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I have 2 discount factor curves;
DF 1
I expected every DF curve to have the shape of the 2nd one (almost a straight line), what does it mean economically when a DF curve has the shape of the 1st one? or maybe the curve is wrong?
How could a shorter CF 2036 offer a higher yield than the latter CF 2041
[![enter... |
Looking at the spread between 3 month commercial paper and the 3 month bill (using say, Fred), how/why (economically speaking) can this spread be negative? Are there some mechanics in the commercial paper markets at play that could make this happen? Or are there some idiosyncrasies with how these data-series/rates are ... |
How can Commercial Paper Spreads be Negative? |
I'm working on a Interes Rate Risk in Banking Book model for EVE calculation. It doesn't matter if you know what it is or not, I just need help with one step. That step is the creation of risk free yield curve for Euro currency. I'm using Moorad Choudhry book 'Banking Principles 2nd'.
In one of the examples, he pro... |
Looking at the spread between 3 month commercial paper and the 3 month bill (using say, Fred), how/why (economically speaking) can this spread be negative? Are there some mechanics in the commercial paper markets at play that could make this happen? Or are there some idiosyncrasies with how these data-series/rates are ... |
For a pairs trade, when calculating the zscore should I include the intercept point in the calculation:
```
spread = price2 - (gradient * price1) - intercept
zscore = (spread - average)/standard_deviation
```
or should I exclude the intercept:
```
spread = price2 - (gradient * price1)
zscore = (spread - ave... |
For a pairs trade, when calculating the zscore should I include the gradient from OLS in the calculation:
```
spread = price2 - (gradient * price1)
zscore = (spread - average)/standard_deviation
```
Should the spread calculation include the gradient:
```
spread = price2 - (gradient * price1)
```
or just
```... |
For Bloomberg, there are technically two swap curves that could work:
-`ICVS 133` for EUR OIS and
-`ICVS 514` for €STR.
I agree with @Dimitri Vulis that you should use €STR. With Bloomberg, you will have a few issues here though:
- The user agreement with a terminal license will not allow you to use it for ... |
For a pairs trade, when calculating the zscore should I include the gradient from OLS in the calculation:
```
spread = price2 - (gradient * price1)
zscore = (spread - average)/standard_deviation
```
Should the spread calculation include the gradient:
```
spread = price2 - (gradient * price1)
```
or just
```... |
For a pairs trade, when calculating the zscore should I include the gradient (slope) from OLS in the calculation:
```
spread = price2 - (gradient * price1)
zscore = (spread - average)/standard_deviation
```
Should the spread calculation include the gradient:
```
spread = price2 - (gradient * price1)
```
or j... |
For a pairs trade, when calculating the zscore should I include the gradient (slope) from OLS in the calculation:
```
spread = price2 - (gradient * price1)
zscore = (spread - average)/standard_deviation
```
Should the spread calculation include the gradient:
```
spread = price2 - (gradient * price1)
```
or j... |
This exactly composition I have never seen. As far as I know, multiple sequential decisions are not common in OTC trades, so an structure like this would probably be a "single american option", which I mean, once any of the legs is exercised the whole structure cease to exist, as mentioned by jherek here, would have a ... |
why doesn't futures contract just stipulate a specific contract to be delivered. Is it because the futures seller cannot readily buy specific bond contracts? |
With the Fed raising interest rates so fast and so drastically, classical interest rate models such as the Black Karasinski (BK), Hull-White (HW), etc., may have trouble calibrating to current rate levels and at the same time passing backtesting due to resent negative rates,
For example, you can shift BK to captur... |
I am re-reading Michael Lewis' *Flash Boys* book, and I have a question about how a High Frequency Trader was able to front-run an order in a particular example mentioned in the book. On page 78, chapter *Ronan's Problem*, it describes how the president of a large hedge fund noticed that his trading costs had increased... |
How were High Frequency Traders able to front-run in this example in Flash Boys? |
I have persistent, deep problems with the concept of 'risk-neutrality'. To make it more precise, let's look at the following explanation taken from a book:
> "In a world where investors are risk neutral, the expected return on
> all securities is the risk-free rate of interest, r. The reason is
> that risk-neutral... |
Conceptual problem with risk neutrality-What is a 'risk-neutral world', exactly? |
What is a 'risk-neutral world'? It is not a real world- it is a purely mathematical construct which is defined by your statements (the present value of cashflows can be correctly found bydiscounting at risk free rates). We build this construct purely to make it easier to price certain financial contracts, chiefly deriv... |
A little bit of history. This goes back to the early days when the Black Scholes formula for options was becoming popular but was still new and somewhat mysterious.
It was (and is) widely accepted in Finance that long term rates of return for stocks $r$ are higher than the return on T-Bills $r_F$ (also known as the ... |
A little bit of history. This goes back to the early days when the Black Scholes formula for options was proposed but was still new and somewhat mysterious.
It was (and is) widely accepted in Finance that long term rates of return for stocks $r$ are higher than the return on T-Bills $r_F$ (also known as the risk fre... |
A little bit of history. This goes back to the early days when the Black Scholes formula for options was proposed but was still new and somewhat mysterious.
It was (and is) widely accepted in Finance that long term rates of return for stocks $r$ are higher than the return on T-Bills $r_F$ (also known as the risk fre... |
A little bit of history. This goes back to the early days when the Black Scholes formula for options was proposed but was still new and somewhat mysterious.
It was (and is) widely accepted in Finance that long term rates of return for stocks $r$ are higher than the return on T-Bills $r_F$ (also known as the risk fre... |
A little bit of history. This goes back to the early days when the Black Scholes formula for options was proposed but was still new and somewhat mysterious.
It was (and is) widely accepted in Finance that long term rates of return for stocks $r$ are higher than the return on T-Bills $r_F$ (also known as the risk fre... |
On Jorion's 'Value at Risk' chapter about risk mapping, interest rate swaps are decomposed in a portfolio of forward contracts so they can be mapped into risk factors.
I'm trying to implement this for some commodity swaps which P&L depend on three risk factors: the commodity forward price, the BRL risk free rate, and ... |
QuantLib: How to check or access the QuantLib version in conda prompt or spyder? |
It could be worse. You're not asked to price rate exotics like accreters that might need more inputs besides implied vol cube :) and you're only asked to make markets. I.e., if I understand the question correctly, you don't intend to keep much rate vega / sensitivity to the poorly observable implied rate vol, unless in... |
I am looking for a portfolio of ETFs and mutual funds that tracks market, size, value and momentum factors.
One ETF/mutual fund per factor. So say that I want an ETF that tracks the value factor (let's call the return on that ETF $r^{value}_t$), what I am looking for is for an asset whose regression:
$r^{value} ... |
What ETFs and Mutual funds track best the Cahart 4 factors? Or in other words how to replicate these factors cheaply? |
I am trying to code the HAR (and eventually the HARQ) from Bollerslev et al 2016 and Corsi 2009.
$$
RV_t = \beta_0 +\beta_1 RV^d_{t-1} + \beta_2 RV^W_{t-1}+\beta_3 RV^M_{t-1}+u_t
$$
Bollerslev estimates the parameters as: $\beta_0 = 0.1123, \beta_1 = 0.2273, \beta_2 = 0.4903$, and $\beta_3= 0.1864 $
With the... |
What is wrong with my HAR model - constantly increasing? |
I am working on a project and need to map different IDs. Is LEI and Bloomberg Ticker one to one mapping? I can use Bloomberg formular =BDP(A1,"LEGAL_ENTITY_IDENTIFIER") to convert ticker "DUK US Equity" in excel A1 to LEI, but did not find formular to reverse it. So I suspect there will be a non-1-1 mapping issue here.... |
Is LEI and Bloomberg Ticker one to one mapping. How about LEI, Bloomberg Ticker, Bloomberg ID, ISIN and CUSIP? |
In page 34 of "Treasury Bond Basis" (Third Edition) by Burghardt et al, it says:
>If the yield curve has a positive slope, carry for someone who is long bonds and short futures is positive. Every day that goes by is money in the bank. The implied repo rates simply confirm this.
Why is this the case?
Up to t... |
I am trying to code the HAR (and eventually the HARQ) from [Bollerslev et al 2016][1] and [Corsi 2009][2].
$$
RV_t = \beta_0 +\beta_1 RV^d_{t-1} + \beta_2 RV^W_{t-1}+\beta_3 RV^M_{t-1}+u_t
$$
Bollerslev estimates the parameters as: $\beta_0 = 0.1123, \beta_1 = 0.2273, \beta_2 = 0.4903$, and $\beta_3= 0.1864 $
... |
I need to compute monthly realized variance from daily data for Fama-French factors. Knowing that Fama-French factors is the difference of return between different type of stocks, for example SMB factor is the difference between returns on portfolios of small stocks and portfolios of big stocks, should I again take sum... |
I am looking for a portfolio of ETFs and mutual funds that tracks market, size, value and momentum factors.
One ETF/mutual fund per factor. So say that I want an ETF that tracks the value factor (let's call the return on that ETF $r^{value}_t$), what I am looking for is for an asset whose regression:
$r^{value} ... |
What ETFs and mutual funds track the Carhart 4 factors best? I.e. how to replicate these factors cheaply? |
Model is economically significant, but has negative $R^2$? |
I need to compute monthly realized variance from daily data for Fama-French factors. Knowing that Fama-French factors is the difference of return between different type of stocks, for example SMB factor is the difference between returns on portfolios of small stocks and portfolios of big stocks, should I again take the... |
How were High Frequency Traders able to front-run in this example from Flash Boys? |
Tradition mean-variance optimization uses the following objective function in optimization:
$$
\mu w^T - \lambda w^T \Sigma w
$$
Which I'm trying to adapt to a factor model. I've come up with:
$$
f \mu w^T - \lambda w^T \Sigma w f f^T
$$
where:
- $f$ is the factor loadings (exposures)
- $\lambda$... |
That's not ideal. Why don't you just do the standard MV problem but including the factors themselves as assets? Since they generate positive alpha, the mean-variance problem will give them $w>0$, and your tangency portfolio would be higher. |
Is it true that far wings of the volatility smile have an outsized influence on the price of a variance swap? Is there a mathematical argument demonstrating this idea? What do we generally refer as far wings (5% probability to hit the level or 1% probability etc.)? I could find no paper detailing this dependence. |
I've created some macroeconomic factors (e.g. analogs of real GDP growth) that I believe have explanatory power for asset returns. By a factor here, I mean a stationary time-series of real numbers.
I'd like to create so-called "mimicking portfolios" for these factors - e.g. portfolios of assets in my base universe ... |
I've created some macroeconomic factors (e.g. analogs of real GDP growth) that I believe have explanatory power for asset returns. By a factor here, I mean a stationary time-series of real numbers.
I'd like to create so-called "mimicking portfolios" for these factors - e.g. portfolios of assets in my base universe ... |
I've created some macroeconomic factors (e.g. analogs of real GDP growth) that I believe have explanatory power for asset returns. By a factor here, I mean a stationary time-series of real numbers.
I'd like to create so-called "mimicking portfolios" for these factors - e.g. portfolios of assets in my base universe ... |
When trying to value an American option we often use grid-based methods (e.g. Monte Carlo in combination with Longstaff Schwartz; or Finite Difference Methods). As such, we are in fact estimating the value of a Bermudan option with discrete time points where we can exercise the option, i.e. $0=t_0 < t_1 < ... < t_n = T... |
Is this paper useful? Discussed usage of Richardson extrapolation for such purposes
http://www.fin.ntu.edu.tw/~conference2002/proceding/5-4.pdf |
I know that $$\sum_{i=1}^n i \frac{CF_i}{CF_{Total}}$$ is Macaulay Duration, but what is $$\sum_{i=1}^n i^2 \frac{CF_i}{CF_{Total}}$$. I have given it a thought like it is a second moment of something and for a few internet search this has a correlation with Convexity. Is it just convexity if not, what is it ? |
I have heard that traders use a straddle to hedge volatility swaps (in the FX context), although I could not figure out the specifics. Is this type of hedge used in practice? And if yes, how does it work? Is there an approximation formula that could be written down to justify such a hedging strategy? This is a question... |
So there are 3 ways that I know of to do this --- none of those, unfortunately, uses the likelihood ratio (when I tried to do the calculation with the likelihood ratio, eg. how policy gradients are calculated in reinforcement learning, I found that swapping expectation and derivative was giving me trouble and making th... |
When we talk about the single-period CAPM, the return in a particular period t can be defined as (Pt - Pt-1)/Pt-1. Investors plan at t-1 and get a payoff at t.
After this period, the same mechanics take place. **Does the “new” Pt-1 have to necessarily be equal to Pt?** In other words, is the return in each period c... |
How do asset prices behave in a single-period and multi-period model? |
So we are looking at some security names with limited amount of listed options. Some of them only have listed options that expire in less than a year. Is there a quick way to extrapolate the vol surface / term structure based on listed options, forward price, and maybe index options with longer maturity? Many thanks! |
In a BS world (constant volatility, no transaction costs, continuous hedging) If I buy or sell an option and continuously delta-hedge, I know how to calculate the final PnL based on implied vs realized volatility, but how do I calculate the PnL at some point in time before expiry of the option?
For example, I buy ... |
In a BS world (constant volatility, no transaction costs, continuous hedging) If I buy or sell an option and continuously delta-hedge, I know how to calculate the final expected PnL based on implied vs realized volatility, but how do I calculate the PnL at some point in time before expiry of the option?
For exampl... |
In a BS world (constant volatility, no transaction costs, continuous hedging) If I buy or sell an option and continuously delta-hedge, I know how to calculate the final expected PnL based on implied vs realized volatility, but how do I calculate the PnL at some point in time before expiry of the option?
For exampl... |
I am currently calculating daily returns of a stock with the following formula:
$$R_t = \frac{P_t - P_{t-1}}{P_{t-1}}$$
However, once I have the data, I am unable to establish a range to classify the daily returns as a usual move or as an unusual move
Is there a statistical method to differentiate the days wit... |
I am currently calculating daily returns of a stock with the following formula:
$$R_t = \frac{P_t - P_{t-1}}{P_{t-1}}$$
However, once I have the data, I am unable to establish a range to classify the daily returns as a usual move or as an unusual move
Is there a statistical method to differentiate the days wit... |
Here's an apparent paradox that puzzles me.
EMH states that asset prices reflect all information available. Investors are assumed to be rational. We can note:
$E(p_{t+1}/\Phi_{t}) = (1+E(r_{t+1}/\Phi_{t}))*p_{t}$
Where E is the expected value operator. $p_{t}$ the price at time t, $r_{t+1}$ the expected one-peri... |
Efficient Market Hypothesis paradox? |
Here's an apparent paradox that puzzles me.
EMH states that asset prices reflect all information available. Investors are assumed to be rational. We can note:
$E(p_{t+1}|\Phi_{t}) = (1+E(r_{t+1}|\Phi_{t}))*p_{t}$
Where E is the expected value operator. $p_{t}$ the price at time t, $r_{t+1}$ the expected one-peri... |
I'm running some stress tests and I have data on equity shocks available. Is there a relationship which, for the same issuer, links the returns of the shares with those of the bonds issued?
|
Here's a question that's been on my mind on-and-off for some time now.
It's well known that Black-Scholes is an unsuitable model for pricing in the current (post 80s) market as it fails to capture the volatility smile/skew. A crude way around this is to calibrate a volatility surface by finding the volatility for wh... |
What does implied volatility say about the underlying? |
What is the PDE for this interest rate derivative? |
Say I have a portfolio of stocks, stock A, stock B and stock C, with the below positions:
- stock A: long 100 USD
- stock B: long 50 USD
- stock C: short 200 USD
How do I calculate the portfolio variance given the covariance matrix?
I guess this question boils down to: how do I obtain the weights for each stoc... |
Is it possible to perform a VaR approach to the LMM? |
Let me define the Spot price process of an underlying as follows: $$dS_{t}=\mu_{S}S_{t}dt+\sigma_{S}S_{t}dW_{t},$$
where $\left(W_{t}\right)_{t\geq0}$ is an appropriate Wiener-process, so $\left(S_{t}\right)_{t\geq0}$ is a simple geometric Brownian motion.
Let me define the following payoff:
$$X=S_{T}-K$$
In this... |
What is the dynamic of the forward price process under $\mathbf{Q}$? |
Is it possible to perform a VaR analysis based on the forwards obtained by the LMM? |
In view of [this](https://quant.stackexchange.com/questions/73938/how-does-one-calibrate-a-vasicek-model-to-actual-cap-prices) question I asked some time ago, I tried to calibrate a Vasicek model to some cap volatilities, given as follows. I consider the maturities (in years)
$$
0.5,1,2,3,4,5,7,10,15,20
$$
and the ... |
Are my fitted Vasicek model parameters market consistent or realistic? |
I am building a tool with Quantlib (Python) to work on the forward pricing of different types of assets (inflation linked, amortizing, vanilla, zero coupon bonds).
For a number of reasons I am using the bonds cashflow series as provided by an internal system. From the same system I can get the discount factors asso... |
UPDATE: I manually recalculated the forward discount factors and the NPV that I get matches the one that I get with
`P = ql.CashFlows.npv(cfs, discountTermStructure, True, reference_date)`
Note that in the above I have changed the boolean value False to True, as in my case, the asset (loan or bond) was issued at ... |
I am building a tool with Quantlib (Python) to work on the forward pricing of different types of assets (inflation linked, amortizing, vanilla, zero coupon bonds).
For a number of reasons I am using the bonds cashflow series as provided by an internal system. From the same system I can get the discount factors asso... |
I am trying to add a holiday to my calendar in QuantLib such that my option pricing model considers this in pricing where I would expect that the time to expiry should decrease with the inclusion of a holiday, and my option reduce in price. However, when I use the `.addHoliday` method it successfully adds the holiday t... |
For a swaption, I had 2 questions:
1. how would I guage the PnL based on RV vs IV on a swaption?
I'm guessing its 0.5 *gamma* (RV^2-IV^2)(or realized variance - implied variance)
Not 100% sure on this.
2. I understand to calculate the theta of a swaption it's
0.5*gamma*IV^2 (daily bp vol)
However for s... |
For a swaption, I had 2 questions:
1. how would I guage the PnL based on RV vs IV on a swaption?
I'm guessing its 0.5 x gamma x (RV^2-IV^2)(or realized variance - implied variance)
Not 100% sure on this.
2. I understand to calculate the theta of a swaption it's
0.5 x gamma x IV^2 (daily bp vol)
However... |
For a swaption, I had 2 questions:
1. how would I guage the PnL based on RV vs IV on a swaption?
I'm guessing its 0.5 x gamma x (RV^2-IV^2)(or realized variance - implied variance)
Not 100% sure on this.
2. I understand to calculate the theta of a swaption it's
0.5 x gamma x IV^2 (daily bp vol)
However... |
**This post is Quant Stack Exchange's master list of data sources.**
Please append your links to other data sources to the list below.
## Economic Data ##
See [What are the most useful sources of economics data?][1] on Cross Validated SE.
**World**
- <https://macrovar.com/macrovar-database/> includes free... |
I'm new to this, and just trying to understand what options prices imply about asset growth. I'm looking at the following expression for the underlying asset price in the Black-Scholes model, in particular:
`S(t) = S(0)*exp((r - 0.5*\sigma^2)*dt + \sigma*dW(t)`
Where `S(t)` is the asset price at time `t` in year... |
Does Black-Scholes imply that the expected return for an asset is fixed as the volatility increases? |
How does the quantlib set up hour time, say in the example below:
ql.Date(20, 1, 2023), US calendar,
what is the time, 12 AM US time? local machine time?
say I would like to set up a NY 4 pm time, is it possible? |
We have 2 risky and 1 risk-free asset.
E1 = 4%, STD1=10%
E2 = 5.5%, STD2 = 20%
rf=1.5%
The covariance matrix and it's inverse are given:
(0.01, 0.006)
(0.006, 0.04)
inverse:
(109.9, -16.5)
(-16.5, 27.5)
ue (vector of excess returns)
(2.5,4)
Now the formula for the weights of the tangency por... |
Calculating tangency portfolio weights with the given information? (2risky +riskfree asset) |
We have 2 risky and 1 risk-free asset.
E1 = 4%, STD1=10%
E2 = 5.5%, STD2 = 20%
rf=1.5%
The covariance matrix and it's inverse are given:
|0.01 0.006|
|0.006 0.04|
inverse:
|109.9 -16.5|
|-16.5 27.5|
ue (vector of excess returns)
(2.5 4)
Now the formu... |
We have 2 risky and 1 risk-free asset.
E1 = 4%, STD1=10%
E2 = 5.5%, STD2 = 20%
rf=1.5%
The covariance matrix and it's inverse are given:
|0.01 0.006|
|0.006 0.04|
inverse:
|109.9 -16.5|
|-16.5 27.5|
ue (vector of excess returns)
(2.5 4)
Now the formu... |
We have 2 risky and 1 risk-free asset.
E1 = 4%, STD1=10%
E2 = 5.5%, STD2 = 20%
rf=1.5%
The covariance matrix and it's inverse are given:
|0.01 0.006|
|0.006 0.04|
inverse:
|109.9 -16.5|
|-16.5 27.5|
ue (vector of excess returns)
(2.5 4)
Now the formu... |
I'm trying to assess the attractiveness of real estate debt funds. I'm very surprised when I look at the investment performance of many of those funds. Many of them have no negative returns, and can yield up to 10% p.a. See for instance : https://ca.fierarealestate.com/wp-content/uploads/2022/12/Fiera-Real-Estate-Mezza... |
How can I correctly assess the risk of real estate debrt fund? |
I'm trying to assess the attractiveness of real estate debt funds. I'm very surprised when I look at the investment performance of many of those funds. Many of them have no negative returns, and can yield up to 10% p.a. See for instance : https://ca.fierarealestate.com/wp-content/uploads/2022/12/Fiera-Real-Estate-Mezza... |
How can I correctly assess the risk of real estate debt fund? |
I'm trying to understand this Python code that uses Quantlib to calibrate the parameters of the Heston model. The data that is provided in the code is the spot price, the risk free interest rate, the dividends of the underlining, the day of calibration, expiration dates of options, their strike prices, and their implie... |
When finding the value of a cross currency swap you need to take into account the collateral posting currency of the CSA agreement and adjust the discount factors accordingly, see this reference for example going through the rationale https://insights.londonfs.com/modern-derivatives-pricing-csa-discounting.
My quest... |
I think the answer to this question is that it's not as simple as you're making it out to be.
If I'm market making options, there is no requirement that I hedge that option with the exact same strike. Perhaps I am happy to sell a different (portfolio of) option(s) such that I am net receiving premium and am comforta... |
The general - and short - answer would be **no**: Except for some hypothetical cases, unless you have a convincing model for the residual spread-over-swap, you cannot use swaps to value your bond.
##### Quick comparison
Bonds are traded in the bond market. The cash flows are uncollateralized (of course) and carry t... |
Consider a path-dependent GBM model for a stock price:
$$dS_t = \mu(t, S_.)S_tdt + \sigma(t, S_.) S_t dB_t,$$
where $\mu, \sigma : [0,\infty)\times C_{[0,\infty)}\to \mathbb{R}$ are previsible path-functionals.
Does anyone know of any references of papers on this generalization and if there are any standard choic... |
Consider a path-dependent GBM model for a stock price:
$$dS_t = \mu(t, S_.)S_tdt + \sigma(t, S_.) S_t dB_t,$$
where $\mu, \sigma : [0,\infty)\times C_{[0,\infty)}\to \mathbb{R}$ are previsible path-functionals.
Does anyone know of any references of papers on this generalization and if there are any standard choic... |
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