instruction stringlengths 15 26.1k |
|---|
I'm first going to describe how I believe the futures contract mechanics work, and please correct me where I'm wrong:
A contract seller (in a short position because usually they don't actually physically own the commodity yet) writes up a contract that stipulates that a certain amount of a certain commodity will be ... |
Why are futures contracts on the secondary market described as having 1 price, instead of 1 price for contract buyers and a 2nd price for sellers? |
Let's say we have 3 currencies:
- EUR/USD
- USD/GBP
- EUR/GBP
For a minute let's assume that we calculated the EUR/USD-USD/GBP correlation for the last N days and the result was 0.0 (I know this is not realistic but please bear with me). Other assumptions:
- EUR/USD volatility = 0.1
- USD/GBP volatilit... |
If I have 2 uncorrelated currencies, why is the volatility of their product higher than either of the volatilities? (better explanation inside) |
Let's say we have 3 currencies:
- EUR/USD
- USD/GBP
- EUR/GBP
For a minute let's assume that we calculated the EUR/USD-USD/GBP correlation for the last N days and the result was 0.0 (I know this is not realistic but please bear with me). Other assumptions:
- EUR/USD volatility = 0.1
- USD/GBP volatilit... |
There is a fascinating book from 1904 (yes, published more than 100 years ago) written by S. A. Nelson called *The A B C of Options and Arbitrage* (a reprint of it used to be available on Amazon [here](https://www.amazon.co.uk/gp/product/0217568386/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1), for example)
Quot... |
How is the Arrow Debreu Price related to Green's function at an intuitive level and how is this used in practice?
Note Added 2021/02/01
I came across this in the Black Derman Toy model paper by Boyle, Seng Tian (2000) and see Green's function used without explanation in other BDT articles. Green's function is als... |
There is a fascinating book from 1904 (yes, published more than 100 years ago) written by S. A. Nelson called "*The A B C of Options and Arbitrage*" (a reprint of it used to be available on Amazon [here](https://www.amazon.co.uk/gp/product/0217568386/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1), for example)
Qu... |
The call-based and put-based spreads do not differ, and the net effect of choosing either should be the same. Their payoffs are identical.
You can prove this by considering the following:
BUY 1x bear call spread @ Strike $X/$Y expiring Day D
SELL 1x bear put spread @ Strike $X/$Y expiring Day D
This m... |
Given a Brownian motion $W(t)$ I want to show that
\begin{align}
\lim_{n\rightarrow\infty}\mathbb{E}\left[\left|\sum_{j=0}^{n-1}\frac{jT}{n}\left(W\left(\frac{(j+1)T}{n}\right)-W\left(\frac{jT}{n}\right)\right) - TW(T)+\int\limits_0^TW(t)dt\right|^2\right]=0 \tag1.
\end{align}
For simplicity we denote the s... |
**EDIT:** Showing this using Ito's lemma is easy, that's NOT what I want to do. I also realised that $2\mathbb{E}[S\xi]\neq 2\xi\mathbb{E}[S]$ since $\xi$ is also a random variable. Nontheless, if this is the case I have no idea how to calculate the expectation of $S\xi$ anyway.
----------
Given a Brownian mo... |
I think it depens on the inner workings of the preferred language in the first place.
I suppose many order books are nowadays written in JS. So after considering many data structures like priority queues etc i think the best turns out to be a simple array and you don't even have to implement binary searches whatsoev... |
Consider a portfolio with 4 assets (A, B, C, D) with prices, quantities, current weights, and target weights as follows:
[![enter image description here][1]][1]
I want to rebalance the portfolio from the current weights to the target weights. There is a 0.2% transaction fee that is charged on the rebalance amount... |
I am trying to implement the pricing formula for a European (call) option given in Ales Cerny's paper "*Introduction to Fast Fourier Transform in
Finance*" (paper can be found [here][1]), as follows:
[![enter image description here][2]][2]
My python code below does not return the correct answer, and in partic... |
Let's say we have 3 currencies:
- EUR/USD
- USD/GBP
- EUR/GBP
For a minute let's assume that we calculated the EUR/USD-USD/GBP correlation for the last N days and the result was 0.0 (I know this is not realistic but please bear with me). Other assumptions:
- EUR/USD volatility = 0.1
- USD/GBP volatilit... |
I have a quick question: why does EMH assume the stock prices follow a martingale process?
I understand that the discounted prices under the risk-neutral probability measure is a martingale. This can be shown explicitly. But how is this related to the statement that (pre-discounted, and under the true distribution) ... |
why do stock prices follow a martingale? |
Are Cont's "stylized facts" based on reliable evidence? |
It only means that the directions of future movements of stock prices are impossible to forecast.
For a more mathematical explanation, consider this [document][1].
[1]: https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwi-uZalscvuAhXLwAIHHduNCMgQFjABegQIBBAC&url=http%3A... |
I recently read Marcos Lopez de Prado's book "Advances in Financial Machine Learning" where I was introduced to the concept of using volume/dollar bars instead of time bars. As far as I understand, whereas time bars have you taking a measurement every set time interval (ex. once per hour), using volume/dollar bars mean... |
Is it possible to use volume/dollar bars instead of time bars when analyzing multiple variables? |
I have a quick question: why does the Efficient Market Hypothesis (EMH) assume that stock prices follow a martingale process?
I understand that discounted prices under the risk-neutral probability measure are a martingale. This can be shown explicitly. But how is this related to the statement that (pre-discounted, a... |
Why do stock prices follow a martingale? |
I am trying to replicate the steps of the Barras, Scaillet, Wermer(2010) paper for a Monte-Carlo Simulation. More specifically the steps in Appendix B.1 (Attached image).
I have so far done the regressions for all the funds, sampled 1,400 funds, and adjusted the alphas as the authors did.
But I am having trouble und... |
I wouldn't sweat this one. He's just making a simple "on average" assumption and not examining the wings of the actual distribution. Below is the actual quote you're referring to; and why this one isn't quite right in this case.
But the point he's trying to make isn't invalid just because he chose a bad example to ... |
When analyzing the performances of a strategy, the profits are computed as the final balance divided by the starting balance. What happens if the quote quantity has changed in between ?
For example, let's say that I want to trade crypto, on ETH/BTC. I start trading with 1 BTC on January 1st. On February 1st, I have ... |
I am trying to implement the pricing formula for a European (call) option given in Ales Cerny's paper "*Introduction to Fast Fourier Transform in
Finance*" (paper can be found [here][1]), as follows:
[![enter image description here][2]][2]
My python code below does not return the correct answer, and in partic... |
I am looking at mainly value and growth factor coefficients of a fund during the recent Covid market “crisis”.
I have found that said fund had a negative coefficient to value at the start of 2020 (let’s say around -0.4) and a positive growth coefficient (around 0.3).
The correlation at this time between the two... |
Is there a way using matrix algebra to add portfolios to a covariance matrix of assets? |
When I simulate a stock's price path using geometric brownian motion I am sometimes able to get a pretty good forecast that fits the real values very well. But if I run the simulation again, the results are different. This is probably due to the random process of brownian motion.
Is there a way to run the same simu... |
stock price path simulation using GBM, is it possible to run the same simulation over and over again? |
Say Bob wants to buy \$30 million worth of APPL stock at a price of \$130.
He decides to use a limit order.
But posting a $30 million limit order would drive the price up and prevent him from being filled.
Obviously he must post only a fraction of this amount and then slowly top it up each time he gets filled... |
How does a trader choose how to size his limit order? |
When reading RegSho, I see a table like this:
```
Date Symbol ShortVolume ShortExemptVolume TotalVolume Market
20210202 A 93137 2300 297479 B,Q,N
20210202 AA 1174892 2077 3055114 B,Q,N
20210202 AAA 8 0... |
What does Short Volume in FINRA RegSho actually measure? |
I'm trying to understand the term "risk premium". I keep seeing statements like
this (from
[Investopedia](https://www.investopedia.com/terms/r/riskpremium.asp)) "A risk
premium is the investment return an asset is expected to yield in excess of the
risk-free rate of return." The explanation then goes on to say "A r... |
Does "risk premium" imply a difference in expected value? |
I'm trying to understand the term "risk premium". I keep seeing statements like
this (from
[Investopedia](https://www.investopedia.com/terms/r/riskpremium.asp)) "A risk
premium is the investment return an asset is expected to yield in excess of the
risk-free rate of return." The explanation then goes on to say "A r... |
A more risky investment doesn't necessarily need to have a downside as in loss, just the possibility of earning less than a less risky asset.
Let's walk through a simplified example - please tell me which parts are not clear.
Suppose we have a choice of two investments. The "riskless" investment costs $1 now, and... |
Here are some alternatives:
1) Utilize [Accumulate Distribute](https://www.interactivebrokers.com/en/index.php?f=4985) algorithm to reduce market impact.
2) Place an iceberg order.
3) Place a LOC (limit on close) order to execute it at the closing cross. |
Based on the latest data published by ECB,€STR = -0.56%. Is this the rate a bank would pay to borrow overnight or it's an annualised overnight rate so the actual overnight rate can be approximated with -0.56% ^(1/365)? |
Based on the latest data published by ECB,€STR = -0.56%. Is this the rate a bank would pay to borrow overnight or it's an annualised overnight rate so the actual overnight rate can be approximated with (1 - 0.56%)^(1/365) - 1? |
can you add to your screenshot a bit further to the left? i am guessing that 2nd row is a 6m fra, in which case to work out the discount factor, you probably need an interpolation assumption as to how the 1m is gotten |
Have you tried using **ccxt**? This library is available on GitHub and offers *most* of what you’re looking for. It offers minutely candle data from several dozen exchanges as well as a backtesting framework which implements indicators really well. I’m not sure if they offer intra-candle strategies but their features s... |
Actually, I have no experience with binary options trading but on the internet, I see that people talk about them in a bad way.
Why does binary options trading has a bad reputation?
Thanks |
Why does Binary Options has a bad reputation? |
Why do Binary Options have a bad reputation? |
Can you please confirm if the underlying rate of US overnight indexed swaps is SOFR or Fed funds? |
I have a collection of client transactions representing the trades of a single portfolio across multiple securities. What I'd like to do is the calculate the accurate ROI of each security and of the whole portfolio (total and by year).
Sounds simple but it's not in a number of dimensions:
1. I only have all the tr... |
Resources to learn the applications of SVD in quant finance? |
I've done a bit more research and I'll attempt a self-answer here.
### The top level definition is correct, all of the inferences that follow it are wrong.
> What do these numbers actually represent? People on reddit are claiming that ShortVolume is the sum of shares in transactions where the seller did not actua... |
In the meantime, Gianluca de Nard has published [Oops! I Shrunk the Sample Covariance Matrix Again: Blockbuster Meets Shrinkage][1], which works out the idea eluded to in the comments explicitly.
[1]: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3400062 |
I just started learning about credit products.
Let $B_t^T$ be the price of a risk free zero coupon bond at time $t$. Similarly, let $C_t^T$ be the price of a zero coupon risky bond from some fixed issuer (no recovery). Both pay one dollar at maturity.
Let $T_1 < T_2$ and define a recovery bond as an asset that pa... |
I've done a bit more research and I'll attempt a self-answer here.
### The top level definition is correct, all of the inferences that follow it are wrong.
> What do these numbers actually represent? People on reddit are claiming that ShortVolume is the sum of shares in transactions where the seller did not actua... |
I am trying to understand the difference between FOK and IOC orders. If I send a market FOK or IOC order to sell 100 shares of StockX - what would happen if the orderbook looked like this?
SELL SIDE OF ORDER BOOK
50 @ 300
25 @ 301
100 @ 302
|
A more risky investment doesn't necessarily need to have a downside as in loss, just the possibility of earning less than a less risky asset.
Let's walk through a simplified example - please tell me which parts are not clear.
Suppose we have a choice of two investments. The "riskless" investment costs $1 now, and... |
I am trying to understand the difference between FOK and IOC orders. If I send a market FOK or IOC order to sell 100 shares of StockX - what would happen if the orderbook looked like this?
SELL SIDE OF ORDER BOOK
50 @ 300
25 @ 301
100 @ 302
|
When using the Black 76 model for pricing European index options I've often seen people use 2 different rates: the typical risk free rate used to get the discount factor, and a growth rate used to get the forward price. The adjusted equation for a call option (assuming no dividends) using $r_g$ as the growth rate and $... |
@DimitriVulis explained it well. The dynamic that is the source of your uncertainty here is that "risk premium" can mean slightly different things, when seen from slightly different perspectives. Much of the confusion around this subject stems from inconsistency in the use of these close and related but distinct concep... |
Would it be appropriate to say that the scaling ($b$) on the weights ($w_{t,i}$) is irrelevant because you can just pick a scaling of $w_{t,i}$ that satisfies this requirement?
Furthermore, if $a \neq 1$ later in the paper they define $R^e_{t+1,i} = \beta_{t,i}F_{t+1} + \epsilon_{t+1,i}$ where $F_{t+1} = w_t^{\text{... |
Are option dealers usually net sellers or buyers of single name stock options? |
Some say the presence of autocorrelation (aka serial correlation) in a stock's financial return time series helps with forecasting its next-day movements, unlike a stock that has low serial correlation between its return observations.
Does this mean that a stock with high serial correlation should be weighted more h... |
Should a stock with high return autocorrelation be weighted more heavily in a portfolio? |
Hmm... some notable implicit assumptions made en passant here ;-) How persistent are these autocorrelations (ACs)? Let's unpick a little.
One obvious question is whether your AC process is strong enough to overcome transaction costs and slippage, if markets are almost-random. Then someone trying to trade that could ... |
The distribution of drawdown is highly sensitive to the trading strategy you are running. The distributions of drawdown for a Black Swan strategy and carry strategy are very different. Only you know what you are doing. If you are good, drawdown will have thin upper tail. If you are not good, it may have fat upper tail ... |
The distribution of drawdown is highly sensitive to the trading strategy you are running. The distributions of drawdown for a Black Swan strategy and carry strategy are very different. Only you know what you are doing. If you are good, drawdown will have thin upper tail. If you are not good, it may have fat upper tail ... |
The distribution of drawdown is highly sensitive to the trading strategy you are running. The distributions of drawdown for a Black Swan strategy and carry strategy are very different. Only you know what you are doing. If you are good, drawdown will have thin upper tail. If you are not good, it may have fat upper tail ... |
# Drifts under $\mathbb{Q}$ and $\mathbb{P}$
Some good answers already. Let me just repeat for clarity: **under the risk neutral measure $\mathbb{Q}$, the drift of all assets has to equal to the rate at which the Numeraire appreciates**, i.e. typically this is the risk-free rate $r$ of the money market.
The reas... |
# Drifts under $\mathbb{Q}$ and $\mathbb{P}$
Some good answers already. Let me just repeat for clarity: **under the risk neutral measure $\mathbb{Q}$, the drift of all assets has to equal to the rate at which the Numeraire appreciates**, i.e. typically this is the risk-free rate $r$ of the money market.
The reas... |
# Drifts under $\mathbb{Q}$ and $\mathbb{P}$
Some good answers already. Let me just repeat for clarity: **under the risk neutral measure $\mathbb{Q}$, the drift of all assets has to equal to the rate at which the Numeraire appreciates**, i.e. typically this is the risk-free rate $r$ of the money market.
The reas... |
# Drifts under $\mathbb{Q}$ and $\mathbb{P}$
Some good answers already. Let me just repeat for clarity: **under the risk neutral measure $\mathbb{Q}$, the drift of all assets has to equal to the rate at which the Numeraire appreciates**, i.e. typically this is the risk-free rate $r$ of the money market.
The reas... |
In article from Reuters: [Big U.S. banks hunger for loans, capital relief as deposits pile up][1], we read:
> Combined with rules that require more capital for bigger balance sheets, that makes deposits more expensive to hold, instead of profitable.
If I understand correctly, it means that the banks has to keep c... |
Why do banks have capital requirements on deposits? |
In article from Reuters: [Big U.S. banks hunger for loans, capital relief as deposits pile up][1], we read:
> Combined with rules that require more capital for bigger balance sheets, that makes deposits more expensive to hold, instead of profitable.
If I understand correctly, it means that the banks has to keep c... |
In article from Reuters: [Big U.S. banks hunger for loans, capital relief as deposits pile up][1], we read:
> Combined with rules that require more capital for bigger balance sheets, that makes deposits more expensive to hold, instead of profitable.
If I understand correctly, it means that the banks has to keep c... |
Is there a forward contract on a forward contract?
Let us take a simple example: Persons $A$ and $B$ agree that $A$ sells $B$ some asset tomorrow at the fixed price $K_1$. This is a normal forward contract on the asset.
Let us then assume that persons $B$ and $C$ agree that $B$ sells $C$ the previously described ... |
Is there a forward contract the underlying of which is another forward contract? |
Is there a forward contract on a forward contract?
Let us take a simple example: Persons $A$ and $B$ agree that $A$ sells $B$ some asset tomorrow at the fixed price $K_1$. This is a normal forward contract on the asset.
Let us then assume that persons $B$ and $C$ agree that $B$ sells $C$ the previously described ... |
I am learning about portfolio theory and been using Markowitz. I wondered, however, if I can use distributional and asymmetric information of the returns to solve the problem. For instance, I have a process that follows Frechet distribution, and it does have a finite variance, for which such optimization would be very ... |
In article from Reuters: [Big U.S. banks hunger for loans, capital relief as deposits pile up][1], we read:
> Combined with rules that require more capital for bigger balance sheets, that makes deposits more expensive to hold, instead of profitable.
If I understand correctly, it means that the banks has to keep c... |
Another problem is the bank's GSIB score. There are about 10 components that go into the GSIB score calculation, but one of them is (bank equity)/(balance sheet).
Having a poor GSIB score means the bank will have to a surcharge assessment on it's balances.
So in other words, if a bank just takes in more de... |
Another problem is the bank's GSIB score. There are about 10 components that go into the GSIB score calculation, but one of them is (bank equity)/(balance sheet).
Having a poor GSIB score means the bank will have to a surcharge assessment on it's balances.
So in other words, if a bank just takes in more de... |
My book says:
"By construction, the cash flows of inflation linked bonds are indexed, using daily indexation factors that are applied to the real price of a bond to arrive to the dirty price of the bond. This means that holding a linker for a given time gives you a positive carry effect during periods when inflation... |
Why does holding a linker give you positive carry when inflation indices move up? |
# Drifts under $\mathbb{Q}$ and $\mathbb{P}$
Some good answers already. Let me just repeat for clarity: **under the risk neutral measure $\mathbb{Q}$, the drift of all assets has to equal to the rate at which the Numeraire appreciates**, i.e. typically this is the risk-free rate $r$ of the money market.
The reas... |
Currently reading A. Damodaran‘s book Investment Valuation. In chapter 5 in order to value an option using black-scholes model he adjusts risk free rate using the following formula:
1-exp(-r)
I. E. If given risk free rate is 3,6
it becomes 1-exp(-0,036) = 3,54%
Why is that? I wasn’t able to find any explanation o... |
Currently reading A. Damodaran‘s book Investment Valuation. In chapter 5 in order to value an option using black-scholes model he adjusts risk free rate using the following formula:
$1-\exp(-r)$
I. E. If given risk free rate is 3,6
it becomes $1-\exp(-0,036) = 3,54\%$
Why is that? I wasn’t able to find any explan... |
Currently reading A. Damodaran‘s book Investment Valuation. In chapter 5 in order to value an option using black-scholes model he adjusts risk free rate using the following formula:
$1-e^{-r}$
I. E. If given risk free rate is $3,6%$
it becomes $1-e^{(-0,036)} = 3,54\%$
Why is that? I wasn’t able to find any expla... |
I am currently working with a pretty large panel dataset containing the investment holdings of many individuals over time (i.e., for each individual I know the positions per stock over time). I was wondering what the best measure is to examine portfolio allocation changes over time. In the mutual fund literature, resea... |
I was reading this definition: https://investorplace.com/2018/08/what-is-implied-volatility-concern-investors-invtlk/
> If its IV stands at 20%, a movement of 20%, or $20 per share, over a 12-month period would be equal to one standard deviation.
So then why do 1 DTE options have 80% IV at say \$320 strike on spy... |
What is IV really? Why does an option that is about to expire have such high IV for OTM options? |
I stumbled on this not so complicated concept and couldn't figure out what it's called.
I want to buy something that costs $M$ units of money, and have to pay it in $n$ months at a rate of $\frac M n$ every month, with no interest (just to simplify the calculations). I take $M$ units of money and immediately invest ... |
What is the name of this concept/formula? |
I am working on a project to choose the perfect combination of 5 stocks from a total of 15 stocks to get the "highest gains". Here's the approach I plan to use.
Run a loop for all combinations of 5 stocks from 15 (i.e. 15C5). Once I have the eigenvalues for each combination, I have learnt that the portfolio with the ... |
There is a wide literature on optimal execution, among others:
* [Rigorous Strategic Trading: Balanced Portfolio and Mean-Reversion, by Lehalle, 2009, Vol. 4, No. 3: pp. 40-46][1]
* [Optimal Control of Trading Algorithms: A General Impulse Control Approach, by Bouchard, Dang, Lehalle, in SIAM J. Finan. Math., 2(1),... |
There is a wide literature on optimal execution, among others:
* [Rigorous Strategic Trading: Balanced Portfolio and Mean-Reversion, by Lehalle, 2009, Vol. 4, No. 3: pp. 40-46][1]
* [Optimal Control of Trading Algorithms: A General Impulse Control Approach, by Bouchard, Dang, Lehalle, in SIAM J. Finan. Math., 2(1),... |
If US 10yr = 2%, does it mean if I hold the bond until maturity/for next 10 years the yield is 2% or I get an annual return of 2% for 10 years?
For example the yields in the link:
https://www.investing.com/rates-bonds/world-government-bonds
|
Are government bond yields usually expressed as yield to maturity (YTM) or annual yield? |
Why must we find the beta of a variable first before running the cross sectional regression for a factor model. Why can’t we just directly run the cross section of market cap versus return say for each time point? |
I am struggling with the concepts and variables of corporate bonds returns.
Bai, Bali and Wen (2019) define monthly corporate bond returns as:
<img src="https://latex.codecogs.com/gif.latex?r_{i,t}&space;=\frac{P_{i,t}+&space;AI_{i,t}&space;+&space;C_{i,t}}{P_{i,t-1}+&space;AI_{i,t-1}}&space;-1" ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.