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What is this option strategy called? |
I'm sure this falls short of proper philosophical precision, but here goes. Hark back to a slightly modified rehash of Donald Rumsfeld's infamous:
*Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know ... |
A colleague mentioned the following: She wanted to look at some bonds in Reuters/Bloomberg to see if they if they "correctly break-out the swap curve and z-spread".
Would anyone understand what she is trying to say/do? Would be much appreciated |
[MarketWatch](https://www.marketwatch.com/tools/markets/bonds/a-z/U) daily OHLC bars for bonds **yields** are sourced from [Tullett Prebon](https://tullettprebon.com).
Here's a sample output for [U.S. 10 Year Treasury Note](https://www.marketwatch.com/investing/bond/tmubmusd10y/downloaddatapartial?startdate=02/06/20... |
I'm looking to analyze recent Fed treasury purchases for an analysis and [found a slew of spreadsheets](https://www.newyorkfed.org/markets/domestic-market-operations/monetary-policy-implementation/treasury-securities/treasury-securities-operational-details) with the full details.
My problem is that I'm not sure how ... |
I'm looking to analyze recent Fed treasury purchases for an analysis and [found a slew of spreadsheets](https://www.newyorkfed.org/markets/domestic-market-operations/monetary-policy-implementation/treasury-securities/treasury-securities-operational-details) with the full details.
My problem is that I'm not sure how ... |
[MarketWatch](https://www.marketwatch.com/tools/markets/bonds/a-z/U) daily OHLC bars for bonds **yields** are sourced from [Tullett Prebon](https://tullettprebon.com).
Here's a sample output for [U.S. 10 Year Treasury Note](https://www.marketwatch.com/investing/bond/tmubmusd10y/downloaddatapartial?startdate=02/06/20... |
I understand to plot correlation and volatility smiles, we have to plot the implied normal vol vs strike and observe a U-shaped relationship. How are these smiles different? Does a vol smile plotted for a correlation product (CMS spread for example) become to be called a Correlation smile? |
What is the difference between a volatility smile and a correlation smile? |
Your book is right. Samuleson--you'll find his name written all over EMH's history--proved it in 1973.
https://www.jstor.org/stable/3003046?seq=1#metadata_info_tab_contents
The pertinent section, "properly anticipated future prices fluctuate randomly--i.e. contain a martingale sequence, or a generalized martingal... |
I am trying to understand which is the best way to construct the parameters using the cvxpy engine.
I have seen this post:
[more of list-like][1] way of constructing constraints etc
and this post:
[more matrix-like notation][2] way of constructing constraints etc.
I want to ask: is there any problem followi... |
In Modern Portfolio Theory, I often see that people seem to view Standard Deviation and Variance as equivalent. Example from Markowitz himself:
*"Thus far I have used the standard deviation (or ***equivalently***, the variance) of return as a measure of the risk involved in the portfolio”* (p.50, see referen... |
Equivalence of Standard Deviation and Variance as a risk measure - WRONG? |
Re: Options, Futures & Other Derivatives, Hull 9th Ed, p744.
1. What does "m(t)" represent? I am struggling to understand the definition provided of:
"Index for the next reset date at time t; this means that m(t) is the smallest integer such that t <= t_m(t)"
2. In equation 32.8 (lower half od page 744), what ... |
When constructing a replicating portfolio for a short position in a call option under Black Scholes, I am not able to pinpoint the source of gains from theta decay. When theta decay materializes, I don't understand how the replicating portfolio generates the gains necessary to finance the new, higher value (less negati... |
I am trying to understand the mechanics of resettable xccy basis swaps and put together a numerical example. I'd like to know if 1) periodic interest payments are calculated on the original notional exchanged at inception or at the reset notional? 2) at expiry how is determined the notional to be exchanged back (at the... |
I would disagree more with the initial premise (ie the intellectual "straw man" you then kill) than with any of your perfectly cogent arguments that follow.
I trust we both accept that stdev and var are monotonic in nature, each being the square (root) of the other?!?! The basic premise of Markowitz is thus indeed g... |
where can I find the current FRA (Forwad Rate Agreement) quotes? I know this is an OTC contract, but I would like to see what the rates for such contracts look like at the moment. |
From the option chain of a security, we can calculate the implied probability density at the maturity
$T$ (assume the options are European. Now suppose we have our own view/prediction on the probability density of the underlying price at time $T$. What is the best way to trade this view?
For example, say the impl... |
I'm comparing the performance of mutual funds using monthly returns data from Bloomberg. I use the Day to Day Total Returns (Gross Dividends) field represented in Excel by DAY_TO_DAY_TOT_RETURN_GROSS_DVDS
My question is if this value is calculated net of fees. I have tried looking into the definition of Total Return... |
Is Total Return data for mutual funds on Bloomberg adjusted for fees/expense ratio? |
Is there a possibility to configure the period the barrier is active, using Quantlib for python? Namely to set up the start and the end dates we compare the spot vs the barrier.
If we look at quantlib-python-docs (https://quantlib-python-docs.readthedocs.io/en/latest/instruments/options.html?highlight=BarrierOption#... |
From the option chain of a security, we can calculate the implied probability density at the maturity
$T$ (assume the options are European. Now suppose we have our own view/prediction on the probability density of the underlying price at time $T$. What is the best way to trade this view?
For example, say the impl... |
I am trying to run a Fama Macbeth analysis in R, where I am using the 'pmg' function with the following code:
Fpmg1 <- pmg(ret ~ HML_OBS + SMB + Mktrf + HML, Analysis4_Weighted, index = c("permno"))
summary(Fpmg1)
I currently have 1,354,623 entries and 11 total columns. I get the below output where the e... |
I am given a list of `Options` positions consisting of various combinations of `Underlying` and `Strikes`. I am also given the `Vega` values for each go these positions.
Now, given this information, I want to calculate total `Vega` exposure of this portfolio. Should I just add up the individual `Vegas` and report th... |
What is the market convention for discounting the future cash flows of FX forwards? In particular, I would be interested to know what discounting curves are used for both collateralised and not collateralised FX forwards.
|
Let $C(t,S)$ be the value function of a call option. I want to price that option using (explicit) finite differences and the Black Scholes PDE. To this end, I need three boundary conditions
- Payoff: $C(T,S)=(S-K)^+$
- Low stock price: $C(t,0)=0$
- High stock price: $C(t,S_{max})=S_{max}$
But isn't there a *... |
Let $C(t,S)$ be the value function of a call option. I want to price that option using (explicit) finite differences and the Black Scholes PDE. I consider the grid $0=t_0<t_1<...<t_{N-1}<t_N=T$ and $S_0<S_1<...<S_{M-1}<S_M$.
I impose the boundary conditions
- Payoff: $C(t_N,S_j)=(S_j-K)^+$ for all $j=0,...,M$,
... |
Currently working on a validation and testing of a yield curve model (one factor short rate model). Have been reading Andersen and Piterbarg, and Mercurio and Brigo. Good for true understanding, but bad in terms of practicality. Veronesi is a bit more practical and doesnt go too much in the details, yet enough. Same wi... |
I was having a discussion with a colleague in the industry, who mentioned in passing that CVA on a cross currency swap from EUR into USD (pay EUR) is always higher than if paying USD and receiving EUR... why? |
Why might a cross currency swap from EUR into USD have higher CVA than a cross currency swap from USD into EUR? |
I'm comparing the performance of mutual funds using monthly returns data from Bloomberg. I use the Day to Day Total Returns (Gross Dividends) field represented in Excel by DAY_TO_DAY_TOT_RETURN_GROSS_DVDS
My question is if this value is calculated net of fees. I have tried looking into the definition of Total Return... |
I have a mean reverting time series and want to find the Ornstein-Uhlenbeck (OU) parameters of it. I researched the internet and found that we can calibrate the model as a simple AR(1) process,
$$\text dS_{t} = \lambda(\mu-S_t)\text dt+\sigma \text dW_t,$$ where $\lambda$ is the mean reversion rate, $\mu$ the mean and... |
In Euan Sinclair's book, Option Trading, he writes that $c <= S$, the price of a European call must be lower than the price of the underlying stock. To prove it, he applies the principle of no arbitrage:
> Imagine a European call is trading for more than the underlying. We then choose to sell the call and buy the u... |
Say I am a market maker.
The ask (me selling it) formula is pretty common in textbooks etc by no arbitrage:
$$F = S \cdot \text{exp}(r-d)$$
where $r$ is interest rate and $d$ -- dividend.
Again, by no arbitrage, if I am buying it, i.e. quoting a bid, would it be:
$$F = S \cdot \text{exp}(d-r)$$
? |
Bid Price of a Forward? |
I doubt with regards to this. If for instance, we have the same two 5-year swaps one of them with a Mandatory Break clause in year one, what would be the differences in the CCR profile during the first year?
Would it be the same profile for both of them, since the break clause still hasn't been executed?
If this... |
What happens to a Swap CCR if there is a mandatory breaking clause? |
Imagine someone bought 100K SPY as a long term investment. Now he wants to hedge against the downside risk of 10% or more. He is considering the following options:
1. Buy UVXY which is a 1.5X VIX ETF inversely correlated with SPY. If one buys 5K, in case of a 10% SPY crash, one would make ~50% or 2.5K (not sure how ... |
How do you finance theta decay when replicating an option? |
I am trying to implement a local volatility pricer using Monte Carlo and Dupire's equation in function of implied volatilities and I was told that first of all I have to check Dupire is well implemented so I was reccommended to prove it like this:
-The first step, to check Dupire's function, was to get the local vol... |
The Brookings explaining the yield cure control writes:
*Interest rate pegs theoretically should affect financial conditions and the economy in many of the same ways as traditional monetary policy: lower interest rates on Treasury securities would feed through to lower interest rates on mortgages, car loans, and cor... |
I would like to find a way to measure Liquidity for Commodities Futures. I found the following 4 papers/definitions:
1) Volume (Share / Dollar) ([Dollar Volume Liquidity][1])
2) Amivest Liquidity Ratio ([Comparison of Liquidity Measures in the Stock Markets][2])
3) Amihud: ([The Night and Day of Amihud's (200... |
I am currently reading some notes which state that
> For one-factor models, the value of a European option on a coupon bond can be calculated as the sum of European options on zero-coupon bonds (ZCBs). The process is described in Hull Section 31.4.
For two-factor models, this doesn’t apply because yield curve chang... |
Very short answer... The central bank cuts rates, and assumes that this should then make banks more willing to lend, which finances more of those car/student/credit-card loans etc. Except when it doesn't, the central bank worries about the economy being caught in a "liquidity trap". That's the economics done - read Key... |
The EGARCH is a special GARCH model that treats the leverage effect of the volatility. The HARV does not make a distinction between negative and positive returns. Is there a special HARV that deals with the leverage effect? If not, is there a reason why the leverage effect is perhaps unimportant for HARV? |
Is there a HAR that deals with the leverage effect? |
While searching time-series data for different interest rate benchmarks, I found that for the USD, all observations are missing for the period between March 2020/April 2020.
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/OLC27.png
This discontinuity is also justified when i retrieve ... |
[MarketWatch](https://www.marketwatch.com/tools/markets/bonds/a-z/U) daily OHLC bars for bonds **yields** are sourced from [Tullett Prebon](https://tullettprebon.com).
Here's a sample output for [U.S. 10 Year Treasury Note](https://www.marketwatch.com/investing/bond/tmubmusd10y/downloaddatapartial?startdate=02/06/20... |
[MarketWatch](https://www.marketwatch.com/tools/markets/bonds/a-z/U) daily OHLC bars for bonds **yields** are sourced from [Tullett Prebon](https://www.tullettprebon.com).
Here's a sample output for [U.S. 10 Year Treasury Note](https://www.marketwatch.com/investing/bond/tmubmusd10y/downloaddatapartial?startdate=01/0... |
I am lookin at https://www.cmegroup.com/trading/interest-rates/stir/eurodollar_quotes_volume_voi.html?foi=O&optionProductId=3#tradeDate=20210312. It says about 16 million in options was traded. When I look at the https://www.cmegroup.com/trading/interest-rates/stir/eurodollar_quotes_globex_options.html?optionProductId=... |
Hello quant community.
I am looking for more information about a very interesting index: BAML-ICE MOVE index. There is very little literature online that details how the index levels are calculated beyond. This is surprising given the wealth of information available about the SPX volatility tracker VIX.
One piece... |
Hello quant community.
I am looking for more information about a very interesting index: BAML-ICE MOVE index. There is very little literature online that details how the index levels are calculated beyond. This is surprising given the wealth of information available about the SPX volatility tracker VIX.
One piece... |
Attempting Copula in R for Stock Returns, Bond Returns, and Inflation Rates. This is my first attempt with Copulas but I have looked many places and cannot determine what I'm doing wrong. My Marginal Distribution for Stock Returns includes negatives but my copula is non-negative? I studied math in college but somehow d... |
Gaussian Copulas: My Marginal Distribution Includes Negatives but My Copula is Non-Negative? |
As opposed to
[![enter image description here][1]][1]
Robust Bayesian Allocation solves
[![enter image description here][2]][2]
see https://hudson-and-thames-portfoliolab.readthedocs-hosted.com/en/latest/bayesian/robust_bayesian_allocation.html.
I don't get it. Why is this a worthwhile problem to solve?... |
Why is Robust Allocation a worthwhile problem? |
I would like to download stock market data from the internet (for example by scraping…) and organize them in a database (I am using python and SQL) which updates daily or on request.
(The idea is to create a screener, do back testing and so on…)
I am not very familiar with databases, so I am looking for some suggesti... |
It will also depend on the kind of CSA. For example if does it allow posting of collateral in EUR? |
Here is the simple analogy
Price of the Food shop = Price of all the apples + Price of all the oranges + Price of all the equipment - Amount of Debt in the books.
Is the bid price the opposite?
*Ask the right question you will get the answer! |
We trivially have that:
$$\frac{Z(t_0,t_1)}{Z(t_0,t_2)}=1+\tau L(t_0,t_1,t_2)$$
Where $L(t_0,t_1,t_2)$ is the forward Libor between $t_1$ and $t_2$, as of $t_0$.
Simply inverting this relationship then yields:
$$\frac{Z(t_0,t_2)}{Z(t_0,t_1)}=\frac{1}{1+\tau L(t_0,t_1,t_2)}$$
Could one interpret $\frac{1... |
The forward Libor rate $L(t,t_1,t_2)$, with $0 \leq t \leq t_1$, must be a martingale under the T-forward measure associated with the zero coupon bond $P(t,t_2)$ **that matures at time $t_2$.**
Pricing a caplet that "matures" at $t_2$ then becomes trivial (i.e. a caplet where the Libor sets at $t_1$ but the payment ... |
In this post [here](https://quant.stackexchange.com/questions/51311/how-do-we-determine-the-correct-measure/54722#54722) it is shown that the forward Libor rate $L(t,t_1,t_2)$, with $0 \leq t \leq t_1$, must be a martingale under the T-forward measure associated with the zero coupon bond $P(t,t_2)$ **that matures at ti... |
The forward Libor rate $L(t,t_1,t_2)$, with $0 \leq t \leq t_1$, must be a martingale under the T-forward measure associated with the zero coupon bond $P(t,t_2)$ **that matures at time $t_2$.**
Pricing a caplet that "matures" at $t_2$ then becomes trivial (i.e. a caplet where the Libor sets at $t_1$ but the payment ... |
I was looking at [trndbot][1] and it's buy/sell signals are pretty good - what algorithm are they using to generate these signals? Although it maybe similar to bollinger bands, it algorithmically generates these live signals for any trading graph:
[![enter image description here][2]][2]
[1]: https://trndbot.... |
How does trndbot generate buy/sell signals? |
In fact SQL is not a good idea, only NYSE can delivery 100 GB/day, I suggest you to start looking at MongoDB, take a look at this presentation [James Blackburn - Python and MongoDB as a Platform for Financial Market Data][1]
[1]: https://www.youtube.com/watch?v=FVyIxdxsyok |
I am stuck on the 1st equation of the solution where the Weiner process [W_t_(i)]^2 is expanded so that the Ito integral (in terms of infinite sums) looks like the RHS of the first equation of the solution. I can follow the rest of what they did.
[![enter image description here][1]][1]
[1]: https://i.stack.i... |
I understand how to calculate the yield on a 10 yr TNote based on face, price & coupon.
I don’t understand why the yield (and price) on a futures contract about to expire is so different than the market yield (and price) if you buy a note instead.
For example March 21 10 Yr TNote contracts are about 131 which (I ... |
TNote Futures contract YTM vs yield on bought notes? |
I understand how to calculate the yield on a 10 yr TNote based on face, price & coupon.
I don’t understand why the yield (and price) on a futures contract about to expire is so different than the market yield (and price) if you buy a note instead.
For example March 21 10 Yr TNote contracts are about 131 which (I ... |
The calculation is described in the [IEX Rule Book](https://iextrading.com/docs/Investors%20Exchange%20Rule%20Book.pdf), section 11.160 (g). See Quote Instability Factor (QFI) and the accompanying thresholds:
$$ QIF = \frac{1}{1+e^{-(C_0 + C_1N + C_2F + C_3NC + C_4FC + C_5EPos+C_6ENeg+C_7 EPosPrev+C_8ENegPrev + C_9D... |
The calculation is described in the [IEX Rule Book](https://iextrading.com/docs/Investors%20Exchange%20Rule%20Book.pdf), section 11.160 (g). See Quote Instability Factor (QFI) and the accompanying thresholds:
$$ QIF = \frac{1}{1+e^{-x}}$$
where $$x = C_0 + C_1N + C_2F + C_3NC + C_4FC + C_5EPos+C_6ENeg+C_7 EPosPre... |
I have implemented a very simple limit order book. I would like to visualize it in a GUI application. I don't any experience in GUI. What library and widget may be used? Any suggestion in this regard will be helpful.
Is there any special widget or library?
Thanks |
How to visualize limit order book in gui? What Library or widgets to use? |
# Integrating $W_t$
Consider the partition $t_i=it/n$ with $t_0=0$ and $t_n=t$. Then, by definition,
\begin{align*}
\int_0^t W_s\text{d}W_s &= \lim_{n\to\infty} \sum_{i=0}^{n-1} W_{t_i}\left(W_{t_{i+1}}-W_{t_i}\right).
\end{align*}
You can do the limit by using the identity
$$ W_{t_i}\left(W_{t_{i+1}}-W_{t_i}\r... |
I am stuck on the 1st equation of the solution where the Weiner process $W_{t_i}^2$ is expanded so that the Itô integral (in terms of infinite sums) looks like the RHS of the first equation of the solution. I can follow the rest of what they did.
[![enter image description here][1]][1]
[1]: https://i.stack.i... |
As always, any answer to this question is **hugely driven by your use cases**. The following is my interpretation and ansatz. Here on QSE and over at the DB exchange, I have seen various approaches to keeping financial / market data - and the corresponding discussions are quite heated... Some suggest simply dumping/rea... |
I am trying to calculate the performance of a portfolio of fixed-income funds domiciled and operating exclusively in Europe through a multi-factor model. To do this I need historical data of several indices (of the Eurozone). In particular I was looking for:
- a broad investment grade bond index
- a long-term an... |
What are the eurozone bond indices? And where can I find them? |
Yieldbook finds:
broad investment grade bond index - Euro Broad Investment-Grade (**EuroBIG**) Corporate Bond Index https://www.yieldbook.com/x/ixPubDoc/factsheet_i_ebigc.pdf
long-term and a short-term government bond index -
EMU Government Bond Index (EGBI) https://www.yieldbook.com/x/ixPubDoc/factsheet_i_egbi... |
If neutralizing delta requires an addition of a fractional number of shares, e.g. 444.12345 do we generally keep the decimals or round up to the nearest integer? I reckon rounding would no longer make it "neutral"? |
If the primary motivation is being able to query market data with SQL, take a look at [Axibase Time Series Database](https://axibase.com/docs/atsd/finance/?qsed) (_my affiliation_).
**Step 1**: Sign-up for free [Polygon](https://polygon.io/) API key.
**Step 2**: [Install](https://axibase.com/docs/atsd/finance/ins... |
I am new to programming, and I have been exposed to the basic of R and Python. I have been trying to implement the volatility smile function using a unit root function(a traditional procedure) but I am running into problems. Here is the code I am writing:
```
BlackScholesFormulaBach <- function (spot,timetomat,strik... |
I'm in the process of building a Python library to value stocks using a FCF model and one of the first steps is calculating an implied equity premium. I know there a few ways of doing this, but looking at previous correlations (current implied ERPs apparently have 0.763 correlation to next year's implied premium, histo... |
Are there any APIs to retrieve stock buybacks and dividends to calculate ERP? |
I've got a question relating to annuities which I'm stuck on.
You intend to retire when you are 60 and predict you will die when you are 90. You want 50,000 a year for a comfortable retirement, and you plan to get this money through an investment account. The account pays a return of 6%. On your 60th birthday, you ... |
I am new to programming, and I have been exposed to the basic of R and Python. I have been trying to implement the volatility smile function using a unit root function(a traditional procedure) but I am running into problems. Here is the code I am writing:
```
BlackScholesFormulaBach <- function (spot,timetomat,strik... |
I am stuck on the 1st equation of the solution where the Wiener process $W_{t_i}^2$ is expanded so that the Itô integral (in terms of infinite sums) looks like the RHS of the first equation of the solution. I can follow the rest of what they did.
[![enter image description here][1]][1]
[1]: https://i.stack.i... |
Where can I find recent comulative average default rates tables? |
Let $M_{t\to t+2}^{\$}$ be the pricing kernel (SDF) from period $t$ to $t+2$. Let inflation over period $t$ to $t+1$ be denoted by $\Pi_{t \to t+1}$. Is it possible to observe the following quantity in the market (?):
$$\mathbb{E}_t(M_{t\to t+2}^{\$} \Pi_{t \to t+1}). $$
That is, the price of a contract which pays ... |
Is the price of the following inflation derivative observed/traded? |
Where can I find recent tables with the average cumulative default rates? |
I have successfully fit an ARIMA model to a time series of the daily returns of power futures prices. The question I have is: How can I create a prediction interval for the prices? Or, alternatively, is there a nonparametric alternative to ARIMA that you would recommend? I understand econometric models are a bit iffy f... |
> Chronic wariness rules the capital market mindset in the Teens. And little wonder. “Manipulated” market valuations (especially suppressed bond yields) rest on pillars of unprecedented economic stimulus largesse, especially from central banks. Policymakers are assailed for doing too little or too much. In many investm... |
What does this paragraph from the book Capital Markets mean? |
Gary Strumeyer writes in "The Capital Markets: Evolution of the Financial Ecosystem"
> Chronic wariness rules the capital market mindset in the Teens. And little wonder. “Manipulated” market valuations (especially suppressed bond yields) rest on pillars of unprecedented economic stimulus largesse, especially from ce... |
This has been posted a few times now, so I will invest the time on a full response.
### FRA / Futures convexity has **nothing** to do with profits/losses being **immediately** recognised on the future through margin settlement, and potential reinvestment, whilst deferred on the FRA.
Although the opposite seems to... |
A colleague of mine and I are debating how to price an electricity swap. Keeping in mind that electricity futures are delivered *over a period of time* rather than *at a point in time*, I maintain that the value of a swap is simply the difference between the futures price for a given month (the floating leg) and some f... |
Is the theta decay curve you see often given around the internet below in fact valid for American-style options? Often times, calculations for European-style options (Black-Scholes) are passed off as being valid for American-style options, so I wanted to make sure.
[![this one][1]][1]
[1]: https://i.stack... |
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