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If we know the options Implied Volatility (IV) skew for an equity, is it possible to calculate the probability of the equity moving, given a move in the IV?
We can define IV skew as the difference between IV at delta 0.25 compared to IV at delta 0.75. |
Is it possible to estimate the correlation between an equity and its IV, purely from its IV skew? |
Since I began thinking about portfolio optimization and option pricing, I've struggled to get an intuition for the risk premium, i.e. that investors are only willing to buy risky instruments when they are compensated by an add-on above $r$ (the risk free interest rate).
On the one hand this is understandable and bac... |
I'm wondering what API methods there are to determine a company's market cap, i.e. (number of shares issued) * (price per share).
I know IQfeed and perhaps Yahoo will do this - does anyone know of any other API's that will do the job? |
I read in a book that the distance to default of a company is "2.978".
Can anyone please tell me what is the unit implied behind this measure? Are they "years" for instance?
Thanks in advance,
Julien. |
What is the unit of the Distance to Default measure? |
How do I specify the GARCH/TARCH equation in Eviews 6 in the variance regressors frame, if I want to find out whether there are volatilty spillovers from stock markets A and B to stock market C?
P.S. I know I have to set threshold order to 1 ;) |
How to estimate a multivariate GJR or TARCH model in Eviews? |
> ...do you know of any standard
> libraries that can calculate the joint
> probability of stocks A and B, given a
> time series of historical data?
Using [R][1] and the [LSPM package][2] with the code posted [here][3] might be what you are looking for.
[1]: http://www.r-project.org/
[2]: http://lspm.r-... |
In a typical HFT scenario (process incoming UDP quotes and send TCP order entry responses) well written Java can compete with C++ for pure speed. If you need more speed, look to improve the following:
1. Your code (setup a good benchmark and then profile and tune)
2. Your networking environment (low-latency swit... |
Have you considered fitting ARIMA with exogenous regressors model? Linear regression with autocorrelated errors might be appropriate.
R can do this with the arima() function via specifying the xreg argument. |
I'm interested in investing some money in the stock market, and I have the math background that will make following the math used in quantitative finance possible (with some work). What are the resources necessary to apply quantitative finance methods (algorithmic analysis and portfolio management) toward making money... |
I have these posts favorited from stackoverflow. They might help you.
[High Frequency Trading][1]
[What programming language(s) is algorithmic trading software written in?][2]
[Why does a derivative trading position always require C++ knowledge?][3]
Jane Street Capital, a high-frequency market making fir... |
First of all, hi!
I am currently working on my research paper and trying to explain 2 dimensional variable : volume and instrument of corporate debt financing. Independent variables that I believe must be included in the model are specific characteristics (capitalization of the company, debt to equity ratio, may be r... |
I understand that by applying Ito's lemma to the following SDE
$$dX=\mu\,X\,dt+\sigma\,X\,dW$$
one obtains a solution to the above SDE which is as follows:
$${X}\left( t\right) =\mathrm{X}\left( 0\right) \,{e}^{\sigma\,\mathrm{W}\left( t\right) +\left( \mu-\frac{{\sigma}^{2}}{2}\right) \,t}$$
I have been told t... |
I am currently working on my research paper and trying to explain a two-dimensional variable: volume and instrument of corporate debt financing.
Independent variables that I believe must be included in the model are:
- specific characteristics (capitalization of the company, debt to equity ratio, maybe rating)
... |
I understand that by applying Ito's lemma to the following SDE
$$dX=\mu\,X\,dt+\sigma\,X\,dW$$
one obtains a solution to the above SDE which is as follows:
$${X}\left( t\right) =\mathrm{X}\left( 0\right) \,{e}^{\sigma\,\mathrm{W}\left( t\right) +\left( \mu-\frac{{\sigma}^{2}}{2}\right) \,t}$$
I have been to... |
There is much in the literature about time-series and the problem of auto-correlation. Unfortunately the issue of why auto-correlation is actually troublesome is glossed over, and methods for testing a time-series for auto-correlation are presented. Basically, it is assumed that auto-correlation is bad for purposes of ... |
Who cares about autocorrelation? |
Other than Kelly (or fractional derivatives), are there other money management strategies in wide use among quant funds? Certainly Kelly is mathematically optimal, but perhaps there are other approaches that take into account factors beyond optimized return (lower risk, less exposure to X, etc.)? |
Alternate money management strategies to Kelly? |
I understand that by applying Ito's lemma to the following SDE
$$dX=\mu\,X\,dt+\sigma\,X\,dW$$
one obtains a solution to the above SDE which is as follows:
$${X}\left( t\right) =\mathrm{X}\left( 0\right) \,{e}^{\sigma\,\mathrm{W}\left( t\right) +\left( \mu-\frac{{\sigma}^{2}}{2}\right) \,t}$$
I have been to... |
I have implemented a monte carlo pricer for an option. I simply don't know **how many decimals** I need to include in the quoted price. Can anyone please provide guidelines? |
What are the rules for quoting option prices on the market? |
I have implemented a monte carlo simulation for a **plain vanilla** European Option and I am trying to compare it to the analytical result obtained from the BS formula.
Assuming my monte carlo pricer is correctly implemented, am I supposed to get the very same result with both methods (Monte Carlo and BS analytical fo... |
I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result.
I noticed that as I increase (from 1 million to 10 millions) the number of simulations, the **MC result starts to diverge**...
Note that I deliberately only use only one varianc... |
I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result.
I noticed that as I increase (from 1 million to 10 millions) the number of simulations, the **MC result starts to diverge**...
Note that I deliberately only use only one varianc... |
I am trying to implement a vanilla European option pricer with Monte Carlo and compare its result to the BS analytical formula's result.
I noticed that as I increase (from 1 million to 10 millions) the number of simulations, the **MC result starts to diverge**.
Note that I deliberately only use only one variance ... |
I would like to know how stressful this work can be and where the stress could come from. How to avoid it? Does it really depend on the company you are working? Is there a way to know in advance if work in a particular company is stressful or not? |
How stressful is work of quants? |
In discrete time there is one model for an interest rate of the form
$$
I_{n+1} = \alpha I_n+w_n
$$
where $\alpha\in [0,1)$ and $w_n\geq 0$ are i.i.d. r.v. Working with ruin probabilities in model which incorporates such interest rate, I've faced that $I$ can reach any positive value with a positive probability.
... |
Further to my question asked here: [prior post][1]
[1]: http://quant.stackexchange.com/questions/1307/monte-carlo-methods-for-vanilla-european-options-and-itos-lemma
and which left some points unanswered, I have reformulated the question as follows:
**What is Ito's lemma used for in quantitative finance?**... |
What is Ito's lemma used for in quantitative finance? |
I am learning about quantitative finance, and I am struct by how opposite it is from the techniques that make it into magazines and TV; mainly technical analysis. Specifically if they say an indicator (RSI, TRIX, etc.) can predict even short term future prices, then you should be able to run an analysis to see if this... |
If a large order is placed to sell, that takes up many many buy quotes from the book (sorry, don't know all the jargon), are they all filled at once? Or, one buy at a time, with a chance for any new orders to come in between each buy?
|
naive: how does order fulfillment proceed with larger orders? |
I am learning about quantitative finance, and I am struck by how different it is from the techniques that make it into magazines and TV: mainly technical analysis. Specifically if they say an indicator (RSI, TRIX, etc.) can predict even short term future prices, then you should be able to run some analysis to see if t... |
If a large sell order hits many bids from the book, is the order filled at once? Or is it filled one bid at a time with a chance for any new orders to come in between each trade? |
How does order fulfillment proceed with larger orders? |
Consider a market participant $A$ who is mechanically following an automated liquidity providing algorithm (HFT) in a number of large cap stocks on a specific exchange.
Assume furthermore that we are able to observe all orders placed by $A$ and that we know that the algorithm used by $A$ takes only public market dat... |
Pseudorandom number generators are often tested using e.g. a test suite like [Diehard tests][1] or [Dieharder][2]. If one would run these tests e.g. on stock market time series or other financial data, would you expect your financial data to qualify as being a good random number generator or would it fail in many of th... |
How random are financial data series? |
Why don't you try it and report back?
Recall, though, that while a *random walk* is often a rather competitive forecast, realized data is understood to have weak dependence especially in higher moments.
Having worked a bit with DieHarder, I'd suspect it to reject a number of series. But the proof is in the pud... |
While liquidity is one of the key figure of financial markets, It seems to be very difficult to measure. Volume is sometime used as a proxy but can sometimes be completly irrelevant.
Could you point to relevant research on what data to use and how to compute the measure? |
In discrete time there is one model for an interest rate of the form
$$
I_{n+1} = \alpha I_n+w_n
$$
where $\alpha\in [0,1)$ and $w_n\geq 0$ are i.i.d. r.v. Working with ruin probabilities in model which incorporates such interest rate, I've faced that $I$ can reach any positive value with a positive probability.
... |
When the risk is defined by a discrete random variable, is CVaR a coherent risk measure? I stick to the following definition of CVaR:
$$ CVaR_\alpha(R) = \min_v \quad \left\{ v + \frac{1}{1-\alpha} \mathbb{E}[R-v]^+ \right \}$$
where $R$ is the DISCRETE random variable for the loss and $\alpha$ is the confidence ... |
Is Conditional Value-at-Risk (CVaR) coherent? |
The bid-ask bounce is the bouncing of trade prices between the bid and ask sides of the market. It introduces a systematic bias to the data which can cause serious problems in analysis.
What methods can be used to control for the bid/ask bounce when using high-frequency data? One approach is to use the bid/ask mid... |
Control for bid/ask bounce in high-frequency trade data? |
Suppose I have a random walk $X_{n+1} = X_n+A_n$ where $A_n$ is an iid sequence, $\mathsf EA_n = A>0$. How to construct a martingale measure for this case? |
> Rebalancing and diversification go
> hand in hand. **There is no
> diversification benefit without
> rebalancing – otherwise the total
> return will simply be the weighted
> average of the long-term geometric
> returns.** If you don’t rebalance to
> asset types, you will get no
> diversification benefit.... |
I'll take a stab at it, but this is a really broad question.
A direct answer: Bayesian models often use "probability that the counter-party is informed."
Indirect answers:
I think your assumption is that the algorithm operates on each stock individually, and has no knowledge of what it's doing in any other sto... |
Let's say I have two call option liabilities that I want to statically hedge with a single call option.
Liabilities:
Liab_Call_1:
Strike: 100
Notional: 1000
DaysToExpiration: 20
Liab_Call_2:
Strike: 100
Notional: 1000
DaysToExpiration: 30
Assets:
Asset_Call_1:
Strike: 100
Notional: 2000... |
Quantifying Hedging Error Due To Expiration Day Range? |
Let's say I have two call option liabilities that I want to statically hedge with a single call option.
Liabilities:
Liab_Call_1:
Strike: 100
Notional: 1000
DaysToExpiration: 20
Liab_Call_2:
Strike: 100
Notional: 1000
DaysToExpiration: 30
Assets:
Asset_Call_1:
Strike: 100
Notional: 2000... |
Let's say I have two call option liabilities that I want to statically hedge with a single call option.
Liabilities:
Liab_Call_1:
Strike: 100
Notional: 1000
DaysToExpiration: 20
Liab_Call_2:
Strike: 100
Notional: 1000
DaysToExpiration: 30
Assets:
Asset_Call_1:
Strike: 100
Notional: 2000... |
Let's say I have two call option liabilities that I want to statically hedge with a single call option.
Liabilities:
Liab_Call_1:
Strike: 100
Notional: 1000
DaysToExpiration: 20
Liab_Call_2:
Strike: 100
Notional: 1000
DaysToExpiration: 30
Assets:
Asset_Call_1:
Strike: 100
Notional: 2000... |
Let's say you have a dependent variable and many independent variables. What are the preferred metrics for sorting and selecting variables based on explanatory power? Let's say you are not concerned with correlation among your inputs.
My thoughts are below. Let me know if I'm missing anything obvious, or if there i... |
It is a not so well known fact that the [Kelly criterion][1] is only optimal in a nice and well-behaved Merton-world. It is far from optimal when things are getting non-(log)normal (i.e. more realistic!).
**My question**<br>
My question is simply: Why is this so? What are the reasons and is there some intuition for... |
I posted this on Wilmott as well:
Good day ladies and gents,
I need to implement a reverse stress testing model (definition [here](http://www.fsa.gov.uk/pages/About/What/International/stress_testing/firm_s/reverse_stress_testing/index.shtml))
I have searched around and cannot find anything substantial on the t... |
I have 10 years of backtested simulated performance of some trading strategy (using historical prices), and N months of actual trading performance. What statistical test can I do find out if I'm on target with the backtesting numbers? (both, in terms of expected annual returns and expected annual Sharpe ratio) |
I'm working on implementing a 'LOB' and I'm being very careful about choosing my data-structures so as to maximize performance.
Using F# as an example, I need to consider a *List* versus *Array* for holding 'Bids' and 'Asks'.
Because these lists are constantly being updated very rapidly, and the orders that need ... |
I am missing tools to investigate this issue. I am trying to solve this question [here][1]. What kind of issues should you acknowledge over the naive diversification/rebalancing with normal distribution? You could have a different return distribution curve so does the distribution affect the benefits? If you know how t... |
Benefits of Diversification and Rebalancing with negatively skewed leptokurtic return distribution? |
Can you please recommend good reads on statistical analysis related to online fraud detection and prevention of account abuse?
Thank you. |
Can you please recommend good reads on statistical analysis related to online fraud detection and prevention of account abuse? |
Can someone suggest a topic or some reasonably narrow area in financial time series analysis (e.g. statistical, machine learning, etc.) which can make a good topic for a master thesis? By 'good' I mean that it's perspective i.e. can be extended to PhD-level studies, but still manageable in 3-4 month time for an applied... |
What is a good topic on financial time series analysis for master thesis? |
i am wondering if anyone has used NoSQL (mongodb, cassandra, etc.) to store and analyze data.
I tried searching the web but was not able to see if the financial firms had gotten in to using nosql storage.
so far even on this site i have only seen talks of using SQL DBs. I would imagine that NoSql would be much ... |
In the finance world, most data (especially given this forum is for Quant monkeys) is transactional and subject to regulatory reporting.
NoSQL isn't generally transactional and given the shape of, say, risk data, there is no overpowering reason to throw away ACID and RDBMS.
There are more mundane reasons: there a... |
I am wondering if anyone has used NoSQL (mongodb, cassandra, etc.) to store and analyze data.
I tried searching the web but was not able to see if the financial firms had gotten in to using nosql storage.
So far even on this site i have only seen talks of using SQL DBs. I would imagine that NoSQL would be much f... |
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... |
I am testing my model and I interested in options prices on EUR|USD for Jan, 2011. The history can be even daily - but I have never had a deal with fx options, so I don't know where start to look for such history. Could you advise me? |
The first think you have to ask is ¿¿What price??? Monetary price or equity price?? All answers,the ones I read, related to monetary price, but are equity price really risk free????
One of the biggest problem with Black Scholes (personal opinion) is that they consider the behave of equity price as monetary price: Solv... |
[Option Traders Use (very) Sophisticated Heuristics, Never the Black–Scholes–Merton Formula][1]
[Stock Price Clustering on Option Expiration Dates][2]
[Option Returns and Volatility Mispricing][3]
[1]: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075
[2]: http://papers.ssrn.com/sol3/papers.c... |
If you're looking for free data, I've heard this question many times asked to derivatives professors at the end of a lesson. They answered was most of the time to step by their offices so that they could give data they imported from the university data provider. So apparently, if even academy has to do it this way, I'd... |
I am testing my model and I am interested in options prices on EUR|USD for Jan, 2011.
The history can be even daily - but I have never had a deal with fx options, so I don't know where start to look for such history.
Could you advise me? |
I am at the moment writing a program focusing on asset allocation and I am thinking about how I should represent my constraints in the data model.
The first approach that came to mind was to define some categories to classify the constraints so that they could be stored in a table according to their "category" (for ... |
The only requirement if you are risk neutral is the property of martingale on your discounted stock price $M_t=e^{-rt} S_t$.
But if you apply Itô $d( S_t\cdot e^{-rt} e^{rt})=d(M_t\cdot e^{rt})=r_tM_te^{rt}dt + ..dW_t=r_tS_tdt+..dW_t$
you see see that under the risk free probability, the asset price must have $r_... |
I'm completely new to this field, so forgive me if some of what I'm asking doesn't make sense. I've recently started reading some books on asset allocation and portfolio theory but I don't work in the field and don't have much knowledge yet.
So I've been reading up on mean-variance analysis and my question is regard... |
I'm completely new to this field, so forgive me if some of what I'm asking doesn't make sense. I've recently started reading some books on asset allocation and portfolio theory but I don't work in the field and don't have much knowledge yet.
So I've been reading up on mean-variance analysis and my question is regard... |
Inputs are most important to any decision making.
For strategy backtesting, the OHLC data is one of the most inputs.
So to ensure the correctness and integrity of OHLC data, we have checks on the following OHLC issues:
- Outlier Price
- Negative Price
- Corrupted Price (High < Low, etc)
- Missing minute t... |
Is there a standard / methodology to determine and grade the quality of OHLC data? |
I've just downloaded quantlib and started playing around with it, and it looks like it's designed primarily to use Euler discretizations for everything -- so far as I can tell, there's not even a method provided to exactly simulate geometric Brownian motion. Am I missing an obvious feature? If not, is there a fundame... |
Where can I find the standard discount curves for the standard CDS model?
In particular I'm keen to see if ZAR is a supported currency yet... |
Where can I find the standard discount curves for the standard CDS model? |
So you want to calculate $\mathbb{P}[B_1 > B_0 + \varepsilon \;|\; A_1 > A_0 + \varepsilon]$? If you truly have the joint distribution of $A_1$ and $B_1$ and the current prices $A_0$ and $B_0$, this just becomes a simple exercise in integration, by the definition of probability density. Are you asking how to find a c... |
This is a follow-up to my previous question regarding anyone whom wanted to ['donate' data][1]!
So far no one has stepped up *(learning more about buying and selling data, I realize that I'm going to have to buy the data if I want to re-sell it, or give it away for that matter - re: licensing agreements?)*
So I'... |
what do you think of strategies displayed on timelyportfolio.blogspot.com ?
I really like the fact that there is some code to reproduce the strategies, but they seem very.... infantile, by the fact that he does not control for risk factors.
By that I mean that you can have a super complex strategy with lots of be... |
what do you think of strategies displayed on [timelyportfolio.blogspot.com][1]?
I really like the fact that there is some code to reproduce the strategies, but they seem very.... infantile, by the fact that he does not control for risk factors.
By that I mean that you can have a super complex strategy with lots o... |
Yahoo's historical data is sometimes missing dividends. For example:
http://finance.yahoo.com/q/hp?s=VWINX&a=00&b=1&c=2010&d=11&e=20&f=2011&g=v
(VWINX) is missing two dividends for 2011, though it has the ones for 2010.
Also, this paper:
http://arxiv.org/PS_cache/arxiv/pdf/1105/1105.2956v1.pdf
from 2010 repor... |
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 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 need to model the market value of CDS in a portfolio. My current approach is to calculate the present value of the future spread payments - does anybody have a better idea to solve the problem? |
I need to model the market value of CDS in a portfolio. My current approach is to calculate the present value of the future spread payments - does anybody have a better idea to solve the problem?
Edit:
I calculated the spread in the following way (as in Hull-White):
$PV_{surv} = \sum_{i=1}^T {(1−p_d )^i \cdot... |
As you know, the _key equation_ of risk neutral pricing is the following:
$\exp^{-rt} S_t = E_Q[\exp^{-rT} S_T | \mathcal{F}_t]$
That is, discounted prices are Q-martingales.
It makes real-sense for me from an economic point of view, but is there any "proof" of that?
I'm not sure my question make real sense... |
You should look at Paul Willmott's [Frequently Asked Questions In Quantitative Finance][1].
He offers 12 (I think) ways of deriving BS and I think you'll find what you look for there.
[1]: http://www.amazon.com/Frequently-Asked-Questions-Quantitative-Finance/dp/0470748753/ref=sr_1_3?ie=UTF8&qid=1310552909&sr=8-... |
You should look at Paul Willmott's [Frequently Asked Questions In Quantitative Finance][1].
He offers 12 (I think) ways of deriving BS and I think you'll find what you look for there.
The cool thing is that you really have many different *approaches*; one is the classic PDE, one is done using change of measure, one... |
Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or equivalently Ln(1 + arithmetic return).
The log returns have nice properties -- logarithmic returns prevents security... |
Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or equivalently Ln(1 + arithmetic return).
The log returns have nice properties -- logarithmic returns prevents security... |
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