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I'm pretty new to quant and I'm trying to better understand the Random walk (and EMH) narrative and the idea that using past data is irrelevant to predict future prices.
To illustrate my point, let me share 2 charts.
Monthly Bitcoin chart
[![Monthly Bitcoin chart][1]][1]
Monthly S&P500 chart since 20... |
Do markets really follow a random walk or is this idea outdated? |
No, the idea is not outdated. Fama, who coined the term EMH in 1970 and was awarded the Nobel Prize for his work on market efficiency calls the EMH ``[one of the two pillars of modern asset pricing](https://www.aeaweb.org/articles?id=10.1257/aer.104.6.1467)''.
The EMH describes how asset prices should work in an Eco... |
No, the idea is not outdated. Fama, who coined the term EMH [in 1970](https://www.jstor.org/stable/2325486) and was awarded the Nobel Prize for his work on market efficiency calls the EMH ``[one of the two pillars of asset pricing](https://www.aeaweb.org/articles?id=10.1257/aer.104.6.1467)''.
The EMH describes how a... |
No, the idea is not outdated. Fama, who coined the term EMH [in 1970](https://www.jstor.org/stable/2325486) and was awarded the Nobel Prize for his work on market efficiency calls the EMH ``[one of the two pillars of asset pricing](https://www.aeaweb.org/articles?id=10.1257/aer.104.6.1467)''.
The EMH describes how a... |
I'm very new to pairs trading, and am trying it out on a few dozen pairs.
It seems very natural to me to use a **dynamic** hedge ratio, as it seems likely that the ratio will move over time.
To accomplish this, I am using rolling linear regression (so I choose a lookback period of, say, 100 hours and I keep shift... |
Pairs trading using dynamic hedge ratio - how to tell if stationarity of spread is due to genuine cointegration or shifting of hedge ratio? |
I am late here, but I will give my answer to help any one with same question. Ml tries to find patterns in the data, and if you give labels based on trend this will not be enough. There has to be a strategy so the algorithm can connect the dots. The reason is why meta labeling is done is that you think that for example... |
From the post <https://quant.stackexchange.com/questions/29504/integral-of-brownian-motion-w-r-t-time> we have an argument for
$$\int_0^t W_sds \sim N\left(0,\frac{1}{3}t^3\right).$$
However, how does this generalise for the interval $[t;T]$? I.e. what is the distribution of
$$\int_t^T W_sds.$$
I would exp... |
Given a specified maturity is there a way to compare Vega between different strikes? Surely the Vega of ATM option will be very different from the same Vega in an OTM option |
How can you compare Vega between strikes? |
Is the ytm curve same as the par curve? |
Total newbie here, I am struggling to calculate the correct repo PL on a transaction.
Basically I have a GBP Bond which I repo out as below:
UKT 2.75 09/24 (EK1093963)
so (41,395,983) @ 103.57 and I receive cash in of GBP 42,874,661. Lets assume the TD is 24th Feb and the Repo starts on the 25th of Feb. Repo ... |
EDIT: this question was previously closed because it was 'assumed that it should be common knowledge'. I advise you to READ THE QUESTION PROPERLY and you will find out is is NOT common knowledge at all, due to the fact this is a particular case of bootstrapping.
In regular bootstrapping you would have a bond and spot... |
I am looking at the stock PDN (Paladin Energy) on ASX (Australia Stock Exchange), and I am trying to determine the lowest price traded on the date 2020.03.23 (YYYY.MM.DD). Should not be such a difficult task, eh?
So, lets ask Yahoo Finance, which provides a low price for the day of 0.0350. Ok.
https://finance.yah... |
What was the lowest traded price of Paladin Energy on 2020.03.23? Every source disagrees, then it gets even weirder |
No, the idea is not outdated. [Fama (1970, JF)](https://www.jstor.org/stable/2325486) summarises the early research on stock price behaviour and defines an efficient market as follows:
> *A market in which prices always ''fully reflect'' available information is called ''efficient.''*
This article awarded Fama the ... |
I would like to ask about discount rates calculation algorithm by Bloomberg terminal.[![Zero Curve from Bloomberg Terminal][1]][1]
In the image above is possible to notice the discount rate for each term. The short end, instruments from 1 DY up to 18 MO, is composed by zero coupon swaps. The long end, instruments fr... |
How Bloomberg calculates discount rates for zero rate curves? |
Why do we need a brokerage? |
I am interested to invest `Rs. 1 lacks` in security market. I have securities `A` and `B` for this purpose.
Here is the details:
Security Risk Expected_return
A 10% 12%
B 18% 20%
Coefficient of correlation between `A` and `B` is `0.15`.
If I decide to ... |
I have several questions regarding Fama-French and other (for instance, BAB) equity return factors for practical purposes (portfolio construction, portfolio risk analysis, portfolio return analysis). I am interested in answer for any of the questions below. I am familiar with "factor zoo", so below when I write "factor... |
How to correctly use Fama-French factors (from investment portfolio perspective)? |
Let's say I have a 10 year dataset of Tesla (example) and I am taking the percentage change of lag 2 :
```
tsla <- quantmod::getSymbols("TSLA", from = base::as.Date("2011-01-01"), to = base::as.Date("2022-01-31"), auto.assign = F)
tsla = as_tibble(tsla)
head(tsla)
d = tsla%>%
dplyr::select(TSLA.Adjusted)%>%
... |
Let's say I have a 10 year dataset of Tesla (example) and I am taking the percentage change of lag 2 :
```
tsla <- quantmod::getSymbols("TSLA", from = base::as.Date("2011-01-01"), to = base::as.Date("2022-01-31"), auto.assign = F)
tsla = as_tibble(tsla)
head(tsla)
d = tsla%>%
dplyr::select(TSLA.Adjusted)%>%
... |
I have a set of time series data from a bank that is transaction data from all its clients on a particular currency.
From that data, I attempt to estimate the current "position" of all market participants in that currency.
I do that through a rolling 20 day total (1 month). However sometimes that total changes ... |
Let's say I have a 10 year dataset of Tesla (example) and I am taking the percentage change of lag 2:
```
tsla <- quantmod::getSymbols("TSLA", from = base::as.Date("2011-01-01"), to = base::as.Date("2022-01-31"), auto.assign = F)
tsla = as_tibble(tsla)
head(tsla)
d = tsla%>%
dplyr::select(TSLA.Adjusted)%>%
... |
There are some cryptic things you do in your described procedure. I am unclear why you produce returns based on the 2-lag and whether it is necessary for out-of-sample VaR forecasting. This might be used for in-sample VaR forecasting? It is also unclear, why do you fit a GARCH model (in the end of the code) to standard... |
Let's say I have a 10 year dataset of Tesla (example) and I am taking the percentage change of lag 2:
```
tsla <- quantmod::getSymbols("TSLA", from = base::as.Date("2011-01-01"), to = base::as.Date("2022-01-31"), auto.assign = F)
tsla = as_tibble(tsla)
head(tsla)
d = tsla%>%
dplyr::select(TSLA.Adjusted)%>%
... |
## 1. Portfolio construction stage
#### 1.1
Yes, practitioners really use factor strategies, see [style investing](https://en.wikipedia.org/wiki/Style_investing). Prominent examples are [DFA](https://us.dimensional.com/) and [AQR](https://www.aqr.com/). Both firms were co-founded by former PhD students of Eugene ... |
Let's say I have a 10 year dataset of Tesla (example) and I am taking the percentage change of lag 2:
```
tsla <- quantmod::getSymbols("TSLA", from = base::as.Date("2011-01-01"), to = base::as.Date("2022-01-31"), auto.assign = F)
tsla = as_tibble(tsla)
head(tsla)
d = tsla%>%
dplyr::select(TSLA.Adjusted)%>%
... |
I'm thinking about some sort of behavioral risk factors such as whether different utility functions, such as Prospect Theory according to Kahneman and Tversky, might change the way betas are derived and formulated and whether there are risk factors such as - say- some sort of loss aversion risk premium and such. From ... |
General Markowitz-style optimization (problem objective of $w^T \mu - \lambda w^T \Sigma w$) yields simple optimal weights policy $w \propto \Sigma^{-1} \mu$.
However, I would like to add a series of factor exposure constraints (i.e. $| w^T \beta_i | < k_i$ for factors indexed by $i$, instrument exposure vector to ... |
I am doing spot price forecasting for a market, and so far, the naive forecasting model, which forecasts with the last observed prices, is the best forecasting model. I know that it might be because of my poor forecasting skills; however, how can this situation be explained if it is not the case?
So far, I have com... |
Linear correlation controls two aspects : that of **level** (Basket options) and that of **dispersion** (spread options). Is there a copula that has two separate parameters for each? |
The payoff of a cap/floor is calculated as a payoff of constitutient caplets/floorlets.
The [SABR volatility model][1] has the implied volatility approximations of *Hagan et al.*
$$\sigma^f_{IV}\approx \sigma_{Hagan}(t_0, K, F_0, \alpha, \beta, \rho, \nu)$$
which allows one to price an individual forward-looking L... |
Consider a maturity $T$, for this maturity I have some implied volatility from market denoted $\sigma^{0}_{i}$. I want to interpolate these volatility using Entropy approach, by using $\sigma^{0}_{i}$ as prior.
From $\sigma^0_i$, market prices of options $C_i$ can be obtained, out of which a probability distribut... |
Let's say I have a 10 year dataset of Tesla (example) and I am taking the percentage change of lag 2:
```
tsla <- quantmod::getSymbols("TSLA", from = base::as.Date("2011-01-01"), to = base::as.Date("2022-01-31"), auto.assign = F)
tsla = as_tibble(tsla)
head(tsla)
d = tsla%>%
dplyr::select(TSLA.Adjusted)%>%
... |
Given a specified maturity is there a way to compare Vegas between different strikes? Surely the Vega of an ATM option will be very different from the same Vega of an OTM option |
Does tail risk disappear in the long horizon in any rolling over strategy with shorter frequency? |
I've been told (and have done problems) involving the part of the return of an asset $X$ that is uncorrelated with returns on the market $M$, which can be written as $X - \beta X$. This sort of makes sense, but if someone asked me to explain what "the part of $X$ that is uncorrelated with $M$" is, I would've guessed $X... |
For CLOs, CDOs kind of security, how can I build a cashflow model when the tranche supporting structure is very complex. For example:
After tranche A is paid, the amount going to B is going to depend on balance of tranche B, C, D. What would be algorithm to generic code to determine the percentage of money going to ... |
How to build waterfall models in face of complex structured securities? |
I am submitting applications to entry level Quantitative Developer positions. I come from the mathematical finance side but can code in C++ with simple concurrency. Many of the job postings I see mention that a background in operating systems or networking is a plus, and many Glassdoor interview questions mention being... |
What are good resources on Operating Systems and Networking as they relate to high frequency trading? |
I would like to compute the evolution of the P&L of an FX plain vanilla option. Unfortunately, I am not sure about the correctness of my reasoning.
Let's imagine that I sell a 1W call option on a Monday. On that day, I will receive a premium which in my case, is computed using Garman and Kholagen pricing method. Let... |
In the book "Mathematics of Financial Markets" by R. J. Elliott and P. E. Kopp, Second Edition there is a claim made in the proof of Lemma 2.2.5., namely that $V_0(\theta)=V_0(\phi)$.
I don't see why this would hold without making a rather long argument about EMM, which the book has not gotten to yet. The assumptions o... |
In the book "Mathematics of Financial Markets" by R. J. Elliott and P. E. Kopp, Second Edition there is a claim made in the proof of Lemma 2.2.5., namely that $V_0(\theta)=V_0(\phi)$.
I don't see why this would hold without making a rather long argument about EMM, which the book has not gotten to yet. The assumptions ... |
I just know these products recently: **Performance Total Return Swap (TRS), Performance Fixed TRS and Performance Float TRS.**
But cannot find a detailed explanation of the product, all I can find is an introduction about performance swap: https://www.investment-and-finance.net/derivatives/p/performance-swap.html an... |
What is the Performance Total Return Swap (TRS)? How about Performance Fixed TRS and Performance Float TRS? |
Wiener processes are used to model various assets, and I wonder why we are introducing correlations between the Wiener processes and what is the interpretation? Because when the correlations between two Wiener processes is $\rho$, the the correlations between for example stock prices in Black Scholes model will not be ... |
Why we introduce correlations between Wiener processes? |
I've been studying the application and derivation of a domestic implicit rate in a FX contract when your input are the forward points and the foreing rate. Let's establish some with some ideas first.
The FX market revolves around the spot rate and it's forwards around forward points. Which are added/substracted to t... |
> Does that mean that one can directly calibrate vanilla SABR model for
> LIBOR to the market quotes of SOFR taking care of the differences in
> expiry and settlement, and adjusting the number of caplets in a cap
> (first caplet is omitted for LIBOR)?
I sent an email to the author of the aforementioned paper and ... |
Trying to understand, how to find out which of these bonds are cheap and which are expensive?
The current spot rate is 8.167%. How do I go about finding the cheap vs expensive bonds especially when YTM is same?
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/jRwkh.png |
Between these bonds, how to find out which is one pricey (Higher valuation) and cheap (Lower valuation)? |
Is this correct?
Using discount factors, the 8% coupon bond should be trading at
( 8 * .96154) + ( 108 * .85734) = $100.285
Since it is trading only at $100, the coupon paying bond is cheaper and zero coupon bonds are trading at higher premium.
|
An exotic option is described as follows:
> Let $S_t$ be the underlying at $t$. The holder has the option to lock
> in the current price during the lifetime of the option, which he does for $S_{t}=50$. The strike price is $K=40$. At
> maturity, the option returns the payoff of a traditional European call
> or the... |
What is the name and payoff of this exotic option (where the holder can lock in a price)? |
An exotic option is described as follows:
> Let $S_t$ be the underlying at $t$. The holder has the option to lock
> in the current price during the lifetime of the option, which he does for $S_{t}=50$. The strike price is $K=40$. At
> maturity, the option returns the payoff of a traditional European call
> or the... |
No, you cannot reverse engineer the variance of the prices from the variance of the returns because the variance of the returns must be infinite for any credible candidate distribution for prices. That does not imply that you cannot get information about the variance of prices, but not from the variance of returns.
... |
@Stéphane answer is quite good. There are a few more details to consider:
- the mids may not be arbitrage-free. If you need arbitrage-free prices, you will need to find the closest arbitrage-free quotes, for example following Appendix B of [An arbitrage-free interpolation of class C2 for option prices][1]
- you may i... |
Quant Firm Interview Question
We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? My thinking is as follows.
- EV is 1.25 dollars. Therefore we pay anything less tha... |
How much compensation need to take on risk? |
Are there certain categories of quantitative strategies, such as arbitrage, momentum, etc, that are more resistant to alpha decay than others?
Thanks |
Strategies That Are Resistant To Alpha Decay? |
Strategies That Are More To Resistant To Alpha Decay Than Others? |
I downloaded data from **Refinitiv Datastream** (But I think that you get the same data from **Bloomberg**) to write my thesis. I downloaded prices and volumes.
I have a crucial question now: Are the prices that I downloaded from Refinitiv *(Closing price of day t)* **quote-** or **order-** driven prices?
That is,... |
Downloaded data is quote-driven or order-driven? |
I have never understood the implications of a quote or order-driven market.
When I look up securities on google in a way to see their prices, is that price the price of the exchange? the price of a quote driven market? the price of an order-driven market? Do quote- or order-driven market determine the price in the ... |
Why are unsecured term deposits in EUR yielding lower than a simple overnight deposit at the ECB ? Isn't it supposed to be the opposite ?
The 3 month Euribor just broke -0,50% a few days ago, why was it so low for so long ?
Source : https://sdw.ecb.europa.eu/quickview.do?SERIES_KEY=143.FM.M.U2.EUR.RT.MM.EURIBOR3M... |
Why are/were Euribor rates consistently lower than ECB deposit facility rates since 2020? |
I have the price of a bond and would like to convert it to spreads. Is this possible by just having dollar duration? |
How to correctly express basket of currencies in and index, such that P&L would align?
Assume our index is 20% EURUSD and 80% GBPUSD and rates are 1.10 and 1.31 for T1 and 1.05 and 1.35 for T2. On a USD 100,000 total real P&L is 20,000*(1.05/1.10-1) + 80,000*(1.35/1.31-1) = $1,533.66
Now for the index, whatever I... |
Unless I misread your question, **NO**: Spread calculation (calibration) is a **root-finding** exercise. In the simplest case (flat rate curves), given market price $P$ and reference yield $r$ (e.g. treasury rate), which spread level $s$ ensures that
$$
s:PV(r,s,t,T)\equiv\sum_{i}c_ie^{-(r+s)(T-t_i)}\stackrel{!}{=... |
Let $u(x)=x^{2/3}$, $x>0$ be the utility function, $X \sim U(0, 100)$ is loss, wealth $w=\$150$.
Calculate $\mathbb{E}(u(w_r))$ if a proportional protection is $80\%$ and gross premium is $\$43$.
My attempt is:
$E(u(w_r))=\frac{1}{100}\int_0^{43}(150-43)^{2/3}dt + \int_{43}^{100} (150-0.8t)^{2/3}dt=\$21.3486$... |
How to compute the mean for utility function? |
Maybe you misinterpreted the protection? Also, utility does not stand in $\$$. I'd come up with
$$
\frac{1}{100}\int_0^100(150-43-0.2t)^{2/3}dt=21.103
$$ |
I have the price of a bond and would like to convert it to spreads. Is this possible by just having dollar duration?
Secondly, if I just care about the relative spreads of multiple bonds, is it enough to consider their prices and dollar durations? Would I simply divide the price by the dollar duration to get relative ... |
Maybe you misinterpreted the protection? Also, utility does not stand in $\$$. I'd come up with
$$
\frac{1}{100}\int_0^{100}(150-43-0.2t)^{2/3}\mathrm{d}t=21.103
$$ |
Let $u(x)=x^{2/3}$, $x>0$ be the utility function, $X \sim U(0, 100)$ is loss, wealth $w=\$150$.
Calculate $\mathbb{E}(u(w_r))$ if a proportional protection is $80\%$ and gross premium is $\$43$.
My attempt is:
$E(u(w_r))=\frac{1}{100}\int_0^{43}(150-43)^{2/3}dt + \int_{43}^{100} (150-0.8t)^{2/3}dt=21.3486$
... |
I'm using Quantlib in Python to price an FX option. I'm comparing the result to Bloomberg, to make sure the code is working correct.
I want to calculate the P&L of a certain option trading strategy by using Taylor expansion of P&L (discussed in other post [here][1])
And also by using the NPV of the option.
There... |
I have a question regarding the Cox-Ross-Rubenstein (CRR) model (Cox et al.,1979). While I do understand how the model is constructed, I am now trying to put it into code and am not sure how to translate the phi correctly or what it means in this notation. Could somebody kindly help me on that small matter?
Regards,
... |
What is Phi in Cox-Ross-Rubinstein Binomial Model? |
I am currently trying to predict the close price of the TSLA stock for March 2022 using LSTM model. Initially, I was using TSLA stock data starting from 2012 to of course March 2022. However, I was wondering if this is effective as the TSLA stock has undergone great changes in terms of its volatility, behavior, and mom... |
In stock prediction with LSTM, is there a need to get a dataset for a specific time period in order to predict future close price? |
I see the tickers Z and ZG are for the same company, zillow. But I don't understand what G stands for. Could anybody let me know? |
What does G in ZG stands for? |
ATRO is traded on NASDAQ.
https://finance.yahoo.com/quote/ATRO
ATROB is traded on OTC.
https://finance.yahoo.com/quote/ATROB
I don't understand why a company has one stock on NASDAQ and one stock on OTC. Does anybody know? |
Why a company can have one stock on NASDAQ and one stock on OTC? |
The way to find answers to questions like this is to look in the 10K. For example
https://yahoo.brand.edgar-online.com/displayfilinginfo.aspx?FilingID=15552152-254326-258388&type=sect&TabIndex=2&dcn=0001617640-22-000013
> **Item 5. Market for Registrant’s Common Equity...**
>
> Our Class A common stock has trad... |
**Astronics Corporation (ATRO) has two types of issued stock: Common stock and Corporate Class B stock.**
*The common stock (ATRO)* found on NASDAQ is the "standard" type of equity stock that gives you a 1 to 1 vote to share basis (*usually you get one vote per share owned, which is the case for ATRO*).
*The cor... |
I discussed recently with a trader who told me that put options are priced using historical vol, and call are priced using the implied one.
My guess would be that as the put option market is much more deep and liquid, using the historical vol could make sens. Conversely for call option considering the much less liqu... |
I never heard that, and it sounds a bit like circular logic - IV is ALWAYS the vol derived from back-solving from price, so by definition, ALL options are "priced" using IV. I imagine there is a bit more nuance lost in the question you posed? In some assets classes, option prices may quoted in terms of Vol (FX), perh... |
I am doing some research on the option implied risk neutral distribution and methods calculate it, and so far have come across two ways to do so.
The first way is through the Breeden-Litzenberger formula, which seems like a popular method to calculate the density via a finite differencing approach. There are many go... |
I am working with some real time options tick data (mainly futures options and index options), and in many cases the quotes are single sided (as seen on bloomberg terminal). I will denote a quote as BID_PRICE/ASK_PRICE.
For instance, if a call with strike K does not have a quoted ask price like 100/, what I am curre... |
Re 1: Yes. BL gives you an approximation of the whole density, BKM gives you an approximation of each moment, common implementations offer the first four moments but you should be able to produce more moments.
Re 2: Both ways are viable. IMO, the route via interpolating somewhere between bid/ask prices (instead of ... |
There are so many realized measure have been invented in the past years like TSRV, MSRV, KRVTH, KRVC... But how to choose them in practice?
I know we cannot find the "estimation error" of them, as the true label is unknown. But maybe there is something that can "predict" their error, so we can know which one is more... |
How to determine which realized volatility estimator should be used? |
There are so many realized measure have been invented in the past years like TSRV, MSRV, KRVTH, KRVC... But how to choose them in practice?
I know we cannot find the "estimation error" of them, as the true label is unknown. But maybe there is something that can "predict" their error, so we can know which one is more... |
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