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I have a long-standing confusion around the truncation range of the COS method proposed by Fang and Oosterlee because I find that the results are highly volatile given the different truncation ranges.
To be more specific, given the following three truncation ranges (which I am aware is merely a rule of thumb):
$$
... |
How can I estimate volatility with historical data for Monetary Policy Rate (MPR) to use in a short rate model?
I could use regular techniques like simple standard deviation or max likelihood, but the problem is the data: MPRs usually have 0 variation over months, even years and then big discrete jumps. |
I have a long-standing confusion around the truncation range of the COS method proposed by Fang and Oosterlee because I find that the results are highly volatile given the different truncation ranges.
To be more specific, given the following three truncation ranges (which I am aware is merely a rule of thumb):
$$
... |
Let $v(t)$ be the variance of an underlying stock or index at time $t\in[0,1]$ between the open at $t=0$ and close at $t=1$ of an exchange. Usually $v(t)$ achieves local maxima at $t\in\{0,1\}$. For example,
$$v(t)\propto a+bt+c\cos(2\pi t), \, c>0.$$
How is $v(t)$ used, particularly in options pricing/trading?
|
How is the variance schedule used? |
Let $v(t)$ be the instantaneous variance of an underlying stock or index at time $t\in[0,1]$ between the open at $t=0$ and close at $t=1$ of an exchange. Usually $v(t)$ achieves local maxima at $t\in\{0,1\}$. For example,
$$v(t)\propto a+bt+c\cos(2\pi t), \, c>0.$$
How is $v(t)$ used, particularly in options pricing... |
Let $v(t)$ be the instantaneous variance of an underlying stock or index at time $t\in[0,1]$ between the open at $t=0$ and close at $t=1$ of an exchange. Usually $v(t)$ achieves local maxima at $t\in\{0,1\}$. For example,
$$v(t)\propto a+bt+c\cos(2\pi t), \, c>0.$$
I can see $\int_{T_1}^{T_2}v(t)dt$ can be plugged... |
Let $v(t)$ be the instantaneous variance of an underlying stock or index at time $t\in[0,1]$ between the open at $t=0$ and close at $t=1$ of an exchange. Usually $v(t)$ achieves local maxima at $t\in\{0,1\}$. For example,
$$v(t)\propto a+bt+c\cos(2\pi t), \, c>0.$$
I can see $\int_{T_1}^{T_2}v(t)dt$ can be plugged... |
I am trying to price a call on zero coupon bond under the Vasicek model by Monte Carlo method.
$$C_0 = B(0,T) \ \mathbb{E}^{\mathbb{Q}_T}[(B(T,S)-K)^{+}]$$
But the thing is my result is very different of what I have to find (0.095 found by closed form formulas).
Could you please expose my code errors or maths errors... |
I am trying to price a call option on a zero coupon bond using the Monte Carlo Vasicek model:
$$C_0 = B(0,T) \ \mathbb{E}^{\mathbb{Q}_T}[(B(T,S)-K)^{+}]$$
The problem is that the code I have written for this is yielding a price too different from the expected answer which is 0.095 based on the closed form formula... |
Every time I search calibration methods in short-rate models such as Hull-White I always find information on how to do it with swaptions market data, but I have not found any approach on how to do it in Markets without swaptions.
How can I calibrate Hull-White short rate model in a market without options? It is a ov... |
Let $v(t)$ be the instantaneous variance of an underlying stock or index at time $t\in[0,1]$ between the open at $t=0$ and close at $t=1$ of an exchange. Usually $v(t)$ achieves local maxima at $t\in\{0,1\}$. For example,
$$v(t)\propto f(t)= a+bt+c\cos(2\pi t), \, c>0,$$
where $\int_0^1 f(t)dt=1$.
I can see $\int... |
Every time I search calibration methods in short-rate models such as Hull-White, I always find information on how to do it with swaptions market data. Yet, I can't find anything about how to do it in markets without swaptions.
How can I calibrate Hull-White short rate model in a market without options? It is an over... |
**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... |
**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... |
**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... |
In an internal document in my company, the convexity adjustment for Futures is defined as:
)&space;-&space;E^{Q^{T+D}}(L(T,T,T&plu... |
In an internal document in my company, the convexity adjustment for Futures is defined as:
)&space;-&space;E^{Q^{T+D}}(L(T,T,T&plu... |
In an internal document in my company, the convexity adjustment for Futures is defined as:
)&space;-&space;E^{Q^{T+D}}(L(T,T,T&plu... |
To me there are some semantics involved here, I'd say you need to take a step back and think about a different adjoining question.
More than **calibrate** your parameters you need to **estimate** them since you have no points of reference for calibration i.e. no actively traded to Non-Linear / Vol products on this a... |
I have estimated GARCH and GJR-GARCH with several exogenous variables. Some of the exogenous variables have negative coefficients that are statistically significant. For instance, I can write my GJR-GARCH estimate as:
$h_t = 0.213 + 0.011 \epsilon_{t-1}^2 + 0.847 h_{t-1} + 0.196 u^2_{t-1}I_{t-1<0} - 0.026 X_{t-1} $
... |
I have estimated GARCH and GJR-GARCH with several exogenous variables. Some of the exogenous variables have negative coefficients that are statistically significant. For instance, I can write my GJR-GARCH estimate as:
$h_t = 0.213 + 0.011 u_{t-1}^2 + 0.847 h_{t-1} + 0.196 u^2_{t-1}I_{t-1<0} - 0.026 X_{t-1} $
Wher... |
I have estimated GARCH and GJR-GARCH with several exogenous variables. Some of the exogenous variables have negative coefficients that are statistically significant. For instance, I can write my GJR-GARCH estimate as:
$h_t = 0.213 + 0.011 u_{t-1}^2 + 0.847 h_{t-1} + 0.196 u^2_{t-1}I_{t-1<0} - 0.026 X_{t-1} $
Wher... |
### Positivity of GARCH-X models:
When it comes to GARCH models with exogenous regressors, it is more "tricky" to ensure positivity of the model, due to the unspecified model-dynamics of your exogenous regressor (*moreover exogenous regressors can have drastically different characteristics*). Without any model-spec... |
### Positivity of GARCH-X models:
When it comes to GARCH models with exogenous regressors, it is more "tricky" to ensure positivity of the model, due to the unspecified model-dynamics of your exogenous regressor (*moreover exogenous regressors can have drastically different characteristics*). Without any model-spec... |
I seem to remember the implied volatility skew of European options decreases as the expiry increases. It is true for the Huston model under the approximation. What are the good references that prove this property in general, or at least asymptotically? |
I seem to remember the implied volatility skew of European options decreases as the expiry increases. It is true for the Huston model under some approximation. What are the good references that prove this property in general, or at least asymptotically? |
I seem to remember the implied volatility skew of European options decreases as the expiry increases. It is true for the Heston model under some approximation. What are the good references that prove this property in general, or at least asymptotically? |
I am doing the Fama Macbeth regression analysis for finding the relation between Idiosyncratic volatility and Expected stock return. Stock return is dependent variable and independent variables are: idiovol, beta, size, bm, strev, illiq, max, coskew and idioskew. I have run different models and I get the following resu... |
In the "Treasury Bond Basis" book chapter 2, it says "if the yield curve has a positive slope,carry for someone who is long bonds and short futures is positive". Why is this the case?
Up to that point in the book, IRR is defined (simple version) as:
IRR = (Futures Inoivce Price / Bond Purchase Price - 1) x (360 ... |
I understand "A swaption in which the underlying swap starts at a date materially after the expiration date is called a midcurve swaption. The implied volatilities of these can not be obtained from the regular swaption surface. Market makers calculate implied volatilities for midcurves in a number of ways. One popular ... |
Midcurve Pricing - how to get the spread vol? |
Midcurve Swaption Pricing - how to get the spread vol? |
I understand "A swaption in which the underlying swap starts at a date materially after the expiration date is called a midcurve swaption. The implied volatilities of these can not be obtained from the regular swaption surface. Market makers calculate implied volatilities for midcurves in a number of ways. One popular ... |
I am trying to price a call option on a zero coupon bond using the Monte Carlo Vasicek model:
$$C_0 = B(0,T) \ \mathbb{E}^{\mathbb{Q}_T}[(B(T,S)-K)^{+}]$$
The problem is that the code I have written for this is yielding a price too different from the expected answer which is 0.095 based on the closed form formula... |
I am trying to price a call option on a zero coupon under the Vasicek Model using Monte Carlo method:
$$C_0 = B(0,\theta) \ \mathbb{E}^{\mathbb{Q}_T}[(B(\theta,T)-K)^{+}]$$
The problem is that the code I have written for this is yielding a price too different from the expected answer which is 0.095 based on the c... |
I believe I understand the following (from [the accepted answer](https://quant.stackexchange.com/a/29767/47484) to the Quantitative Finance question called "volatility of a mid curve option"):
> A swaption in which the underlying swap starts at a date materially after the expiration date is called a midcurve swapti... |
Mid-curve swaption pricing - how to get the spread vol? |
I am trying to price a call option on a zero coupon under the Vasicek Model using Monte Carlo method:
$$C_0 = B(0,\theta) \ \mathbb{E}^{\mathbb{Q}_T}[(B(\theta,T)-K)^{+}]$$
The problem is that the code I have written for this is yielding a price too different from the expected answer which is 0.095 based on the c... |
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 was wondering if there is any free resources where I can see/ download total FX long/short positions (size or at least number of contracts) in the market currently? |
In Grinold & Kahn (2000), the authors emphasized the separation of stock selection and benchmark timing in active portfolio management. So if we avoid benchmark timing, the optimal portfolio's beta should be 1 and we need to add this constraint to our portfolio optimization problem:
[![enter image description here][... |
How to deal with benchmark timing in quantitative portfolio management? |
I am trying to price a call option on a zero coupon under the Vasicek Model using Monte Carlo method:
$$C_0 = B(0,\theta) \ \mathbb{E}^{\mathbb{Q}_T}[(B(\theta,T)-K)^{+}]$$
The problem is that the code I have written for this is yielding a price too different from the expected answer which is 0.095 based on the c... |
In Grinold & Kahn (2000), the authors emphasized the separation of stock selection and benchmark timing in active portfolio management. So if we avoid benchmark timing, the optimal portfolio's beta should be 1 and we need to add this constraint to our portfolio optimization problem:
[![enter image description here][... |
In Grinold & Kahn (2000), the authors emphasized the separation of stock selection and benchmark timing in active portfolio management. So if we avoid benchmark timing, the optimal portfolio's beta should be 1 and we need to add this constraint to our portfolio optimization problem:
[![enter image description here][... |
I read somewhere that autocorrelation prevents someone from annualizing variance. But how does it bias it? Let's say you have daily returns. If autocorrelation is high, should that overstate or understate annualized variance when you multiply by 252. What about if you have negative autocorrelation?
Thanks! |
How does autocorrelation bias annualizing variance? |
The "diversification return" of a portfolio is the difference between the geometric average (compound) return of a rebalanced portfolio and the weighted sum of the geometric average returns of the assets. My understanding is this diversification return is always nonnegative in a portfolio with positive asset weights (... |
In Andrew W. Lo's paper, **[The statistics of Sharpe Ratios (2002)](https://www.tandfonline.com/doi/abs/10.2469/faj.v58.n4.2453)** he derives the variance of non-IID returns (*returns that can exhibit serial correlation*) under the assumption of (covariance) stationary returns with common variance (*eq. 19*):
\begin... |
(*First of all, sorry to have taken so much time to see this question...*)
For the paper you refer to (Guéant-L-Tapia), there is a report (in French) by Sophie Laruelle about how to do it in practice:
[Faisabilité de l’apprentissage des paramètres d’un algorithme de trading sur des données réelles][1], this title t... |
> I have a cumulative profit/loss time series below for a trading strategy, what is the appropriate way to calculate the returns in percentage for such a series?
Correct me if I am wrong, but it seems to me there is no such thing as return for P&L. Your series contains net income which itself is a return. You could ... |
I am currently running some Fama French regressions for a number of specified portfolios, consisting of US stocks (for a university level course). The regressions are conducted in R, using the lm funtion.
The models look like this:
```
3F <- lm(ExcessReturn ~ MKT + SMB + HML, data = df)
4F <- lm(ExcessReturn ~ MK... |
I have a question regarding the business day convention. Suppose I have a bond that matures on the 17th of September 2023 and pays annual coupon of $1%$. It has a $30/360$ day count convention an business day adjustment of forward unadjusted.
Now the 17th of September 2021 is a Friday. The 17th of September 2022 is... |
I have a question about Reverse-MIDAS. What program can i use for Reverse-MIDAS ? I know Eviews is used for MIDAS. but Rıverse-MIDAS? |
What program can i use for Reverse-MIDAS? |
I am currently running some Fama French regressions for a number of specified portfolios, consisting of US stocks (for a university level course). The regressions are conducted in R, using the lm funtion.
The models look like this:
```
3F <- lm(ExcessReturn ~ MKT + SMB + HML, data = df)
4F <- lm(ExcessReturn ~ MK... |
I know EViews is used for mixed-data sampling (MIDAS). Can someone pls help me identify a program I can use for reverse MIDAS? Thank you. |
What program to use for reverse MIDAS? |
I am currently running some Fama French regressions for a number of specified portfolios, consisting of US stocks (for a university level course). The regressions are conducted in R, using the lm funtion.
The models look like this:
```
3F <- lm(ExcessReturn ~ MKT + SMB + HML, data = df)
4F <- lm(ExcessReturn ~ MK... |
I have a series of price returns of an asset (4 days worth of data). They are relatively high-frequency.
My ultimate goal is to calculate realized volatility, but using a student-t distribution.
I have fit a TSRV model to the returns, then scaled that by sqrt(252) to annualized volatility. The results look re... |
I have a question regarding the business day convention. Suppose I have a bond that matures on the 17th of September 2023 and pays an annual coupon of $1%$. It has a $30/360$ day-count convention and a forward business day adjustment.
Now the 17th of September 2021 is a Friday. The 17th of September 2022 is a Satur... |
## `Midasr` in R:
**`R` has a package called [midasr](https://github.com/mpiktas/midasr)** that provides econometric methods for working with mixed frequency data. One of the authors have another repository that provide examples on how to fit different reverse-MIDAS regressions (*see **[here](https://github.com/mpi... |
I have a series of price returns of an asset (4 days worth of data). They are relatively high-frequency.
My ultimate goal is to calculate realized volatility, but using a student's t-distribution.
I have fit a two-scale realized volatility (TSRV) model to the returns, then scaled that by sqrt(252) to annualized... |
Is there any way to get cashflow amount including cashflow date in QuantLib? |
I am writing a code in `python` that streams real-time data from the Coinbase Exchange.
def on_open(ws):
print('opened connection')
subscribe_message ={
"type": "subscribe",
"channels": [
{
"name": "ticker",
"produ... |
Does QuantLib has functionality to value ILS Telbor swaps? |
I have a final round with a market making firm coming up and will be asked to play several market making games. I wanted to ask for advice on how to approach these games, especially with an information imbalance.
Here is my general strategy:
- quote evenly around the EV
- toward the beginning when uncertainty is h... |
## `Midasr` in R:
**`R` has a package called [midasr](https://github.com/mpiktas/midasr)** that provides econometric methods for working with mixed frequency data. One of the authors have another GitHub repository that provides examples on how to fit different reverse-MIDAS regressions (*see "**[Reverse MIDAS examp... |
## `Midasr` in R:
**`R` has a package called [midasr](https://github.com/mpiktas/midasr)** that contains econometric methods for working with mixed frequency data. One of the authors have another GitHub repository that provides examples on how to fit different reverse-MIDAS regressions (*see **[Reverse MIDAS reposi... |
I am currently running some Fama French regressions for a number of specified portfolios, consisting of US stocks (for a university level course). The regressions are conducted in R, using the lm funtion.
The models look like this:
```
3F <- lm(ExcessReturn ~ MKT + SMB + HML, data = df)
4F <- lm(ExcessReturn ~ MK... |
## `Midasr` in R:
**`R` has a package called [midasr](https://github.com/mpiktas/midasr)** that contains econometric methods for working with mixed-frequency data. One of the authors has another GitHub repository that provides examples on how to fit different reverse MIDAS regressions (*see **[Reverse MIDAS reposit... |
If the interviewer is the only person you can trade with, and he has full information about the result (e.g. all the numbers of the phone number), while you have none, why would you ever make a trade with him at all?
The only way it makes sense to ever trade with him is as a "fee" to get information in order to make... |
If the interviewer is the only person you can trade with, and he has full information about the result (e.g. all the numbers of the phone number), while you have none, why would you ever make a trade with him at all?
The only way it makes sense to ever trade with him is as a "fee" to get information in order to make... |
Say I have a FRN.
If rates go up, then my cashflows are discounted more, but my coupons also go up, so in the end, my bond may be worth the same.
However, if rates go up, then since my price is unchanged but my coupons are higher, my YTM has also gone up.
This doesn't really make sense to me: why is my YTM hi... |
How to interpret YTM in this situation? |
I was going through the proof about the equality of forward and futures price (assuming constant interest rate) in a book. Somewhere, the authors used the fact that suppose we start with two capitals - say A and B and we end up with the same final capital S, then A=B otherwise there will be arbitrage opportunity. Why a... |
If the interest rate is constant, then the forward price and the futures price are equal? |
How to interpret YTM of FRN when interest rates change? |
I work at an accountancy firm and we use Black-Scholes to value equity in private companies that has option like features. The equity we typically value is akin to deeply out of the money European call options and we source volatility using historical share price volatilities of quoted comparable volatilities.
It's ... |
I’m running a simulation in which I want to calculate the NPV of 100 swaps over 1000 (or even much more) different interest rate curves.
It looks like Quantlib is not really fast in performing these calculations or my code is just not optimal.
Script does the following (for all curves):
- Create Quantlib cur... |
I see in BBG that the Beta of XSPS (an inverse SP500 ETF) to SPX Index is -1.05 and the Adjusted Beta is -0.37.
I get that -1.05 * 2/3 + 0.33 matches these results however does this adjuste Beta make any sense for short positions? Should it not be -1.05 * 2/3 - 0.33 instead?
Thanks |
Can somebody point me to any notes on how to "back out" what's the implied term premium after we have calibrated an affine term structure model?
I was able to calibrate to the yields cov matrix as well as the yield curve (Q-measure). I came across in some book that they were also able to work out the P-measure yield... |
I see in BBG that the beta of XSPS (an inverse SP500 ETF) to SPX Index is -1.05 and the adjusted beta is -0.37.
I get that -1.05 * 2/3 + 0.33 matches the adjusted beta. However, does this adjusted beta make sense for short positions? Should it not be -1.05 * 2/3 - 0.33 instead? |
Adjusted beta for short positions, should we re-adjust the formula? |
What does structured estimator mean? |
Below are my 2 cents only, but this was too long for a comment.
As he shows in the next lines (see also *Variance Swaps* chapter of Bergomi's book)
$$ \sigma_{VS}^2(T) = \int_{-\infty}^{+\infty} \tilde{\sigma}^2(z,T) \phi(z) dz \tag{0} $$
where $\sigma_{VS}(T)$ denotes the volatility of a fresh-start variance swa... |
The optimal entry/exit thresholds for mean reversion trading (assuming an underlying OU process) is derived in the paper "[Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit][1]" by Tim Leung and Xin Li, and these results are also included in the book "[Optimal Mean Reversion Trading Mathematical ... |
Why aren't the optimal entry/exit thresholds for OU pairs trading relatively invariant to shifts in the OU mean? |
The optimal entry/exit thresholds for mean reversion trading (assuming an underlying Ornstein-Uhlenbeck (OU) process) is derived in the paper "[Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit][1]" by Tim Leung and Xin Li, and these results are also included in the book "[Optimal Mean Reversion ... |
The optimal entry/exit thresholds for mean reversion trading (assuming an underlying Ornstein-Uhlenbeck (OU) process) is derived in the paper "[Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit][1]" by Tim Leung and Xin Li, and these results are also included in the book "[Optimal Mean Reversion ... |
The optimal entry/exit thresholds for mean reversion trading (assuming an underlying Ornstein-Uhlenbeck (OU) process) is derived in the paper "[Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit][1]" by Tim Leung and Xin Li, and these results are also included in the book "[Optimal Mean Reversion ... |
This is a very deep question and so the answers cannot be in layman's terms. Bermudan swaptions are very complicated products despite that they are one of the most actively traded rates vol products. Below are a few thoughts from my experience.
1. Why are they popular?
Corporate clients of banks issue calla... |
Those are all very deep questions. Bermudan swaptions are very complicated products despite that they are one of the most actively traded rates vol products. Below are a few thoughts from my experience.
1. Why are they popular?
Corporate clients of banks issue callable bonds but they might not know the good... |
What is the market value of an (index) futures?
I guess the market value is either:
1. `quantity * contract size * price`
2. zero, if the daily unrealized PnL is disregarded
The contract is entered at zero cost, so should the market value also be considered zero? I can see arguments for both alternatives. Is th... |
> _What exactly are the “bounds” in arbitrage bounds?_
The bounds refer to price levels for the combination of related tradable instruments (spreads) outside which arbitrage activity switches from unprofitable to profitable.
Example:
* 3-cookie package price $p_3$
* 1-cookie price $p_1$
* cost to pay some... |
I want to understand the difference between the real and financial assets.
By definition, real assets are structures, equipment, inventories of goods, and land.
Financial assets are bank accounts, corporate stocks, or bonds.
Here are five examples I want to understand: patent, lease obligations, customer goodwil... |
In the book *Warren Buffett and the interpretation of the financial statements*, Mary Buffett explained companies that have enough earning power to be able to pay off their long-term debt in three or four years are good candidates in our search for exceptional companies with a sustainable competitive advantage.
**Q... |
I'm attempting to write a tool that will automatically calculate the expected value of arbitrary options positions, and I need to clarify my understanding. I am neither a statistician nor a professional quant so please permit me a bit of (perhaps unnecessary) exposition:
### Scenario
Suppose I am interested in t... |
I'm new to Quantlib in Python and I'm running into a quite awkward situation.
I have a vol surface from the market on the SPX index. Not all strikes/maturities are populated. In addition, there could potentially be arbitrages in short maturities since we have lots of daily options and I am not correcting yet for arb... |
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