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High open interest for a given option contract is an indicator for interest in that option. For that reason I wanted to take a look at how the open interest of options on volatility have evolved in the last years. To do so, I took a look at VIX options and options on the VXX (ETN on the VIX, options exist since 2010). ... |
What is a delta of a payer and a receiver swaption? Is it negative for receiver swaption and positive delta for payer swaption? |
I am trying to solve the perpetual American option problem. Currently I'm following [this][1] (slide 9). The stock price is modelled as Ito's process.
> $dS_t = (\mu-D_0)S_tdt\ +\ \sigma S_tdW_t $
where $D_0$ is the dividend. Basically the problem tries to find optimal stopping time to exercise the option i.e. we... |
I'm studying Lopez' [Advances in Financial Machine Learning](https://www.amazon.co.uk/Advances-Financial-Machine-Learning-Marcos/dp/1119482089) where he talks about how to sample and structure financial data, as well as how to apply machine learning models to the data. I am also following a [python implementation](http... |
What is the correct order of operations when cleaning and structuring financial time series? |
Wha't the best place to grab historical sophisticated data about stocks? |
Plenty of material is written on how to hedge/arbitrage option price in one period binomial model, but I cannot find anything about hedging in multiple periods. If one to use multiple periods binomial model, how would one try to hedge? It seems like hedge ration always depends on the binary outcome of stock prices. Cou... |
As the SOFR transition kick in, the libor insturments and derivatives link to SOFR which poses natural challenge for numerical methods such as lattice, monte carlo and finite difference, where people used to (at least some people) discretize the time steps to be month basis if the security expired in years.
As the ... |
Receiving fixed or floating?
Assuming floating, the delta would be positive for the receiver and negative for the payer. |
I'm learning about spot rates from Financial Mathematics for Actuaries and something about the definition is confusing me.
Spot rates are used (in the textbook) to specify the interest rate on a payment made at time 0, for some fixed but arbitrary period into the future. But elsewhere, like on Wikipedia, spot rates... |
I am trying to predict the realised daily close to close variance of an equity index.
I checked the literature on volatility forecasting and tried a bunch of things on a dataset for the S&P 500. The most promising approached were an EWMA, GARCH and just using the squared VIX. I measured the performance of my predi... |
How to predict realised variance? |
I need a time series with daily dividend data on the S&P500. I understand most dividend data is on a quarterly basis but I'm looking to model short-term effects of COVID-19 on dividends so I need a daily/weekly frequency. **Does anyone have any ideas?**
Is is possible to use the S&P500 price and total return indexes... |
How to find/calculate daily S&P500 dividends? |
I have referred to the some of the well known papers but none of them has a clear answer for my question. I know that both of these models have some disadvantages but, what is the industry standard for pricing derivatives? I need this information for pricing CVA. |
What is the industry standard model for pricing Swaptions during this time of negative interest rates, normal model or shifted log-normal model? |
Is the implied volatility ATM the same for a currency pair as for the inverted currency pair. I.e, can I expect the same volatility quote ATM for (for an instance) EURUSD as for USDEUR? And does this result hold for all tenors? |
I'm wondering what is the best swaptions or caps portfolio I could use to calibrate the two parameters of H&W 1F model for a structured note with optionality on Libor underlying.
Let's suppose for example that the EUR trade I want to price is paying a coupon = Notional * max(Libor EUR 3M + spread, 0) each year, and ... |
Hull & White 1F - What is the appropriate calibration portfolio for Libor indexed structured note? |
I am trying to run a cash-and-carry (basis) trade. I'm having trouble understanding how to weigh the tradeoffs between yield, annualized yield and duration/time to expiry.
Suppose we are in a contango situation so I am looking to buy spot and short the futures of this asset. There is a contract expiring in 3 month... |
Are you trying to estimate what would happen if there were daily dividends?
If so you could try:
1 find the geometric g rate of all quarterly D
2 Convert the quarterly G rate into daily,
3 find starting day D and from there calculate D(1+g)... till you’ve found all wanted daily dividend streams
T... |
Supposedly we have a following situation.
1) Company A takes a loan from Bank A at a floating interest rate.
2) In order to offset the payments at floating interest rate, Company A enters into an Interest rate swap agreement with Bank B, wherein it receives a floating interest rate 'float' and pays fixed interest... |
What is the best way to hedge a position with negative interest rate? |
I was going through a use case where
At time t, the price of a call option is 'C1' and the price of underlying stock is 'S1'
At time t + 1 day, the price of a call option is 'C2' and the price of underlying stock is 'S2'
Now S2 > S1 which means that C2 > C1 but on the contrary the C2 < C1 ,it turned out that th... |
What is the use of volatility surface and how do traders use it? |
I am new to the field of Mathematical Finance and wanted to get an idea on the intuitive, physical and mathematical meaning of the term "affine" in Affine term structure models. Any literature reference will be appreciated as well.
On another note, is it related to multiscaling and self-similarity properties of vari... |
What does the word "affine" mean in affine term structure models? |
A common objection is _"it works with normal return distributions, but real return distributions have fat tails"_
What is the problem with fat tail distributions, if we can just use stoploss / takeprofit barriers to constrain returns within some arbitrary range?
I appreciate that stoploss / takeprofit barriers a... |
Why worry about fat tails, if you can use stoploss / takeprofit? |
the way I see it, there isn't much to discover about stoploss/takeprofit for the following simple reasoning:
- imagine you devised a trade strategy that on average builds up profit
- you can think of your trades as random walks with positive drift. That is, you can break each trade into a series of steps (e.g. ... |
the way I see it, there isn't much to optimise about stoploss/takeprofit for the following simple reasoning:
- imagine you devised a trade strategy that on average builds up profit
- you can think of your trades as random walks with positive drift. That is, you can break each trade into a series of steps (e.g. ... |
the way I see it, there isn't much to optimise about stoploss/takeprofit for the following simple reasoning:
- imagine you devised a trade strategy that on average builds up profit
- you can think of your trades as random walks with positive drift. That is, you can break each trade into a series of steps (e.g. ... |
the way I see it, there isn't much to optimise about stoploss/takeprofit for the following simple reasoning:
- imagine you devised a trade strategy that on average builds up profit
- you can think of your trades as random walks with positive drift. That is, you can break each trade into a series of steps (e.g. ... |
I am building some well known equity factors on the S&P for research purposes. It means those are going to be used for general evaluation purposes but do not need to be replicable. Would it be a good idea to calibrate each factor daily? |
What I'm imagining is a long list of different types of financial instruments traded on the market along with the model(s) that is industry standard for valuing it. Something like:
European equity options : Black-Schooles model
American equity options : Binomial options pricing model
Asian equity options: Mon... |
I would give GitHub a try. Searching for option pricing or machine learning or anything like that yield a ton of repositories with implementations that you can look through and learn from. Here are 2 search links:
[GitHub Search for C++ machine learning][1]
[GitHub Search for C++ option pricing][2]
After gai... |
Kelly maximises the geometric return in each period. I believe this is equivalent to maximising expectation of log wealth in the next period.
1. If you maximise the arithmetic return, your expected wealth will be higher. However the actual return you will experience is -100% i.e. you will go bust with probability 1.... |
Sorry this might sound a silly question, but -humbly- I don't understand why models assume that returns range from [-∞,+∞] instead of [-stoplimit, +takeprofit].
A common objection to most models is _"it works with normal return distributions, but real return distributions have fat tails"_
What is the problem wit... |
Sorry this might sound a silly question, but -humbly- I don't understand why models assume that returns range from [-∞,+∞] instead of [-stoplimit, +takeprofit].
A common objection to most models is _"it works with normal return distributions, but real return distributions have fat tails"_
But why worry about fat... |
Why worry about fat tails, if you can use stoploss? |
I was going through a use case where
At time $t_{t}$, the price of a call option is $C1$ and the price of underlying stock is $S1$
At time $t_{t+1}$ day, the price of a call option is $C2$ and the price of underlying stock is $S2$
Now $S2 > S1$ which means that $C2 > C1$ but on the contrary the $C2 < C1$ ,it ... |
Suppose we have a following situation:
$1).$ Company A takes a loan from Bank A at a floating interest rate.
$2).$ In order to offset the payments at floating interest rate, Company A enters into an interest rate swap agreement with Bank B, wherein it receives a floating interest rate **float** and pays fixed int... |
Are you trying to estimate what would happen if there were daily dividends?
If so you could try:
1 find the geometric $G$ rate of all quarterly $D$
2 Convert the quarterly $G$ rate into daily,
3 find starting day $D_{0}$ and from there calculate $D(1+g)$... till you’ve found all wanted daily dividend s... |
Are you trying to estimate what would happen if there were daily dividends?
If so you could try:
1. Find the geometric $g$ rate of all quarterly $D$
2. Convert the quarterly $g$ rate into daily,
3. Find starting day $D_{0}$ and from there calculate $D(1+g)$... till you’ve found all wanted daily dividend str... |
I am trying to identify markets makers within an (options-)orderbook. Of course, this is far stretched, but I was wondering what kind of characteristics / patterns I should look at. I got the following sofar:
- likely, but not necessarily best bid and best offer
- symmetry; a similar amount of contracts bid and off... |
How to identify market makers in an orderbook? |
Not sure if this question deserves to be further piled onto, but alas...
Large, institutional portfolios nearly always hold relatively illiquid and OTC traded instruments. There is no stop-loss order on a corporate bond or term loan, as an example. This is unrealistic even in equities. Let's say you hold 5% of the s... |
I watched a speech made by Simon Johnson at UCSB and, at one point, [he claimed][1] that citigroup failed three times since 1980s. For an example, he claims that citigroup failed and has been presumably saved by govt in 1982 because of "bad loans made in emerging markets.". Second such "failure" is placed at the end of... |
Did citigroup really failed three times last 40 years? |
I have a dataset with 3.000 observation (price of an asset).
I want to study the empirical distribution of the logRet of that time series.
How can I do it in Excel? if not possible to do it in Excel, Python? Wolfram?
thanks,
Ciao |
I watched a speech by Simon Johnson at UCSB and, at one point, [he claimed][1] that Citigroup has failed three times since the 1980s. For example, he claims that Citigroup failed and was saved by the government in 1982 because of "bad loans made in emerging markets". The second such failure is at the end of the 1980s b... |
Did Citigroup really fail three times in the last 40 years? |
I've seen this equation floating around :
XCCY = FX OIS + USD LIBOR/OIS - EUR LIBOR/OIS.
This equation is intuitive however there's a mention that discount factors between the two need to be taken into account. What does this mean and how does this apply in the equation? |
I am currently reading John Hull's book and am a bit confused about the Ito's lemma when it is applied to the stock price. Given $dS=\mu Sdt+\sigma Sdz$, by applying Ito's lemma to $G=\ln S$, we have $$dG=(\mu-\frac{\sigma^2}{2})dt + \sigma dz$$
However, it seems that from $dS=\mu Sdt+\sigma Sdz$, if we rewrite it ... |
understanding of Ito's lemma applied to stock price? |
I am trying to identify markets makers within an (options-)orderbook. Of course, this is far stretched, but I was wondering what kind of characteristics / patterns I should look at. I got the following sofar:
- likely, but not necessarily best bid and best offer
- symmetry; a similar amount of contracts bid and off... |
I am trying to solve the perpetual American option problem. Currently I'm following [this][1] (slide 9). The stock price is modelled as Ito's process.
> $dS_t = (\mu-D_0)S_tdt\ +\ \sigma S_tdW_t $
where $D_0$ is the dividend. Basically the problem tries to find optimal stopping time to exercise the option i.e. we... |
I need a help for the following question:
A stock index is constructed by including only two stocks in the index. One of the stocks (Stock $1$)
currently sells for $250$ dollar and the other stock (Stock $2$) sells for $187.5$. The current value of the index is $437.5$. Stock $1$ is expected to pay a dividend of $7... |
I am trying to understand the basics of finance indicators. I have made 15 minute ohlc candles for the past 50 days.
Now if I try to calculate `5EMA`, my doubt is what does 5 refer to? Is it days of number of candles or number of days? Assuming 6 hour trading session, I will have 1200 candles (50 days, 6 hours each ... |
There are many R code examples for portfolio selection
and some for GARCH models in this book:
@BOOK{Gilli2019,
title = {Numerical Methods and Optimization in Finance},
publisher = {Elsevier/Academic Press},
year = 2019,
author = {Gilli, Manfred and Maringer, ... |
I appreciate that both are the direct result of constricting a replicate portfolio using stock and bonds.
Are there deeper relationship between the two? |
What are the relation between the risk neutral measures in binomial tree and in Black Scholes model? |
Been wanting to get my hands dirty with ML for a while now and since I'm interested in finance and trading as well, I figured this would be a good project to get started after reading *Deep LSTM with Reinforcement Learning Layer for Financial Trend Prediction in FX High Frequency Trading Systems* (https://www.mdpi.com/... |
I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the daily squared returns. I saw that there are various estimators based on intraday data, for example Rogers Satchell, Garm... |
I wish to verify my understanding and correctness of my methodology with this question, when calculating the sortino ratio for the SP500. My base data is the total returns SP500 index from Yahoo finance:
https://finance.yahoo.com/quote/%5ESP500TR/history?p=%5ESP500TR
I took the adj. closing price starting with th... |
Did I correctly calculate all the elements of the Sortino ratio? |
I've been an investor for about 12 years now. My annual return, November 2008 until today, is 25.77% on my stock portfolio, which is heavy on AAPL, BRK.B and recently TSLA. Mostly buy and hold, hardly any trades.
I'm starting to expand my financial endeavors into day trading, specifically scalping futures on equity ... |
I am interested in predicting the PnL of a gamma scalping strategy which trades only once per day. For simplicity, let's say we can always trade at the daily close. So, what I need to predict are the daily squared returns. I saw that there are various estimators based on intraday data, for example Rogers Satchell, Garm... |
I'm new to automated trading. I'm in the process of coding the methodology I've been using manually for a few weeks into a quantitative algorithm using IBKR and Python.
I read everywhere I should backtest my strategy before betting money it. Sounds like a great idea, of course.
Just a slight problem. My alogo dep... |
The mean-variance model for portfolio optimization minimizes **portfolio risk** (covariance matrix), which is the *second* statistical moment of multivariate asset returns, and sometimes simultaneously maximizes **portfolio return**, which is the *first* statistical moment of asset returns.
Is it possible to do ass... |
Any portfolio theories not based on asset return moments? |
The mean-variance model for portfolio optimization minimizes **portfolio risk** (covariance matrix), which is the *second* statistical moment of multivariate asset returns, and sometimes simultaneously maximizes **portfolio return**, which is the *first* statistical moment of asset returns.
Is it possible to do ass... |
Remember that asset returns are there because of the **expected utility theory**. More precisely, as long as you can assume a "reasonable" expected utility function to be approximated by a quadratic function, you will always end up with some mean-variance tradeoff in wealth allocation.
You want to base portfolio all... |
There's now a new [LightningChart(R) Trader WPF][1] library available. It is designed to provide simple and straightforward way to add charting capabilities, technical indicators and drawing tools, for WPF apps for trading and finance.
[Short YouTube video][3]
[![LightningChart Trader technical indicators][2]][2... |
For Windows desktop, best interactivity and performance can be achieved with [LightningChart .NET Trader][1].
It's DirectX accelerated to achieve maximum FPS and minimal lag.
See this short [LightningChart Trader video][2]
[![Technical indicators in LightningChart Trader][3]][3]
For JavaScript, web and mobil... |
I am leaning about options, saw various video lectures and read some literature including John C Hull. After a while I forgot where I started and where I am currently and I unable to connect dots. The mathematical equations used in the literature are actually beyond my skill set. But I am trying to understand whats hap... |
What is the use of implied volatility, the skewness and its surface? |
Have you tried to choose an arbitrary number of model, let say 20, each one having its own seed? Then you run your twenty models and use the median of your 20 results as signal. One advantage of that method is that you can also get a confidence estimate of your prediction thanks to the standard deviation of your 20 res... |
The answer is *sort of*. I am going to provide you a history of the mathematics so that you will understand why this discussion is challenging to have in economics. Also, you are probably going to have to ground yourself in math you haven’t looked at before.
In 1867, a young man by the name of Jules Regnault becam... |
I'm reading the book "Financial Markets Under the Microscope" for my market microstructure studies. In the book, the variance of the market maker's gain is calculated as follows:
> Assume that with probability φ, an arriving trade is informed, and
> correctly predicts a price jump of size ±J. Otherwise (with
> pr... |
is the variance calculation correct in the book? |
I'm reading the book "Financial Markets Under the Microscope" for my market microstructure studies. In the book, the variance of the market maker's gain is calculated as follows:
> Assume that with probability $φ$, an arriving trade is informed, and
> correctly predicts a price jump of size $±J$. Otherwise (with
... |
Is the variance calculation correct in the book? |
Recently I've tried SciChart and VisiBlox - beautiful charting tools. Are there any free or open-source tools for visualizing charts in C#?
Thank you for answers. |
What are some popular free/open-source charting controls? |
There are many models for interest rate. If two people use two different models to price the same interest rate derivative, and come to two different prices, doesn't that admit an arbitrage? How should I think about this problem? What is done in practice? |
Do different prices under different models admit arbitrage? |
I need to work with option prices in my master's thesis. Specifically, I investigate index options (S&P 500). Which kind of options could you recommend to use? I have seen that there are options written on the index itself, but also options written on index futures or ETF's.
Therefore I would like to ask if someone... |
Most liquid index options? |
I am using a simulation approach to compare the performances achievable by naive diversification and mean-variance optimization for portfolio selection. My problem is that my results indicate that naive diversification outperforms mean-variance optimization. Is this possible or is there most likely an error in my simul... |
Can naive diversification outperform mean-variance optimization like this, or is there most likely an error? |
This phenomenon is not limited to interest rate derivatives. Any time a product is priced to model - be it equity derivatives, commodity derivatives, simple cash products whose price is not observable but is interpolated from other simple cash products - there is some uncertainty about the model price from
* choice ... |
I'm reading the book "Financial Markets Under the Microscope" for my market microstructure studies. In the book, the variance of the market maker's gain is calculated as follows:
> Assume that with probability $φ$, an arriving trade is informed, and
> correctly predicts a price jump of size $±J$. Otherwise (with
... |
I'm backtesting a strategy that forms stock portfolios on a monthly basis.
It sometimes happen that a stock chosen on month t does not have return data on month t+1, so I can't correctly calculate the portfolio performance.
I've managed to find out why some of those returns are missing (i.e acquisitions and tick... |
How to deal with missing returns? |
It is a pity that **all textbooks now (2020-04-30) are WRONG on CAPM**. Cause there is a Misunderstanding of the market portfolio: The portfolio separation of Tobin (1958) brings the market portfolio front and center. Although investors have different wealth and preferences, investors with mean-variance preferences all... |
I am using a simulation approach to compare the performances achievable by naive diversification and mean-variance optimization for portfolio selection. My problem is that my results indicate that naive diversification outperforms mean-variance optimization. Is this possible or is there most likely an error in my simul... |
I am doing this question that I couldn't find the payout ratio.
>For you, company equity beta is unknown, it has a target i.e. current debt to book equity ratio: 0.5 and target debt to market capitalization ratio: 0.1. Its debt is risk-free since the loan was granted by the government at a low rate to stimulate t... |
How can I find the payout ratio for this company? |
**The Problem:**
Suppose I have a simple jump model for an asset price
$$ dS = S(t-)[\mu dt + YdN(t)] $$
where $N(t)$ is a Poisson process and $Y_i$ are the jump sizes (assume independece of $N(t)$ and $Y_i$). Also for simplicity assume that $Y_i$ can only take two values, lets say $a$ and $b$. What constraint... |
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