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The GBTC (Grayscale Bitcoin) ETF is known for historically having a premium to net asset value (NAV). This led crypto funds to buy bitcoin, deposit their bitcoin into the trust to obtain GBTC, then sell GBTC for a profit.
Recently, this premium turned into a discount, because as a grantor trust, it cannot sell its ... |
I'm currently reading a [paper](https://www.scirp.org/journal/paperinformation.aspx?paperid=82927#ref3) about an optimal stopping time problem. I'm unable to see how the following stochastic equation was derived:
> To reduce the dimension of the problem we define a new process $W$ by:
$$dZ_t = -(\sigma + \omega \p... |
I'm currently reading a [paper](https://www.scirp.org/journal/paperinformation.aspx?paperid=82927) (*The Optimal Stopping Time for Selling an Asset When It Is Uncertain Whether the Price Process Is Increasing or Decreasing*, American Journal of Operations Research, March 2018)
about an optimal stopping time problem. I... |
Why can't the curve find the least squares parameters when I used it in SABR model? (SABR Calibration) |
It seems to have vanished off the web but a few years back Dupire published two tradable realized volatility estimators in 2015, I even asked a question around it here. https://quant.stackexchange.com/questions/34333/what-makes-a-realized-vol-estimate-tradeable
However, the only presentation I could find on the web ... |
It seems to have vanished off the web but a few years back Dupire published two tradable realized volatility estimators in 2015, I even asked a question around it here. https://quant.stackexchange.com/questions/34333/what-makes-a-realized-vol-estimate-tradeable
However, the only presentation I could find on the web ... |
`f` should be the forward rate. I have no idea where this line comes from?
```python
f = alp*np.exp((0.02 - q)*tau)
```
It seems like that `alp` is playing the role of the spot price. You should take `spot` as an input and define
```python
f = spot*np.exp((0.02 - q)*tau)
```
|
If I measure daily returns by simple percent change, a -50% day then a +50% day (or vice versa) results in a true -25% total change, but the average makes it look like you would expect a total 0% change.
Is there a way to measure returns differently that eliminates this effect? For context I have two series of retur... |
How can I measure returns such that the average is useful? |
What does not work with the geometric mean?
$${\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}}$$
which is equivalent to the arithmetic mean in logscale (see [Wikipedia](https://en.wikipedia.org/wiki/Geometric_mean)):
$${\displaystyle \exp {\left({{\frac {1... |
If I have well understood, in the trinomial model we have a kind of risk neutral pricing formula that depends on a parameter. This means thaht as in the binomial model, we could use directly this formula to obtain the price of an option (European type) if there was not this dependency on a parameter. So the problem is ... |
What does not work with the geometric mean?
$${\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}}$$
which is equivalent to the arithmetic mean in logscale (see [Wikipedia](https://en.wikipedia.org/wiki/Geometric_mean)):
$${\displaystyle \exp {\left({{\frac {1... |
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am misunderstanding something at a fundamental level so I apologize in advance.
My main question is how to actually perform a "no... |
How can I estimate value-at-risk of a long/short portfolio without making simplifying assumptions? |
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am misunderstanding something at a fundamental level so I apologize in advance.
My main question is how to actually perform a "no... |
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am misunderstanding something at a fundamental level so I apologize in advance.
My main question is how to actually perform a "no... |
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am misunderstanding something at a fundamental level so I apologize in advance.
My main question is how to actually perform a "no... |
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am misunderstanding something at a fundamental level so I apologize in advance.
My main question is how to actually perform a "no... |
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am misunderstanding something at a fundamental level so I apologize in advance.
My main question is how to actually perform a "no... |
I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am misunderstanding something at a fundamental level so I apologize in advance.
My main question is how to actually perform a "no... |
Am reading a book (*The Complete Practitioner's Guide to the Bond Market* by Steven Dym, 2009) where the author gives an example of someone buying a 5 year par 4.65% treasury and someone else entering an 5 year interest rate swap agreeing to receive 5.75%. The treasury yield moves down .15% to 4.5% The swap spread on... |
Here are some resources that I found useful when learning about this subject, in which I'm very interested. (Some may be more general ESG than just just climate.)
* [Citigroup. Environmental and Social Policy Framework (March 2021)][1]
* [UBS. Suni Harford. Investing in an ESG world - A practitioner’s guide (202... |
High, I am working on an exercise which involves performing a regression analysis to predict market direction (e.g. up or down). I am using daily OHLCV data. I've created various factors from the price data so I can run my regression. One of the factors is `high - low`. However, a similar factor can be `high/low`. Of c... |
# Short version
If you're trying to produce an asset allocation system, it feels pretty natural to split it into an estimation component that forecasts asset means and covariance, and a weighting component that uses those estimates to optimize some metric like maximizing the Sharpe ratio or minimizing the volatility... |
I am using the BA II Plus Texas Instruments calculator.
When I want to calculate an EAR for example, my calculation would be as follows:
(1 + r/m )^m -1 = EAR
So in my calculator, using 5 decimal places I press:
```
1 + ( .03 / 365 ) =
```
This give me the answer:
```
1.00008
```
Then without pressin... |
When using exponents the BA II Plus is returning incorrect answers, what am I doing wrong? |
Follow is the SABR function part of my code in python：
```python
def SABR_func( K, alp, bet, rho, nu ):
"SABR"
f = mV0*np.exp((0.02 - q)*tau)
z = nu/alp*(f * K)**(0.5*(1 - bet)) * np.log(f / K)
xz = np.log((np.sqrt(1 - 2*rho*z + z*z) + z - rho) / (1 - rho))
zdivxz = z / xz
zdivxz[np.isna... |
Reading a paper by Black and Litterman, I'm having trouble understanding the set of valid allocations in which we're trying to optimize expected returns.
In Table III, the authors show two portfolios that are supposed to be optimal (for different shorting constraints). But not only none of the given portfolios sum t... |
For mean-variance portfolio optimization, shouldn't all the allocations sum to 1? |
I've been trying to make sense of how the FX forward market works.
Let's say today is June 13, 2022. And we have the next market info as seen in Bloomberg for the FX cross between USDMXN, assuming mid values for simplicity.
| T| Dates| Fwd
|:---- |:------:| -----:|
| ON| june 14| 20.4579|
| TN| june 15| 20.4609... |
Both [the short course material coded by the CVXPY developers][1] and [an answer on Quant SE][2] suggest that given a desired risk budget $b$, we can find the full-investment portfolio with weights $w$ that has the risk budget (as defined in those materials) equal to $b$ by performing the following convex optimization:... |
Both [the short course material coded by the CVXPY developers][1] and [an answer on Quant SE][2] suggest that given a desired risk budget $b$, we can find the full-investment portfolio with weights $w$ that has the risk budget (as defined in those materials) equal to $b$ by performing the following convex optimization:... |
Reading a paper by Black and Litterman, I'm having trouble understanding the set of valid allocations in which we're trying to optimize expected returns.
In Table III, the authors show two portfolios that are supposed to be optimal (for different shorting constraints). But not only none of the given portfolios sum t... |
What does not work with the geometric mean?
The geometric mean is computed with the following formula: $${\displaystyle \left(\prod _{i=1}^{n}x_{i}\right)^{\frac {1}{n}}={\sqrt[{n}]{x_{1}x_{2}\cdots x_{n}}}}$$
which is equivalent to the arithmetic mean in logscale (see [Wikipedia](https://en.wikipedia.org/wiki/G... |
I'm currently reading a [paper](https://www.scirp.org/journal/paperinformation.aspx?paperid=82927) (*The Optimal Stopping Time for Selling an Asset When It Is Uncertain Whether the Price Process Is Increasing or Decreasing*, American Journal of Operations Research, March 2018)
about an optimal stopping time problem. M... |
at the risk of boring you with another behavioral finance question, i found a bunch of papers on a phenomenon dubbed correlation neglect, where economic agents misperceive the correlation structure of stochastically dependent gambles. Relevant papers in this area are written by Weizsäcker and Ester in 2016 among others... |
How to incorporate "correlation neglect" in a M-V-Framework? |
I'm currently reading a [paper](https://www.scirp.org/journal/paperinformation.aspx?paperid=82927) (*The Optimal Stopping Time for Selling an Asset When It Is Uncertain Whether the Price Process Is Increasing or Decreasing*, American Journal of Operations Research, March 2018)
about an optimal stopping time problem.
... |
In most mean-variance frameworks I have seen, once we clear markets in the model, it determines asset prices (and returns). However, all of these frameworks assume that the correlation matrix of the underlying assets is given exogenously. Is there any mean-variance type model with an endogenous correlation matrix? I.e.... |
Both [the short course material coded by the CVXPY developers][1] and [an answer on Quant SE][2] suggest that given a desired risk budget $b$, we can find the full-investment portfolio with weights $w$ that has the risk budget (as defined in those materials) equal to $b$ by performing the following convex optimization:... |
Market impact as I understand it measure the difference in price between the first share that is bought and the last share that is bought when an buy order of N shares is submitted to the exchange. (Maybe there are other definitions but let's just take that one).
If we take that definition, it seems to me that mark... |
Computing market impact from the order book? |
In posts regarding the $\mathbb{P}$ vs $\mathbb{Q}$ debate (see [1], [2], [3] or [4]), most answers conclude that historical-based forecast are better suited than risk-neutral models for financial predictions.
However, this conclusion seems to be based on sentimental beliefs. In fact, empirical analyses comparing h... |
I'm trying to regress earnings surprises on variable x. However, absolute earnings surprises are mostly influenced by company total earnings and the number of shares outstanding. So I can't just use this in the regression. Relative surprise also doesn't work as the sign of relative surprises does not really say anythin... |
It's mostly OK for larger, more established companies, but see here:
For 'DOCN' why do they have only 1 year?
[![enter image description here][1]][1]
vs Yahoo has 5:
[![enter image description here][2]][2]
I don't believe this is because of the free tier. That's just what they have available. You'll ne... |
I see that there is much literature that uses the correlation notion in the equity returns to construct a graph or look into how they are related to one another. If we want to extend this to Credit default swap (CDS) spreads, how can we interpret this correlation? What does this mean in this context? and why is it impo... |
How significant is impact on dv01 of an at-the-money swap if rates move significantly?
For example: lets say a 5Y USD at the money swap has 4.6 duration. now, if the rate curve move by 150-200bps, what will be the new dv01? Is there a heuristic rule to estimate this?
thanks
|
For a specific coupon, if TBA TOAS is greater than a Specs TOAS, does that imply that the Specs are trading too rich to TBAs (given liquidity risk, payup risk, etc)? I realize relative value comparisons in Specs are usually done against Specs, but am trying to understand what this could mean. Could there be another exp... |
For a European Call option, by proposing the inital price of the underlying asset I am sure to be able to meet my commitments, however this result is not true for a Put option. However, by proposing the strike as a the initial price then I meet my commutments. I would like to know if there is more general results conce... |
Ok so this is bit of a half-answer but perhaps you can find some use in it. I've done some work on earnings surprises so I'll recap common ways to define it.
The first way to look at earnings surprises is by taking a $[-1,+1]$ day window centered around the earnings announcement date. Your feature will then be the e... |
Ok so this is bit of a half-answer but perhaps you can find some use in it. I've done some work on earnings surprises so I'll recap common ways to define it.
The first way to look at earnings surprises is by taking a $[-1,+1]$ day window centered around the earnings announcement date. Your feature will then be the e... |
I'm definitely a fixed income tourist but I'm wondering if there's an easy way to back of the envelope approximate dollar PnL of an interest rate swap
For example, if I'm long 1m fixed 5y USD swap at 3% and tomorrow the quote rises 5bps to 3.05%, assuming I know the carry X bps and rolldown Y bps, what is my dollar ... |
I'm definitely a fixed income tourist but I'm wondering if there's an easy way to back of the envelope approximate dollar PnL of an interest rate swap
For example, if I enter a $1m fixed 5y USD swap at 3% and tomorrow the quote rises 5bps to 3.05%, assuming I know the carry X bps and rolldown Y bps, what is my dolla... |
I am working on each trade day's forward prices of gasoline. I noticed that the autocorrelation at lag 6 is significantly negative. I know how to interpret negative autocorrelation in a statistical way, but how can I interpret it in an economic way? On term structure, the forward prices of gasoline should go up or go d... |
To a very (!) first approximation, the duration of a swap equals the negative of its time to maturity ($\Delta \approx -T$), the gamma equals that squared ($\Gamma \approx T^2$):
Starting from a generic swap valuation formula
$$
\begin{align}
PV&=s\sum_i\delta_{t_i}^{fix}D(t_i)-\sum_i\delta_{t_i}^{float}F(t_{i-1}\... |
I am a quantitative finance student, and during the first year of this Master’s Degree I couldn’t help but notice that there’s a lot of focus on derivatives pricing and little or none on stock pricing.
Shouldn’t stock pricing be important, for example to help determine a fair value? |
Why is there a lot of focus on derivatives pricing and much less on stock pricing? |
Ok so this is bit of a half-answer but perhaps you can find some use in it. I've done some work on earnings surprises so I'll recap common ways to define it.
The first way to look at earnings surprises is by taking a $[-1,+1]$ day window centered around the earnings announcement date. Your feature will then be the e... |
To a very (!) first approximation, the duration of a swap equals the negative of its time to maturity ($\Delta \approx -T$), the gamma equals that squared ($\Gamma \approx T^2$):
Starting from a generic swap valuation formula
$$
\begin{align}
PV&=s\sum_i\delta_{t_i}^{fix}D(t_i)-\sum_i\delta_{t_i}^{float}F(t_{i-1}\... |
In the IR swaption market, we have 24Expire*10Tenor instruments(like a 24*10 Matrix).
Now I have the Vega number for each instrument, and I want to reduce the matrix size with the same total vega risk.
Matrix A(24*10) to Matrix B(7*8), constrain by sum(A)=sum(B)
Any hint for this problem? What method should I thin... |
For a European Call option, by proposing the initial price of the underlying asset I am sure to be able to meet my commitments, however this result is not true for a Put option. However, by proposing the strike as a the initial price then I meet my commitments. I would like to know if there is more general results conc... |
I'm confused as to why Eurodollar futures prices settle to $100-LIBOR$ at expiration. If at the time of settlement the futures contract was meant to represent a 1,000,000 Eurodollar deposit to mature 3 months in the future, then wouldn't we discount the 1,000,000 back to today to get the settlement price. This would me... |
Why are Eurodollar futures settled to 100 minus LIBOR? Is this actually connected to a Eurodollar depsoit? |
There are couple triggers in a structured finance deal . like when pool balance fall blow to a certian ration ( or bond balance fall below to a certain ratio agaist original issuance balance.
But what actually happen when a deal get `called` ?
Does the SPV use cash in account to buy the oustanding bond from inve... |
What is "Call a Deal" in structured finance space? |
To properly backtest long/short strategy one must have data on what the short loan fees were/are. Is there any decent data source for that?
|
To a very (!) first approximation, the delta of a swap equals the negative of its time to maturity ($\Delta \approx -T$), the gamma equals that squared ($\Gamma \approx T^2$):
Starting from a generic swap valuation formula
$$
\begin{align}
PV&=s\sum_i\delta_{t_i}^{fix}D(t_i)-\sum_i\delta_{t_i}^{float}F(t_{i-1}\to ... |
How significant is impact on dv01 of an at-the-money swap if rates move significantly?
For example: lets say a 5Y USD at the money swap has 4.6 duration. now, if the rate curve move by 150-200bps, what will be the new dv01? Is there a heuristic rule to estimate this?
thanks
|
Let's say there is a put option but the premium is paid at exercise.
This means the strike must be seen as the strike + premium.
How would you go about solving this? |
Consider a payoff that pays a certain amount N of a vanilla Call (underlying: S, Maturity= T, strike:K). Every semester date Ts before T, if S>K(Ts), then N is increased by 1.
This product seems time-dependant (the amount of C(T,K) paid dépends on paths that S will take, and doesn’t look to be depending on forward v... |
1. I would like to know What Px_volume data tells us which we extract from Bloomberg?
2. If I want Number of Shares traded of a particular stock then what term I'll use in Bloomberg?
3. When I match the Px_volume data of a particular stock with data which is there on Bombay Stock Exchange website then it is not matc... |
This might sound really naive but I am really confused by this beta hedging idea.
So it seems the standard way to do it is to run a simple OLS on returns (say asset A and B only 2 assets in the portfolio). And then you will have a formula rtn_a = beta * rtn_b + e, which means if B goes up by 1% tomorrow, A will go ... |
Most derivations of the Black-Scholes formula end up with the following dynamics of some (hedged) portfolio:
$$
\int_{t=0}^{T} \left(\frac{\partial f}{\partial \tau}(S(t),t)+\frac{1}{2}\cdot\frac{\partial^2 f}{\partial x^2}(S(t),t)\cdot\sigma^2\cdot S(t)^2\right) \,dt
$$
The process is still **random** because ... |
I am looking for examples for the number of significant digits commonly required to find numerically the price different types of derivatives.
For instance, if we have to price an American put option, what is the confidence interval and numerical accuracy required in the industry?
The only relevant question I ... |
I saw that for one CRSP Permco, there could be multiple CRSP Permnos. Could anybody provide guidance on how to aggregate the market capitalization, returns, etc... by permco and date?
Kind regards,
Guyon |
I saw that for one CRSP Permco, there could be multiple CRSP Permnos. Could anybody provide guidance on how to aggregate the market capitalization, returns, etc... by permco and date? I am currently summing the market capitalization by permco and date, and then I keep the permno with the largest market capitalization. ... |
I saw that for one CRSP Permco, there could be multiple CRSP Permnos. Could anybody provide guidance on how to aggregate the market capitalization, returns, etc... by permco and date? I am currently summing the market capitalization by permco and date, and then I keep the permno with the largest market capitalization. ... |
I would not let the chosen model depend on the payoff function.
For instance, consider a financial derivative where the underlying asset is a perfectly deterministic function of time. Then, your payoff function is also deterministic. So why model this underlying asset with a stochastic process?
The preferred mode... |
I saw that for one CRSP Permco, there could be multiple CRSP Permnos. Could anybody provide guidance on how to aggregate the market capitalization, returns, etc... by permco and date? I am currently summing the market capitalization by permco and date, and then I keep the permno with the largest market capitalization. ... |
I have been out of the market for quite some time and I see that nowadays discounting is a more complicated discipline.
For collateralized trades I do understand the standard method is to use discounting based on curve associated with the collateral index rate. So if we have EUR cash-flow and collateral in EUR, we w... |
This is a basic question. But I wanted to understand how a TBA short (buying the dollar roll) is economically short an MBS? For example, if an investor believes a specific coupon is rich, they could buy the dollar roll. How would they benefit from that coupons TBA reducing in price? |
Does anyone know where to practice mental math for trader interviews? |
I am trying to understand Barra factor model, so bear with me.
I will describe my current understanding because maybe I am missing something.
We have k factors and some defined formulas to compute exposure of stock i to factor k. Let us call this exposure e_ik.
We also know actual return for each stock r_i.
... |
Why do we need regression in Barra factor model? |
I am interested in global equity 1min/5min/15min/1hour trade-bar data to research micro-market anomalies and trade on them. For that, I need a good historical data vendor, as well as a data vendor that offers live data feeds in order to trade based on the constructed strategies. I found out that Refinitiv has very comp... |
Historical data for quantitative research and trading? |
I'm wondering what's the standard (if any) for practitioners to trade volatility on pegged currencies. Is there any specific convention? I'm thinking situations like EURCHF before the unpeg, how were people trading this via options and how were those options priced?
As for the model to price this, I would imagine so... |
I was wondering how to accurately get the correlation between a variable of percent change and a variable of dollar change or basis points. Should I standardize both variables or will that lose relevant information? I would appreciate any guidance. |
I was wondering how to accurately get the correlation between a variable of percent change return and a variable of dollar change or basis points. Should I standardize both variables or will that lose relevant information? I would appreciate any guidance. |
You are looking at a particular stock ticker and its options. You can go long or short on any quantity of the following instruments:
- Each share is priced at \$10.
- A call on the stock with strike price at \$15 is priced at \$2.
- A put on the stock with strike price at \$15 is priced at \$6.
Is there an a... |
How do I extract the arbitrage? |
You are looking at a particular stock ticker and its options. You can go long or short on any quantity of the following instruments:
- Each unit of stock is priced at \$10.
- A call on the stock with strike price at \$15 is priced at \$2.
- A put on the stock with strike price at \$15 is priced at \$6.
Is th... |
Hi I'm currently backtesting an event-driven strategies. Unlike factor strategy which has a regular rebalancing interval, event-driven strategy is conducted whenever there is an event.
Since we do not know how many signals would pop up in the future in the past timepoint, I defined unit position size per one in-out be... |
How to backtest a strategy with irregular in-out signal? |
I was wondering whether there exist product to hedge against specific building materials? Up to now I have not yet found a suitable product to hedge against cement or glass?
If not, how would one hedge against the price increases of these products? I do not believe that there exist products to hedge against price of... |
Do products exist to hedge against specific building materials? |
I was trying to build the implied volatility curve from SP500 options.
In order to adjust the liquidity issue, I used put-call parity to generate the call price from the OTM Put price.(plot 1)
But when I plot the implied volatility curve, there is a "cliff" in the middle.(plot 2)
I think the volatility should be... |
Let's take a look at the standard CAPM:
$$
r_{i} -r_F = \alpha+\beta(r_{MKT}-r_F) + \varepsilon
$$
I would like to consider the alternative formulation:
$$
r_{i} = \alpha+\beta(r_{MKT}-r_F) + \varepsilon
$$
here the return of the asset $i$ is not corrected for the risk free rate. Is there any literature that re... |
I have estimated the term premium for the Polish Government Bonds (POLGBs) using the methods described by [Adrian et al. (2013)][1] (often referred to as ACM). The underlying yields are interpolated from the Nelson-Siegel-Svensson model based on a bootstrapped zero-coupon yield curve.
I have estimated the model for ... |
I have estimated the term premium for the Polish Government Bonds (POLGBs) using the methods described by [Adrian et al. (2013)][1] (often referred to as ACM). The underlying yields are interpolated from the Nelson-Siegel-Svensson model based on a bootstrapped zero-coupon yield curve.
I have estimated the model for ... |
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