
$$VaR_\alpha=\Phi^{-1}(\alpha) \cdot \sigma$$
and
$$SF_\alpha= \frac{... |
How are Expected Shortfall and Variance related? |
The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put).
Is there a smallerstandard deviation (in price terms) to the upside vs. downside?
How is this difference expressed in a model?
Thanks in advance. |
The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put).
Is there a smaller standard deviation (in price terms) to the upside vs. downside?
How is this difference expressed in a model?
|
As all research on the momentum strategy are focused on the indicator, i.e. the entry point. There seem not much discussion on the expected returns of momentum signals? Though there are some discussions on the exit rule, it sill not clearly quantifies the expected profits in advance. Not like a mean-reversion strategy,... |
What is the expected return I should use for the momentum strategy in MV optimization framework? |
As all research on the momentum strategies are focused on the indicator, i.e. the entry point, there seems not much discussion on its expected return? Though there are some discussions on the exit rules, it still doesn't clearly quantify the expected profit in advance. Not like a mean-reversion strategy, where its expe... |
I can help you beat random walk 'in the way you want', i.e. the expected value E[\$] will always be positive even assuming no drift. However, I have to warn people that E[\$] > 0 is NOT really an adequate condition for 'beating' in reality (at least to myself).
Let's define some mathematical notations for derivatio... |
The Quantitative Finance Stack Exchange is intended for **professionals** and **academics** involved in quant modeling or trading. **Basically, if you aren't earning a living at this, it's probably off topic.**
Good questions are focused on an **actual problem you face in the course of your work** as a quant or academ... |
has there been any interesting work or advances on the copula-marginal algorithm (CMA) as proposed by
Attilio Meucci. I am unable to find anything on the web other then the original article, here is the [original article][1] that i am referring too. I'm just curious if any one has built on his research or if this may... |
I have been playing a quantitative investing game (instructions [here][1]) that is actually quite interesting, teams have some time to decide their next moves. It requires all kind of knowledge such as spreadsheet -programming, residual -analysis, portfolion -management, allocation, XYZ -- variables and in the end the ... |
Quantitative Analysis Games on Investing? |
Explain pair trading to a layman. What is it, why would you want to do it, and what are the risks? Provide a real life example. |
The algorithm is certainly useful in that it is non-parametric. [Meucci][1] summarizes the advantages nicely:
> Unlike traditional copula techniques, CMA a) is not restricted to few
> parametric copulas such as elliptical or Archimedean; b) never
> requires the explicit computation of marginal cdf’s or quantile
>... |
The algorithm is certainly useful in that it is non-parametric, fast, and versatile. [Meucci][1] summarizes the advantages nicely:
> Unlike traditional copula techniques, CMA a) is not restricted to few
> parametric copulas such as elliptical or Archimedean; b) never
> requires the explicit computation of marginal... |
Are there libraries in R for estimating time-varying joint distributions via copulas?
Hedibert Lopes has an excellent [paper][1] on the topic here. I know there is an existing packaged called [copula][2] but it fits a static copula.
[1]: http://faculty.chicagobooth.edu/hedibert.lopes/research/pdf/ausin-lopes-... |
I don't know if this is the right forum in which to ask this question, but here goes. I'm working through Luenberger's Investment Science. The form of CAPM model given in the book is
$$\bar{r}_i - r_f = \beta_i (\bar{r}_M - r_f)$$
It says that if your asset has a $\beta$ of zero, then $\bar{r}_i = r_f$. The book ... |
I wanted to see how the stock price and volume relationship is locally.
So I tried ranking both the daily return (at day t) and volume (at day t) base on a 30 day rolling window with historical daily stock data and plotted the distribution as shown in the below figure (top). The ranking is sorted ascendingly, and a... |
I wanted to see how the stock price and volume relationship is locally.
So I tried ranking both the daily return (at day t) and volume (at day t) base on a 30 day rolling window with historical daily stock data and plotted the distribution as shown in the below figure (top). The ranking is based on sorting values i... |
I can help you beat random walk 'in the way you want', i.e. the expected value $E[\$]$ will always be positive even assuming no drift. However, I have to warn people that $E[\$] > 0$ is NOT really an adequate condition for 'beating' in reality (at least to myself).
Let's define some mathematical notations for deriv... |
I am trying to evaluate weight of stocks in portfolio for an investor. For this purpose
I use SEC13F filings for particular quarters and historical prices from Yahoo. There are stocks in portfolio which have zero volume from time to time. Is it correct to use price when volume is zero? Should I just ignore these sto... |
Background: For a dissertation I have a multi-agent stock market model that I am using to assess different mechanisms for producing particular dynamic regimes. A key point is assessing how closely it reflects the real world, this will be done by comparing it with historical price data of 5 large-caps in 5 different sec... |
How to use volatility to assess the accuracy of a stock market model? |
How to annualize log returns? |
My intuition says that both approaches, discrete time models and continuous time models will be *models* (i.e. approximations) of reality. Therefore it should be possible to develop useful models in both domains.
*Continuous time models* have more mathematical elegance and can therefore probably bring more mathemat... |
What are the main differences between discrete and continuous time models when modeling asset price dynamics? |
If I have calculated the sample mean, variance, skew and kurtosis of a set of data, how would I go about fitting a probability distribution to match these moments (i.e. choosing a probability distribution and optimizing its parameters to fit the sample moments). Are there any packages in R/MATLAB/etc. that are capable ... |
How to fit probability density function from sample moments? |
I want to know the joint dynamics of a stock and it's option for a finite number of moments between now and $T$ the expiration date of the option for a number of possible paths.
Let $r_{\mathrm{s}}$ and $r_{\mathrm{o}}$ denote the return on the stock and the option. Then I'm interested in knowing $\mathrm{E}_t([r_{... |
I want to know the joint dynamics of a stock and it's option for a finite number of moments between now and $T$ the expiration date of the option for a number of possible paths.
Let $r_{\mathrm{s}}$ and $r_{\mathrm{o}}$ denote the return on the stock and the option. Then I'm interested in knowing $\mathrm{E}_t([r_{... |
Brealey & Myers provide a certainty-equivalent version of the present value rule, using CAPM, as follows:
$$PV_0=\frac{C_1 - \lambda_m *cov(C_1, r_m)}{1 + r_f}$$
$PV_0$ - Present Value of cash flow 1 at time 0.
$\lambda_m$ - Market price of risk = $\frac{r_m-r_f}{\sigma_m^2}$
$cov(C_1, r_m)$ - Covariance of... |
Suppose you backtest the EUR/USD (or GBP/USD) forex pair with this system on the 1min timeframe:
1) Enter the market at any time n: go long if the "future" bar n+1 has a higher close as the close on bar n; go short otherwise
2) Place a stop loss of 50 pips and a take profit target of 25 pips
Clearly, with this... |
Suppose you backtest the EUR/USD (or GBP/USD) forex pair with this system on the 1min timeframe:
1) Enter the market at any time n: go long if the "future" bar n+1 has a higher close as the close on bar n; go short otherwise
2) Place a stop loss of 50 pips and a take profit target of 25 pips
Clearly, with this... |
To be honest I dont fully comprehend your question. Not sure what you try to achieve. You should however not occupy yourself with questions that imply the impossible -> looking ahead. You stand at time t and must make a decision to trade or not to trade and if you trade then in what direction, how much notional, what k... |
Suppose you backtest the EUR/USD (or GBP/USD) forex pair with this system on the 1min timeframe:
1) Enter the market at any time n: go long if the "future" bar n+1 has a higher close as the close than bar n; go short otherwise
2) Place a stop loss of 50 pips and a take profit target of 25 pips
Clearly, with th... |
Yeah I'm talking about the CBOE published index VIX and SKEW.
To start with, I consider the variance dynamics and calibrate the market data into the Heston model, then it's not hard to derive the dynamics of VIX.
But how about SKEW, how could I relate the Heston Model to it? Or I shall employ further stochastic ... |
SKEW and VIX relations? |
Yeah I'm talking about the CBOE published index VIX and SKEW.
To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX,VIX futures) into the Heston model, then it's not hard to derive the dynamics of VIX.
But how about SKEW, how could I relate the Heston Model to it? O... |
My question is about the CBOE published index VIX and SKEW.
To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston model. After that it's not hard to derive the dynamics of VIX.
But how about SKEW, how could I relate the Heston Model ... |
How to calculate underlying implied volatility from ATM (near month) option prices? |
Is there an open source alternative to Reuters Kondor+?
Basically, I'm looking for a system which have trading(in a demo account), book keeping, profit/loss and risk calculation capability across different asset classes such as bond, repo, equity, foreign exchange, derivatives etc.
Thanks!
|
How to calculate COMPOSITE underlying implied volatility from ATM (near month) option prices? |
There is a relationship:
$ \log \delta^{-1} = \frac{\sqrt{Var[r(t)]}}{\sqrt{p(1-p)}}$
Which relates the jump size to the volatility of short rate and risk neutral jump probability.
The vol of short rate is chosen to be const in basic model, could be time-varying, but makes things complicated.
To solve for $\... |
Brealey & Myers provide a certainty-equivalent version of the present value rule, using CAPM, as follows:
$$PV_0=\frac{C_1 - \lambda_m *cov(C_1, r_m)}{1 + r_f}$$
$PV_0$ - Present Value of cash flow 1 at time 0.
$\lambda_m$ - Market price of risk = $\frac{r_m-r_f}{\sigma_m^2}$
$cov(C_1, r_m)$ - Covariance of... |
Brealey & Myers provide a certainty-equivalent version of the present value rule, using CAPM, as follows:
$$PV_0=\frac{C_1 - \lambda_m *cov(C_1, r_m)}{1 + r_f}$$
$PV_0$ - Present Value of cash flow 1 at time 0.
$\lambda_m$ - Market price of risk = $\frac{r_m-r_f}{\sigma_m^2}$
$cov(C_1, r_m)$ - Covariance of... |
These questions are in regards to the Kalman filter and the Hough Transform.
What are the Pros and Cons of using each method?
In what situations is it better to prefer one over the other?
|
There is a rationale here and it has to do with the connection between diversification and portfolio size.
Suppose we purchase an equal-weighted portfolio of *n* stocks. The variance of the return is then:
$\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_j$Cov($R_i$,$R_j$)
* note the sigmas are summing over $i$ and $j$ ... |
There is a rationale here and it has to do with the connection between diversification and portfolio size.
Suppose we purchase an equal-weighted portfolio of *n* stocks. The variance of the return is then:
$\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_j$Cov($R_i$,$R_j$)
-- note the sigmas are summing over $i$ and $j$... |
There is a rationale here and it has to do with the connection between diversification and the number of assets in a portfolio.
Suppose we purchase an equal-weighted portfolio of *n* stocks. The variance of the return is then:
$\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_j$Cov($R_i$,$R_j$)
-- note the sigmas are sum... |
If I send a market order with quantity greater than quantity of the inside quote at that exchange and if another exchange has quantity to fill the residual portion at NBBO, will my order by routed to that exchange ? Will I be charged a routing fee ? How does the exchange decide where to route the order in case of a tie... |
I'm using Idzorek's version of the Black-Litterman model for estimating asset returns. Idzorek's version bypasses the need to estimate directly the covariance matrix $\Omega$ of errors in the various views by allowing an investor to specify confidence levels for each view. The entries in $\Omega$ can then be calculat... |
What are some quantitative ways to obtain the view confidences in Idzorek's version of Black-Litterman? |
The minimum variance solution loads up on securities that have low variances and co-variances. Theoretically you are correct that this should have a low expected return profile.
However, it turns out - in contradiction to modern portfolio theory - that securities that have low-volatility or low-beta experience *high... |
The primary alternative to Bayesian subjective probabilities is the frequentist approach. This would involve measuring the % of times where international bonds outperformed US bonds by 25 bps over the relevant period in market history and using that as your confidence level.
A quantitative view in-between the Bayesi... |
The primary alternative to Bayesian subjective probabilities is the frequentist approach. This would involve measuring the % of times where international bonds outperformed US bonds by 25 bps over the relevant period in market history and using that as your confidence level.
A quantitative view in-between the Bayesi... |
I'm not sure if this question is a better fit http://money.stackexchange.com or here.
Are there any online tools (ideally I can invoke with uncomplicated fetchers like `wget`) that given an existing portfolio, calculate how well a new candidate position would score to increase combined diversification/decrease risk?... |
I'm not sure if this question is a better fit at http://money.stackexchange.com or here.
Are there any online tools (ideally I can invoke with uncomplicated fetchers like `wget`) that given an existing portfolio, calculate how well a new candidate position would score to increase combined diversification/decrease ri... |
Where can I find some examples of high frequency or stat arb trading algorithms beyond basic textbook pairs trading? |
I'm not sure if this question is a better fit at http://money.stackexchange.com or here.
Are there any online tools (ideally I can invoke with uncomplicated fetchers like `wget`) that given an existing portfolio, calculate how well a new candidate position would score to increase combined diversification/decrease ri... |
Not Purely Tactical however some of this should answer your question:
I included the minimum variance portfolio as a "active" (with lots of rebalancing)
Value and Momentum: http://pages.stern.nyu.edu/~lpederse/papers/ValMomEverywhere.pdf
A tl;dr: long undervalued stocks (book/market) that have strong up momentum... |
I am not sure they are comparable as they serve for slightly different purposes. In robotics (specifically vision), Hough Transform is used for objects (or shape) detection. This can subsequently be used for objects tracking, but Hough Transform has no prediction phase. On the other hand, Kalman Filter is a two phase a... |
There is a rationale here and it has to do with the connection between diversification and the number of assets in a portfolio.
Suppose we purchase an equal-weighted portfolio of *n* stocks. The variance of the return is then:
$\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_j$Cov($R_i$,$R_j$)
-- note the sigmas are sum... |
There is a rationale here and it has to do with the connection between diversification and the number of assets in a portfolio.
Suppose we purchase an equal-weighted portfolio of *n* stocks. The variance of the return is then:
$\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_j$Cov($R_i$,$R_j$)
In the above notation, t... |
There is a rationale here and it has to do with the connection between diversification and the number of assets in a portfolio.
Suppose we purchase an equal-weighted portfolio of *n* stocks. The variance of the return is then:
$\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_j$Cov($R_i$,$R_j$)
In the above notation, t... |
There is a rationale here and it has to do with the connection between diversification and the number of assets in a portfolio.
Suppose we purchase an equal-weighted portfolio of *n* stocks. The variance of the return is then:
$\sigma_{p}^2$ = $\sum$ $\sum$ $w_i$$w_j$Cov($R_i$,$R_j$)
In the above notation, t... |
When it comes to comparing returns of instruments like stocks, are there any "official" formulas, or ones in common use, that place greater emphasis on recent correlations more than on historical correlations farther in the past?
An analogy could be the relationship between a *simple moving average* and an *expon... |
Isn't this a simple mathematical rule?
$$\Delta r_{t}=r_{t} - r_{t-1} = ln(p_{t}) - ln(p_{0}) - ln(p_{t-1}) + ln(p_{0})=ln(\frac{p_{t}}{p_{t-1}})$$
i.e. logarithmic or continuously compounded return. As a result:
$$E=\sum_{t=1}^{T}\Delta r_{t} = \sum_{t=1}^{T}ln(\frac{p_{t}}{p_{t-1}})=ln(\prod_{t=1}^{T}\frac{p_{t}... |
If I send a market order to an exchange with quantity greater than the quantity of the inside quote at this exchange, and if another exchange has quantity to fill the residual portion at NBBO, will my order by routed to that exchange? Will I be charged a routing fee? How does the exchange decide where to route the orde... |
When it comes to comparing returns or prices of instruments like stocks/ETFs, are there any well-established formulas, or ones in common use, that place stronger emphasis on recent correlations more than on historical correlations farther in the past?
An analogy could be the relationship between a *simple moving a... |
I don't know if this is the right forum in which to ask this question, but here goes. I'm working through Luenberger's Investment Science. The form of CAPM model given in the book is
$$\bar{r}_i - r_f = \beta_i (\bar{r}_M - r_f)$$
It says that if your asset has a $\beta$ of zero, then $\bar{r}_i = r_f$. The book ... |
I don't know if this is the right forum in which to ask this question, but here goes. I'm working through Luenberger's Investment Science. The form of CAPM model given in the book is
$$\bar{r}_i - r_f = \beta_i (\bar{r}_M - r_f)$$
It says that if your asset has a $\beta$ of zero, then $\bar{r}_i = r_f$. The book ... |
Quantitative finance formular are mostly based on martingales, Poisson jump, GBM, CEV, etc..
The logic behind it is that martingale means the future could not be predicted, or, EMH (Efficient-market hypothesis).
fair enough. however, EMH is only a hypothesis now, the other side of the story, that the market is ine... |
Assumptions based on non-martingale? |
Well, it sounds like "How to do an empirical test for a pricing model?" but it's a bit more complex. let me try explain.
Take the classic GBM (geometric Brownian motion) model for stock as an example:
ds = mu * S * dt + sigma * S * dW.
, it leads to classic Black-Scholes formular.
The model says volatili... |
Is it possible to state a pricing model is better than another? |
Might be a bit overlapping with nicolas' answers, but here it goes:
Id say you would have to look at the prediction-power of the model at hand. What if you do a backtest where you set a time t in the future?
Set a price range for the stock at time t, and check with market data how often the price have been withi... |
Isn't this a simple mathematical rule?
$$\Delta r_{t}=r_{t} - r_{t-1} = ln(p_{t}) - ln(p_{0}) - ln(p_{t-1}) + ln(p_{0})=ln(\frac{p_{t}}{p_{t-1}})$$
i.e. logarithmic or continuously compounded return. As a result:
$$E(\Delta r_{t})=\frac{1}{T}\sum_{t=1}^{T}\Delta r_{t} = \frac{1}{T}\sum_{t=1}^{T}ln(\frac{p_{t}}{p_{... |
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