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There's a relatively new product in the market / on the Nasdaq called [Alpha Indexes][1]. It lets one own a company -- e.g. Apple, GE, Google, etc -- as the difference between how that company does (the "target"), and a benchmark (e.g. SPY). That seems like a "stock analyst's dream", being able to say they believe co... |
You can calculate the value of an option free bond or swap by using the spot curve and discounting cashflows accordingly.
Can someone explain why we refer to using short-rate models for pricing option-free instruments? For a swap, for example, I've seen the fixed side get valued by discounting cashflows, and the flo... |
You can calculate the value of an option free bond or swap by using the spot curve and discounting cashflows accordingly. Alternatively, apparently you can use a single-factor short rate model in a binomial tree as you would for options.
Can someone explain why we refer to using short-rate models for pricing option-... |
My concern is how to handle a negative value for the Kelly formula. Even when you have a system that has positive expectancy, you can (and usually will) sustain a number of losses, sometimes consecutively. This is usually most relevant at the beginning of trading system signals, each loss has a large impact on the form... |
Hello I am doing an analysis on covered calls with and extra amount of naked calls. Ignore the symbol and current macroeconomic events.
I couldn't find any reference to this strategy (unbalanced is an adjective I chose, referring to the non-equivalent legs), it looks favorable because of the amount of premium that c... |
This is blowing my mind a little bit, when someone wants to calculate a 30-day moving average of a commodity, do they mean 30 business days, or 30 calendar days? I'm looking for the general consensus, not "you could do it this way or that way". |
When people say calculate moving average for 30 days include weekends or not? |
I have two cross and an account in EUR:
1. EUR/USD
2. GBP/USD
I would like to do a balanced linear regression using R. With "balanced" I mean that I would like to normalize it by calculating the difference in pips from the previous day and the current, and then multiply by the respective (middle) pip value.
... |
How to balance two Forex crosses correctly to do a linear regression? |
I'm trying to model interest rates, and will use the following equation:
dr = mu*r dt + sig*r dW
I'm also being told that interest rates are 40% correlated to S&P returns. How can I include correlation to the S&P into this equation? (It is pretty weird that interest rates are being correlated to S&P returns) |
Are there comprehensive analyses of how much theta a weekly options loses in a day, per day?
I know what the shape of theta decay looks like, in theory, where the approaching of zero happens more rapidly the closer you get to expiration.
<img src="http://www.tradingonlinemarkets.com/Articles/Options/time_decay_op... |
The paper by Tavi Ronen is interesting in its analysis of the liquidity and price discovery.
- [Where Did All the Information Go? Trade in the Corporate Bond Market][1]
As I pointed out above a simple measure is the one by Boa et al in their
- "Illiquidity of corporate bonds" (see link in my comment to Bri... |
I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a realization of a noncentral chi-squared random variable. What variance reduction techniques may be applied in this case? Can on... |
How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation? |
Are there comprehensive analyses of how much theta a weekly options loses in a day, per day?
I know what the shape of theta decay looks like, in theory, where the approaching of zero happens more rapidly the closer you get to expiration.
<img src="http://www.tradingonlinemarkets.com/Articles/Options/time_decay_op... |
Volatility is mean reverting if the underlying security doesn't drop to zero.
If the security has some underlying "value" then its price is co-integrated with that "value". The volatility is the uncertainty of that price as it tracks the security's "value".
![enter image description here][1]
Edit 12/03/... |
Volatility is mean reverting if the underlying security doesn't drop to zero.
If the security has some underlying "value" then its price is co-integrated with that "value". The volatility is the uncertainty of that price as it tracks the security's "value".
![enter image description here][1]
Edit 12/03/... |
I'm trying to model interest rates, and will use the following equation:
$dr = \mu r dt + \sigma r dW $
I'm also being told that interest rates are 40% correlated to S&P returns. How can I include correlation to the S&P into this equation? (It is pretty weird that interest rates are being correlated to S&P retu... |
The historical Calibration is used in the banking industry for forecast an asset’s performances and not for replicating them.
Mathematically, it's known that historical vs options calibration is equivalent to observing an asset through two different probabilities (historical vs the neutral one). This is why you wil... |
GMM method is a powerful method to calibrate historically, only. Also, the historical Calibration is used in the banking industry for *forecast* an asset’s performances and **not** for *replicating* them.
Mathematically, it's known that historical vs options calibration is equivalent to observing an asset through t... |
Do you evaluate a strategy in a backtest based on the cumulative returns generated by the strategy ( i.e. looking at the cumulative returns of the trades that occur ) or do you start with a certain dollar amount and look at the cash at end to compute the annualized return. The reason I ask is because things like positi... |
I was asked today to "quantify" the precision of an estimated the standard deviation from a small sample, I was not sure how to answer.
The case is quite simple, I have a sample of $n=25$ measures (returns as you would have guessed). I used the classic unbiased estimator for the standard deviation:
$$\sigma_x = \... |
Are there comprehensive analyses of how much theta a weekly options loses in a day, per day?
I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more rapidly the closer you get to expiration.
<img src="http://www.tradingonlinemarkets.com/Articles/Options/time_decay_opt... |
Are there comprehensive analyses of theta decay in weekly options? |
My concern is how to handle a negative value for the Kelly formula. Even when you have a system that has positive expectancy, you can (and usually will) sustain a number of losses, sometimes consecutively. This is usually most relevant at the beginning of trading system signals, each loss has a large impact on the form... |
How to apply the Kelly criterion when expected return may be negative? |
How to generate a random price series with a specified range and correlation with an actual price? |
I was asked today to "quantify" the precision of an estimated the standard deviation from a small sample, I was not sure how to answer.
The case is quite simple, I have a sample of $n=25$ measures (returns as you would have guessed). I used the classic unbiased estimator for the standard deviation:
$$\sigma_x = \... |
Following up on my recent question on [variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation][1], I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, to generate quasi-Monte Carlo interest rate paths.
As [before][2], the objective is to estimate the value of a p... |
How to apply quasi-Monte Carlo to path-dependent options? |
Say I want to calculate a correlation matrix for 50 stocks using 3-year historical daily data. And there are some stocks that were recently listed for one year.
This is not technically challenging because the correlation function in R can optionally ignore missing data when calculating pair-wise correlation. But ho... |
How do I adjust a correlation matrix whose elements are generated from different market regimes? |
Pricing of VIX futures is complicated, because it is not possible to use a standard
hedging argument to get a value similar to stock futures.
What different approaches for pricing VIX futures exist? Which ones are used
in practice by traders and others? |
What is the market standard for pricing VIX futures? |
I am starting a project and would be grateful for some practical advice. My focus is on the informational content of equity derivatives‘, (index, ETF & stocks). A central metric here is obviously IVOL. My question is what are the “industry” standards models for backing out IVOL from equity option prices? By “industry”... |
How to properly evaluate backtest returns? |
This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some corporate bonds, than to exchange traded options.
Much more so than market participants in exchange traded options, which... |
Does fitting sub-optimal option exercise strategies to market data yield better option values? |
A convertible bond denominated in USD is issued by an Indian company (with equity traded in INR). The bond will be repaid in USD and if converted into equity in the company, the conversion price will be based on a pre-determined fixed USD/INR rate. When valuing the option embedded in the bond, should we use the USD ris... |
Which risk-free rate to use to price a bond issued in one currency but convertible into equity in another? |
I am trying to work out how to value the following transactions. It should be straight forward, since it breaks down into a series of well known instruments, yet I am not sure how to evaluate it:
1. Receive Cash payment amount of \$X
2. Subsequent pay out \$Y per calendar month into perpetuity
3. Have the option t... |
How would I value a perpetual bond with an embedded option? |
Intraday seasonality is a major factor in comparing volatility at different times of day. Most time series display significantly higher volatility in the morning EST than mid-day. For US exchange-traded products, volatility picks up again just before 4:00 PM EST. This is known as the u-shaped volatility pattern for ... |
How to annualize intra-day volatility on minute data? |
Intraday seasonality is a major factor in comparing volatility at different times of day. Most time series display significantly higher volatility in the morning EST than mid-day. For US exchange-traded products, volatility picks up again just before 4:00 PM EST. This is known as the u-shaped volatility pattern for ... |
A simple top-down shortcut calculation :
1. Set annualized alpha = compounded alpha = 1 + a1 + a2 + a1*a2 + ... = $\Pi$ (1 + $\alpha_t$)
2. Set annualized return from factors = compounded factor return = $\Pi$ (1 + $factorReturn_t$)
3. Interaction Term contribution is then = Compounded Security Return - Compounded... |
The Quantitative Finance Stack Exchange is intended for **professionals** and **academics** involved in securities valuations, risk modeling, and other topics related to 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 ... |
What are some quantitative method behind etf vs cash arbitrage? |
Volatility is mean reverting if the underlying security doesn't drop to zero.
If the security has some underlying "value" then its price is co-integrated with that "value". The volatility is the uncertainty of that price as it tracks the security's "value".
![enter image description here][1]
Edit 12/03/... |
honestly your question is hard to understand. Are these two questions the same?
1. "Does fitting sub-optimal option exercise strategies to market data yield better option values?"
2. "which modeling approach leads to better predictions and better relative value measures?"
I think you want to ask 1 and I think ... |
This is a hard question because you have to explain i) why does volatility mean revert, AND the opposite effect ii) why does volatility exhibit clustering/persistence? GARCH models can describe this behavior but they do not explain.
We need a model of investor behavior that can explain both phenomenon. I think Rama ... |
> **Possible Duplicate:**
> [How should I calculate the implied volatility of an American option in a real-time production environment?](http://quant.stackexchange.com/questions/1489/how-should-i-calculate-the-implied-volatility-of-an-american-option-in-a-real-ti)
<!-- End of automatically inserted text -->
I am ... |
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A quick Google search gives a few hints:
- [http://etf.about.com/od/etfinvestingstrategies/a/ETF_Arbitrage.htm][1]
- [http://ftalphaville.ft.com/blog/2011/05/18/572086/how-profitable-is-etf-arbitrage/][2]
- [http://www.iijournals.com/doi/abs/10.3905/jii.2010.1.1.107][3]
- [http://seekingalpha.com/article/6806... |
F# provides you with many data structures pour collections, but in functional programming, you try to have *immutable* data structures, such as the F# `List`. It becomes quite handy if you want to do some parallel computing for example.
You can have a look at my [post][1] on [SE][2] which is probably where you could... |
I have read some papers on quantitative trading strategies and it seems like strategies that focus on mean reversion or statistical arbitrage give signals that are dependent on some quantitative model.
But when you turn to momentum strategies, people start talking about moving averages to generate signals. Why is th... |
Can momentum strategies be quantitative in nature? |
F# provides you with many data structures for collections, but in functional programming, you try to have *immutable* data structures, such as the F# `List`. It becomes quite handy if you want to do some parallel computing, for example.
You can have a look at my [post][1] on [SO][2] which is probably where you could... |
This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some corporate bonds, than to exchange traded options.
Much more so than market participants in exchange traded options, which... |
Which approach yields better value measures, rational or behavioral option exercise strategies? |
Which approach is better for modeling option exercise strategies, rational or behavioral? |
How to fill in gaps using related time series? |
How to create a Stochastic Process through pre specified points? |
How about adapting Ledoit-Wolf shrinkage to average correlation? You calculate the ratio of average correlations in two regimes to get a sense of the magnitude of regime shift. Use this ratio to adjust the correlations of short-lived stock with others. The method is simple and result will definitely make sense to you. ... |
It is known (see for example Joshi-Chan "Fast and Accureate Long Stepping Simulation of the Heston SV Model" available at SSRN) that for a CIR process defined as :
$$dY_t= \kappa(\theta -Y_t)dt+ \omega \sqrt{Y_t}dW_t$$
$Y_0=Y$ together with a correct set of constraints on parameters' value.
Then the law of $\in... |
Quant Guy's list is really impressive! However, I am not sure they will readily solve your specific problem? I think there is one **missing piece**.
Please note that imputing missing data is a very broad topic. There are many recipes to impute missings but that's for their specific 'assumptions' and purposes. They ... |
How to interpolate gaps in a time series using closely related time series? |
Quant Guy's list is really impressive! However, I am not sure they will readily solve your specific problem? I think there is one **missing piece**.
Please note that imputing missing data is a very broad topic. There are many recipes to impute missings but that's for their specific 'assumptions' and purposes. They ... |
This answer only deals with obtaining higher frequency data from low frequency data. The second method is taken from the draft of a master thesis of a friend of mine, i.e. most of this is taken from an unpublished source.
Jones (1998) propose an algorithm to this using something similar to Gibbs sampler to get the m... |
This answer only deals with obtaining higher frequency data from low frequency data. The second method is taken from the draft of a master thesis of a friend of mine, i.e. most of this is taken from an unpublished source.
[Jones (1998)][1] propose an algorithm to this using something similar to Gibbs sampler to get ... |
Specialised NoSQL database systems are used a lot for time series storage, particularly for tick data:
- [Kx / Kdb](http://www.kxsystems.com) is one prominent solution; from Arthur Whitney et al who did [A+](http://www.aplusdev.org) at Morgan Stanley
- [Onetick](http://www.onemarketdata.com) is another, newer ent... |
> When you are "long gamma", your position will become "longer" as the
> price of the underlying asset increases and "shorter" as the
> underlying price decreases.
>
> source: http://www.optiontradingtips.com/greeks/gamma.html
My intuition tells me that if you're long gamma, all that means is that if gamma incr... |
What does it mean to be long gamma? |
The Quantitative Finance Stack Exchange is intended for **professionals** and **academics/students** 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 quan... |
Sorry for what must be a beginner question, but when I went to write code I realized I didn't understand *exactly* how volatility is defined. [Wikipedia][1] tells me "volatility is the standard deviation of the instrument's logarithmic returns", and [logarithmic return is defined][2] as ln(Vf/Vi), where Vf is closing p... |
How to calculate volatility? |
I came across an example where a well-known weakness of a credit risk model was dealt with by augmenting some of the existing risk factors via increased factor loadings. This made the the model more conservative in terms of the required economic capital it recommended.
What does that mean? Is it a matter of increas... |
What does it mean to modify the factor loadings of a credit risk model? |
This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some corporate bonds, than to exchange traded options.
Much more so than market participants in exchange traded options, which... |
Im a software developer (freelance) working in investment banking, and I'm looking to improve my CV by gaining a better understanding of the financial quant role and the software used by quants to create and test models.
Ideally I'd like to write a high-performance desktop application in order to understand this area ... |
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, bootstrapping, taylor series, numerical integration, and risk neutral valuation. It also includes a ma... |
How to calculate intraday volatility? |
Sorry for what must be a beginner question, but when I went to write code I realized I didn't understand *exactly* how historical volatility, or statistical volatility, is defined. [Wikipedia][1] tells me "volatility is the standard deviation of the instrument's logarithmic returns", and [logarithmic return is defined]... |
How to calculate historical intraday volatility? |
Your code for volatility seems correct, if you want minute volatility, but is that really what you want? See [this recent question][1]. Also, using first and last tick is what is generally done, but over very short time intervals such as a minute, you will have [microstructure issues][2]. It doesn't really make sens... |
Your code for volatility seems correct, if you want minute volatility, but is that really what you want? See [this recent question][1]. Also, using first and last tick is what is generally done, but over very short time intervals such as a minute, you will have [microstructure issues][2]. The state-of-the-art technol... |
Your code for volatility seems correct, if you want minute volatility, but is that really what you want? See [this recent question][1]. Also, using first and last tick is what is generally done, but over very short time intervals such as a minute, you will have [microstructure issues][2]. [Another question here][3] d... |
Your code for volatility seems correct, if you want minute volatility, but is that really what you want? See [this recent question][1] on annualizing volatility from intraday data. Also, using first and last tick is what is generally done, but over very short time intervals such as a minute, you will have [microstruc... |
What tools and libraries may be used to model limit/stop systematic trading? |
GARCH models were developed by Robert Engle precisely to deal with the problem of auto-correlated residuals in time-series regression. To ask "Why are GARCH models used to forecast volatility if residuals are often correlated?" misses this point. |
This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some corporate bonds, than to exchange traded options.
Much more so than market participants in exchange traded options, which... |
I am using a multiple linear regression model to predict 1 minute intraday prices. Each period has 4 prices, Open, High, Low, Close. The model has X1 and X2 as the explanatory variables at time t0. Y is the 1 minute return at time t1.
My question is what price to use to make R squared and the other results of the ML... |
I was looking again at [this question][1] which basically haunts every quant I believe, and I was thinking about the effect of these gaps when computing volatility of the series.
Let's define the problem more specifically for clarity.
Say you're working on a simple mean variance optimization for asset allocation.... |
How do you estimate the volatility of a sample when points are irregularly spaced? |
Daily data, such as open and close prices, is often available for much longer periods than high-frequency data. However, whenever backtesting any strategy that examines instruments traded in different time zones and at different exchanges, one faces the problem of how to reconcile differences in open and close times. W... |
How to account for open/close time differences? |
I am using a multiple linear regression model to predict 1 minute intraday returns. Each period has 4 prices, Open, High, Low, Close, from which I can calculate Close to Close returns. The model has X1 and X2 as the explanatory variables at time t0. Y is the 1 minute Close to Close return at time t1.
My question is ... |
The Quantitative Finance Stack Exchange is intended for **professionals** and **academics/students** 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 ... |
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] by Ruey Tsay
- [An Introduction to High-Frequency Finance][2] by Dacorogna et al
- [Probability and Stati... |
Daily data, such as open and close prices, is often available for much longer periods than high-frequency data. However, whenever backtesting any strategy that examines instruments traded in different time zones and at different exchanges, one faces the problem of how to reconcile differences in open and close times. ... |
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