instruction stringlengths 15 26.1k |
|---|
I want to perform an ML analysis on NASDAQ, based on historical fundamentals.
Suppose I want to take a temporal window of 10 year and quarterly data.
I have a question:
I suppose I should know the composition of Nasdaq in the previous years. I mean, its symbols in 2012,2013 and so on.
There is a service, ... |
So when using this method to price exotic options , it's stated that we need to calculate the vanna (how vega changes with respect to change in spot prices) of the exotic option and the volga ( how vega changes with respect to change in implied vol) of the exotic option. How on earth we would do that? Cause to calculat... |
So when using this method to price exotic options , it's stated that we need to calculate the vanna (how vega changes with respect to change in spot prices) of the exotic option and the volga ( how vega changes with respect to change in implied vol) of the exotic option. How on earth we would do that? Cause to calculat... |
### An extended comment:
As written in Mark Leeds comments, [De Prado, et al. (2011)](https://jpm.pm-research.com/content/37/2/118.short) wrote an article that proposed a new method to estimate the presence of informed traders called the Volume-syncronized Probability of Informed Traders (VPIN). This is an extension... |
After reading the modern portfolio theory, I am wondering why the portfolio return is defined that way. Suppose there are $n$ assets in a portfolio, the simple return of an individual asset $i$ at time $t$ is defined as $r^i_{t} = (P^i_{t} - P^i_{t-1})/(P^i_{t-1})$. The portfolio return is then defined as the weighted ... |
Why the portfolio return is defined as a weighted return? |
After reading the modern portfolio theory, I am wondering why the portfolio return is defined that way. Suppose there are $n$ assets in a portfolio, the simple return of an individual asset $i$ at time $t$ is defined as $r^i_{t} = (P^i_{t} - P^i_{t-1})/(P^i_{t-1})$. The portfolio return is then defined as the weighted ... |
I am looking for limit order book data for an academic paper that has a snapshot for every change in the orderbook (1st five levels are fine, but more is better) or can be built from ITCH files. Any market and geolocation work as long as the priority is price/time. The only data I found on this is the lobsterdata resou... |
Are there open source or academic-only limit order book data sets available? |
After reading the modern portfolio theory, I am wondering why the portfolio return is defined that way. Suppose there are $n$ assets in a portfolio, the simple return of an individual asset $i$ at time $t$ is defined as $r^i_{t} = (P^i_{t} - P^i_{t-1})/(P^i_{t-1})$. The portfolio return is then defined as the weighted ... |
As far as I understand, perpetual contracts are like regular futures except they can be held open indefinitely. However, I dont know about any other brokers out there, but in binance, when you open a perpetual contract, you do so by interacting with an order book, meaning, for every position you open there is an opposi... |
How to Delta Hedge and the PnL is indeed affect if real volatility is not constant (either deterministic ou stochastic). The exactly difference will depends on the model choose.
I don't recall this specific chapter in Wilmott book (are you talking about the condensed or full version? I may give it a check.), but not... |
Probably not.
The first question, why? Why would banks do that? Would you this attract more clients and business? Or would it be irrelevant?
How? Continuous (or at least intraday funding) would require a big update in banking infrastructure. Also, how would be the 1/100th of 1/10th of cent would be registered in ... |
Perpetual contracts are supposed to track the spot prices through the *funding* mechanism. Typically, if the future has traded above the spot in the last averaging period used to compute the funding, then the funding will be positive, and the long will pay the short exactly at the end of the averaging period. It is eno... |
## An extended comment:
As written in Mark Leeds comment, **[De Prado, et al. (2011)](https://jpm.pm-research.com/content/37/2/118.short)** wrote an article that proposed a new method to estimate the presence of informed traders called the Volume-synchronized Probability of Informed Traders (VPIN). This is an extens... |
So the bloomberg article that I'm referring to (Bloomberg. Variations on the Vanna-Volga Adjustment. Travis Fisher. Quantitative Research and Development, FX Team. January 26, Version 1) states that volga and vega are considered to be fungible whereas vanna isn't. I can understand why vanna isn't considered to be so , ... |
So the bloomberg article that I'm referring to (Bloomberg. Variations on the Vanna-Volga Adjustment. Travis Fisher. Quantitative Research and Development, FX Team. January 26, Version 1) states that volga and vega are considered to be fungible whereas vanna isn't. I can understand why vanna isn't considered to be so , ... |
As several responses mention, the easiest to see it, is the replication. Please allow me not to use BS formula for options, it is easier to price a forward, and it will contain the important effect that you are trying to understand.
If I enter into a forward contract with you, I am obligated to give you 1 stock for ... |
As several responses mention, the easiest to see it, is the replication. Please allow me not to use BS formula for options, it is easier to price a forward, and it will contain the important effect that you are trying to understand.
If I enter into a forward contract with you, I am obligated to give you 1 stock for ... |
As several responses mention, the easiest to see it, is the replication. Please allow me not to use BS formula for options, it is easier to price a forward, and it will contain the important effect that you are trying to understand.
If I enter into a forward contract with you, I am obligated to give you 1 stock for ... |
As several responses mention, the easiest to see it, is the replication. Please allow me not to use BS formula for options, it is easier to price a forward, and it will contain the important effect that you are trying to understand.
If I enter into a forward contract with you, I am obligated to give you 1 stock for ... |
Well, question is in the title. Assume I have two different models (for example a local volatility model and a stochastic volatility model such as a Dupire model and a SABR model for example) and I am looking at European options only. Let's assume that both models have a parameter set in which they produce the exact sa... |
If two models imply the same volatility surface, do their greeks still differ? |
As a follow-up of another question (which is I feel slightly separate, hence a new question). Assume we want to fit a volatility surface with the goal of calculating good *greeks*, not prices. We can choose between a SV or a LV model (SLV is a very distant but also possible choice). Now assume that
1) We manage to fin... |
I have Black and Scholes (1973) implied volatilities computed and I would like to convert these IVs to digital option prices using a Black and Scholes type of formula, I can't find a formula to do this. How can I convert IVs to digial option prices? |
This is an interesting and not so easy question. Here's my 2 cents:
- First, you should distinguish between **mathematical models** for the dynamics of an underlying asset (Black-Scholes, Merton, Heston etc.) and **numerical methods** designed to calculate financial instruments' prices under given modelling assumpt... |
I want to simulate the following CEV process : $$ dM_t = \sigma_t M_t^{\eta} dW_t $$
Using Euler discretization to $M_t$, if at a given time $t$, $M_t$ takes a negative value then $M_{t+1} = M_t + \sigma_t M_t^{\eta} \sqrt{dt} \epsilon$, where $\epsilon$ follows a standard Gaussian distribution, gives *'NaN's* when ... |
I want to simulate the following CEV process : $$ dM_t = \sigma_t M_t^{\eta} dW_t $$
Using Euler discretization to $M_t$, if at a given time $t$, $M_t$ takes a negative value then $M_{t+1} = M_t + \sigma_t M_t^{\eta} \sqrt{dt} \epsilon$, where $\epsilon$ follows a standard Gaussian distribution, gives *'NaN's* when ... |
I want to simulate the following CEV process : $$ dM_t = \sigma_t M_t^{\eta} dW_t $$
Using Euler discretization to $M_t$, if at a given time $t$, $M_t$ takes a negative value then $M_{t+1} = M_t + \sigma_t M_t^{\eta} \sqrt{dt} \epsilon$, where $\epsilon$ follows a standard Gaussian distribution, gives *'NaN's* when ... |
I want to simulate the following CEV process : $$ dM_t = \sigma_t M_t^{\eta} dW_t $$
Using Euler discretization to $M_t$, if at a given time $t$, $M_t$ takes a negative value then $M_{t+1} = M_t + \sigma_t M_t^{\eta} \sqrt{dt} \epsilon$, where $\epsilon$ follows a standard Gaussian distribution, gives *'NaN's* when ... |
The local volatility can be derived from the implied volatility. But in practice how we deal with the first-order and second-order derivatives?
$$
\sigma_{\mathrm{Dup}}(T, K)^{2}=\frac{\frac{\partial w}{\partial T}}{1-\frac{y}{w} \frac{\partial w}{\partial y}+\frac{1}{4}\left(-\frac{1}{4}+\frac{1}{w}+\frac{y^{2}}{w^... |
I'm just curious there is any useful "meaning" or interpretation we can assign directly to $r_c$. Of course one can directly calculate the non-continuously compounded interest from $r_c$, but exactly *is* $r_c$ itself? (e.g. it is NOT the rate at which something is being infinitely compounded by).
To give a more con... |
How should we interpret r_c in continuously compounded interest? |
I'm just curious there is any useful "meaning" or interpretation we can assign directly to $r_c$. Of course one can directly calculate the non-continuously compounded interest from $r_c$, but exactly *is* $r_c$ itself? (e.g. it is NOT the rate at which something is being infinitely compounded by). Perhaps I am just bei... |
I have a doubt regarding the daily SOFR OIS Curve published by CME.
https://www.cmegroup.com/trading/interest-rates/cleared-otc-sofr-swaps.html#sofroiscurve
If we refer to the curve dated 22 Jul 2022... [![SOFR OIS on 22 Jul 2022][1]][1]
[1]: https://i.stack.imgur.com/4yiUm.png
The one year OIS rate is ... |
I would say it is more of theoretical concept and does not have any meaning in real world. In real world you cannot have infinite number of periods (what is an example of infinity in real world?). Moreover, the difference between fixed periods and continuous won't be much anyway. |
I'm trying to map the standard CDS documentation clauses that we receive from Markit:
- CR/CR14
- MR/MR14
- MM/MM14
- XR/XR14
to the credit event types that we are seeing:
- BANKRUPTCY
- FAILURE TO PAY
- RESTRUCTURING
- OBLIGATION ACCELERATION
- OBLIGATION DEFAULT
- REPUDIATION/MORATORIUM
-... |
Is there a mapping that ties Credit Events to standard CDS documentation clauses? |
The local volatility can be derived from the implied volatility. But in practice how we deal with the first-order and second-order derivatives?
I have seen this formula
$$
\sigma_{\mathrm{Dup}}(T, K)^{2}=\frac{\frac{\partial w}{\partial T}}{1-\frac{y}{w} \frac{\partial w}{\partial y}+\frac{1}{4}\left(-\frac{1}{4}... |
I have Black and Scholes (1973) implied volatilities computed and I would like to convert these IVs to digital option prices using a Black and Scholes type of formula, I can't find a formula to do this. How can I convert IVs to digital option prices? |
I want to simulate the following CEV process : $$ dM_t = \sigma_t M_t^{\eta} dW_t $$
Using Euler discretization to $M_t$, if at a given time $t$, $M_t$ takes a negative value then $M_{t+1} = M_t + \sigma_t M_t^{\eta} \sqrt{dt} \epsilon$, where $\epsilon$ follows a standard Gaussian distribution, gives *'NaN's* when ... |
Are there any other mathematical tests besides Granger that quants use to determine casual relations between two time series? If so what are they? How about convergent cross mapping?
Thanks |
Alternative To Granger Causality? |
Are there any other mathematical tests besides Granger that quants use to determine casual relations between two time series? If so what are they? How about [convergent cross mapping][1]?
Thanks
[1]: https://en.wikipedia.org/wiki/Convergent_cross_mapping |
Let's say a fund's net returns are described by the following table:
|Long|Short|Total
|----|-----|-----
|1.0%|0.25%|1.25%
|1.0%|0.25%|1.25%
|...|...|...
|1.0%|0.25%|1.25%
After 12 months the net performance of the fund would be calculated to be (1+1.25%)^12-1 = 16.08%. My question is how would one go about ... |
Let say $P_{i,j}, j = 1,2,3, DEF$ are the probabilities of transitions from an initial rating $i$ to rating $j$, where $P_{i, DEF}$ represents the default probability from that initial rating.
Now let say, based on some other information I require to modify above default probability to $R_{i, DEF}$ - which is consid... |
I am working on my thesis about option pricing models beyond classical Black-Scholes Model by looking for some recent **innovations on **mathematical processes behind the pricing structures****. By that I mean doing some essential modification on traditional GBM framework or even replaced it with other mathematical pro... |
Any innovations in mathematical processes behind option pricing models? |
I work on designing quant and mix of quant+fundamental trading strategies, but find it is really unproductive to do it at home by myself, and looking to find someone who to do it together with.
I've built my own backtester, invested quite a lot of time on it, but don't really know where to find someone socially.
... |
Where to find someone to work on quant trading strategies together? |
If we are calculating local volatilities, it is usually because we want to calculate prices either by numerically solving a PDE, or by simulating in Monte Carlo. Depending which of these two approaches we are using, the practical approach differs slightly.
To begin with, we assume we are given a nice smooth volatili... |
If we are calculating local volatilities, it is usually because we want to calculate prices either by numerically solving a PDE, or by simulating in Monte Carlo. Depending which of these two approaches we are using, the practical approach differs slightly.
To begin with, we assume we are given a nice smooth volatili... |
I am looking to compute the following using Ito's formula.
$$u(t,\beta_t) = \mathbb{E}(\int_t^T\beta_s^2ds|\beta_t)$$
Knowing the properties of brownian motion, it is rather easy to show that the above is equivalent to $T-t$; however, i'm looking to apply Ito's formula to come up with a similar result. Given that... |
I am looking to compute the following using Ito's formula.
$$u(t,\beta_t) = \mathbb{E}(\int_t^T\beta_s^2ds|\beta_t)$$
Knowing the properties of brownian motion, it is rather easy to show that the above is equivalent to $T-t$; however, i'm looking to apply Ito's formula to come up with a similar result. Given that... |
I'm trying to calculate the VIX index according to the methodology of CBOE. I found that at some time, like at this minute, there are 13 call options out of the money, but there're 3 or fewer put options out of the money. How to deal with such asymmetric problem? Any suggestion or hit is helpful. |
When calculating VIX, how to deal with the problem of asymmetry of put and call data? |
I'm trying to calculate the VIX index according to the methodology of CBOE. I am looking at commodity options. I found that at some time, like at this minute, there are 13 call options out of the money, but there're 3 or fewer put options out of the money. How to deal with such asymmetric problem? Any suggestion or hit... |
There are two methods.
1. Only the numerator the average realized return will be rolling (10 years) while the downside deviation is calculated from full time period.
2. Both numerator and denominator are rolling.
Which one would be correct? |
How to create Rolling Sortino Ratio? |
This is perhaps a bit of a stretch but how about inferring the value of the puts by using the put-call parity principle?
|
I have high frequency data for financial stocks (5-minute periodicity) and I want to forecast volatility.
I'm familiarized with the usual ARCH/GARCH models and their variants for daily data but after doing some research I've learnt that these models don't work well with high frequency data.
Which model is best ... |
I am looking to compute the following using Ito's formula.
$$u(t,\beta_t) = \mathbb{E}(\int_t^T\beta_s^2ds|\beta_t)$$
Knowing the properties of brownian motion, it is rather easy to show that the above is equivalent to $\frac{1}{2}(T^2-t^2)$; however, i'm looking to apply Ito's formula to come up with a similar r... |
Suppose that I have two portfolios: A and B. The factor model used to compare these two portfolios is the same.
Now, suppose model A has an alpha of 0.3 while model B has an alpha of 0.8. Assume that both are statistically significant. So, both portfolios have a positive (statistically significant) alpha. Next, ass... |
I can only offer apriori solutions which are slightly overfit:
- to calculate the slope of N lookback periods and drop the ones that have a low and high std dev (how to determine low and high?)
- the pattern you are trying to track has 4 points, xN. it seems that the slope of (x1 - x2) = (x3 - x4), so in order to... |
I can only offer apriori solutions which are slightly overfit:
- to calculate the slope of N lookback periods and drop the ones that have a low and high std dev (how to determine low and high?)
- the pattern you are trying to track has 4 points, xN. it seems that the slope of (x1 - x2) = (x3 - x4), so in order to... |
In [this article][1] I have read that:
> A risk-neutral world is one where all investors are indifferent to risk and don’t require any extra risk premium for the risk they bear. In this world, all assets (irrespective of their risk) will earn the risk-free rate.
Investors’ risk appetite and true/real world probabi... |
I noticed when both assets sortino ratios are negative the asset with the worse return and worse downside deviation has better Sortino Ratio. Is there a way to fix this? |
From my point of view, to calculate the price of a bond, we just need to add the discounted cash flows.
The discount factor calculation is as follows:
[![enter image description here][1]][1]
In my theory knowing the z-spread of a bond I can recalculate bond price price by calculating the discount factor as f... |
The problem is with the changing volume of assets which changes the weights. I want to use the formula for portfolio risk but cannot figure out the weights. Should taking average weight of an asset work? |
How to calculate the portfolio risk and return if daily share prices, volume held on that day is given for all assets? |
The definition of Treynor ratio is given by
$$
T = \frac{r_i-r_f}{\beta_i},
$$
where $r_i$ is the portfolio $i$'s return, $r_f$ is the risk-free rate and $\beta_i$ is the portfolio $i$'s beta. I am stunned after reading this definition. Isn't it exactly the market premium?
The CAPM model says that
$$
E[r_i]... |
Sorry if this has been asked before. I've been baffled by a question I'm facing.
Assuming I know there are some certain demands for some stocks in near future, and I put them in a basket as a portfolio. What I found is in short period, prices of some of them keep increasing and then at certain point revert. This rev... |
How to predict a portfolio's reversion? |
Just reading a book about about portfolio optimisation. You hear left and right that MVA is out of date, creates suboptimal portfolios in practice and so on because its assumptions are flawed etc. - well, one could think that you just have to create a better model.
You could for example add things to your process... |
Have more complex MVA-style models become obsolete? |
Just reading a book about about portfolio optimisation. You hear left and right that MVA (Mean Variance Analysis of Markowitz) is out of date, creates suboptimal portfolios in practice and so on because its assumptions are flawed etc. - well, one could think that you just have to create a better model.
You could ... |
I saw a post of trader sharing his expectations of implied interest rates on different meetings dates of different Central banks using STIRs [ScreenShot][1] and am trying to figure out how he did it ?
my second question is what are the STIR futures of RBA,RBNZ,BOC,BOJ,SNB
[1]: https://prnt.sc/ZahNwhsuLDDr |
how to calculate the implied interest rates using STIRs futures? |
Fame & French in 2010 describe this table
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/UN5Pg.png
But they do not explain how to get it the net alpha exactly with the formula. So, I was wondering if the formula contains fee then I can get the net alpha. Or how do I get it by what f... |
how to introduce fees into the returns of a mutual fund? |
Fame & French in 2010 describe this table
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/UN5Pg.png
But they do not explain how to get it the net alpha exactly with the formula. So, I was wondering if the formula contains fee then I can get the net alpha. Or how do I get it by what f... |
No, your logic is not correct. As a disclosure note, I am an opponent of the method you are using.
Let us assume that you run a Frequentist regression of *any* kind on phenomena $A$ and $B$. You are asserting a null hypothesis in order to get significance. $A$ could be that gravity has no effect on the motion of ... |
No, your logic is not correct. As a disclosure note, I am an opponent of the method you are using.
Let us assume that you run a Frequentist regression of *any* kind on phenomena $A$ and $B$. You are asserting a null hypothesis in order to get significance. $A$ could be that gravity has no effect on the motion of ... |
In the paper by Fama & French (2010) *Luck versus Skill in the Cross-Section of Mutual Fund Returns*, from J. of Finance ([link][1])
the following table is given (Table II, page 1920):
[![enter image description here][2]][2]
But they do not explain how to get it the net alpha exactly with the formula. So, I ... |
How to introduce fees into the returns of a mutual fund? |
I have a rather silly question, from my understanding in the futures market (commodities in this case) There should be a buyer and a seller for every futures position that is initiated.
- Open interest: Total number of outstanding futures contracts for a given commodity
So the total Long open interest and the t... |
Consider the single factor model in time series form, e.g:
$$
r_t^i = \alpha_i + \beta^i f_t +\epsilon^i_t \quad (1)
$$
Here $i$ is not an exponent but a superscript, e.g. it represents the return on security $i$.
Assuming we have a single factor model, which then states that:
$$
\mathbb{E}[r^i] =\alpha_... |
No one is better at explaining asset pricing than [John Cochrane](https://www.johnhcochrane.com/). He explains it in detail in [his brilliant textbook](https://www.johnhcochrane.com/research-all/asset-pricing). The following videos from his video course are pure gold
- [2.2 Time-Series and GRS](https://www.youtube.com... |
First a comment, as discussed [here][1] the (correct) expression you have stated here is not the one stated and derived in Rouah.
As for calculating the derivatives, the best case would be if your underlying market was such that you could first calibrate a paramterisation of the implied variance, $w(y,t)$, such as ... |
Please bear with me - I know this I'm supposed to do this with a bunch of greek letters but I don't know how so I'll just describe the data I have and what I am trying to do.
I have an expected return for the next month for a universe of say 200 stocks. I also have the volume over the past month for each stock. Fina... |
Please bear with me - I know I'm supposed to do this with a bunch of Greek letters but I don't know how so I'll just describe the data I have and what I am trying to do.
I have an expected return for the next month for a universe of say 200 stocks. I also have the volume over the past month for each stock. Finally I... |
In "Volatility Trading" Euan Sinclair defines Yang-Zhang volatility estimator as
$$ \sigma = \sqrt{\sigma^2_o + k\sigma^2_c + (1-k)\sigma^2_{rs}} $$
where
$$
\sigma^2_o \propto Variance\left(ln\left(\frac{o_i}{o_{i-1}}\right)\right)
$$
$$ \sigma^2_c \propto Variance\left(ln\left(\frac{c_i}{c_{i-1}}\right... |
Natenberg mentions in chapter titled "Volatility Spreads" :
>under the assumptions of a traditional theoretical pricing model, a delta-neutral ratio spread
where more options are purchased than sold should always result in a credit.[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/leOOV.pn... |
Why should delta-neutral backspread always result in credit? |
On the Avellaneda Stoikov Model we have the following definition of reserve price:
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/fy1Tj.png
This means that when q > 0 and the market maker has a long position, the reservation price decreases. So there is a greater chance that the marke... |
How do we relate time-horizon with reducing inventory risk in the Avellaneda-Stoikov model? |
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/4gQBj.jpg
So this the question and the answer to the first one states that only the 5 year swap rate will be adjusted for convexity and the answer to the second one states that neither of the rates will be adjusted for convexity.
My qu... |
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/4gQBj.jpg
So this the question and the answer to the first one states that only the 5 year swap rate will be adjusted for convexity and the answer to the second one states that neither of the rates will be adjusted for convexity.
My qu... |
In the derivation of the Black-Scholes PDE, using delta hedging, how is this linked to the risk neutral valuation? |
In Bloomberg's VCUB, what is the difference between the "strike" volatility and changing this option to "straddle"? It seems like the "straddle" vol should be the same as the strike vol but it is not? |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.