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What does the theta curve of an american option look like? |
I am wondering what metric is better at incorporating credit risk, is that OAS or effective yield for the floater coupon bonds? What intuition each of them carries out? When would I use or the other for estimating the volatility? |
We need to offer an estimated return of a non-hold-to-maturity strategy. Essentially, we borrow money from the market and buy a bond. Instead of holding the bond to mauturity and locking in a return equal to YTM, we will sell the bond before maturity. How should we provide an estimated return/quote for such strategy?
... |
Is YTM a relatively accurate reference to measure the return of a non-hold-to-maturity strategy? |
I'm currently reading the paper: Willmot and Ahmad: Which free lunch would you like today, Sir? Delta Heding, volatility arbitrage.
In case 1: They delta hedge with the actual volatility, by going long in the option and shorting delta. There is one part of their derivation of the guarenteed profit that's confusing my ... |
I'm writing my master's thesis about stock price prediction using machine learning methods. During my literature review, I noticed that a lot of research produced on this topic is of poor quality, published in non-finance related journals or unpublished/peer reviewed alltogether. There is no paper to be found in leadin... |
Why are there no papers about stock prediction with machine learning in leading financial journals? |
I think you're overlooking a third explanation:
Nobody that found a successful technique to generate alpha has published it. I can think of the following causes:
1. If you're an academic, why share your brilliant idea?
2. These techniques require a lot of data and financial data can be expensive, researches that... |
Adding to the answer of @Bob Jansen there are some additional *worries* with *complex* machine learning models (eg. Neural Networks of any kind and complex tree-based approaches) that you can encounter, within the setting of volatility forecasting (or forecasting in general).
1. **The mechanisms behind the results c... |
This is a soft, and probably also an opinion based question.
Suppose I am writing a library for numeric linear algebra for the purposes of working with financial data. My goals are:
1. Since I work with big data, I want to make it as fast as possible by using parallel computing.
2. I want my colleagues to use th... |
I'm not sure you're 100% right there. To me, it feels as if academics use machine learning frequently. It's _very_ trendy right now.
**There are very many finance papers using machine learning!**
- One the of the top finance journals is the Review of Financial Studies (RFS). [You find **87 published and peer-r... |
I'm not sure you're 100% right there. To me, it feels as if academics use machine learning frequently. It's _very_ trendy right now.
### There are very many finance papers using machine learning!
- One the of the top finance journals is the Review of Financial Studies (RFS). [You find **87 published and peer-r... |
I'm not sure you're 100% right there. To me, it feels as if academics use machine learning frequently. It's _very_ trendy right now.
### There are very many finance papers using machine learning!
- One the of the top finance journals is the Review of Financial Studies (RFS). [You find **87 published and peer-r... |
I am sure there will be more thorough answers provided by others, but let me have a quick go at the first part: "what is meant by $\int_0^T W_t dW_t$ in finance?".
I like to interpret Ito Integral as the outcome of a gambling strategy. In general, Ito Integral can be written as:
$$I_t:=\int_{h=0}^{h=t}f(Y_h)dX_h... |
I have this bond assigment where I have to calculate the CF each quarter, given a constant EURIBOR3M rate of -0,539%. There is also a 1,6% margin per annum that I have to take into account. The repayment is going to happen 4 times each year. My question is: What is the quarterly yield/rate and the yearly yield/rate?. D... |
I am sure there will be more thorough answers provided by others, but let me have a quick go at the first part: "what is meant by $\int_0^T W_t dW_t$ in finance?".
I like to interpret Ito Integral as the outcome of a **gambling strategy** (which fits in well with the fundamental property of the Integral: i.e. that i... |
Adding to the answer of @Bob Jansen there are some additional *worries* with *complex* machine learning models (eg. Neural Networks of any kind and complex tree-based approaches) that you can encounter, within the setting of volatility forecasting (or forecasting in general).
1. **The mechanisms behind the results c... |
I am of the understanding the true carry of a bond is yield - repo rate. And not simply coupon + repo cost because this doesn’t include pull to par.
Please could someone explain why yield - repo is the real carry? ie why it is equivalent to coupon =
+ financing cost + pull to par?
Secondly, where does the idea ... |
I am of the understanding the true carry of a bond is `yield - repo rate`. And not simply `coupon + repo cost` because this doesn’t include pull to par.
Please could someone explain why `yield - repo rate` is the real carry? ie why it is equivalent to
coupon + financing cost + pull to par ?
Secondly, whe... |
I have come across people calculating parametric VaR who scaled the standard deviations by say square root of 10 to scale up to a 10 day horizon.
Elsewhere I have seen textbooks suggesting that it is the whole VaR figure which should be multiplied by the square root of 10.
Which is correct, and are both equivalent?... |
Is scaling the standard deviations in the VaR formula (parametric) equivalent to scaling the VaR figure at the end? |
I upvote @BobJansen's points; and add one small incremental observation.
Institutional investor scepticism about quant isn't so much scepticism about quant. It's more the fear that quant describes the current regime. Which investors believe (maybe correctly, maybe not) they already understand. Unless quant can tel... |
Adding to the answer of @BobJansen there are some additional *worries* with *complex* machine learning models (eg. Neural Networks of any kind and complex tree-based approaches) that you can encounter, within the setting of volatility forecasting (or forecasting in general).
1. **The mechanisms behind the results ca... |
I upvote @BobJansen's points; and add one small incremental observation.
Institutional investor scepticism about quant isn't so much scepticism about quant. It's more the fear that quant describes the current regime. Which investors believe (maybe correctly, maybe not) they already understand. Unless quant can tel... |
I have been studying the relation between exchange rates and the inflation of the currencies, but I am far from understanding the most relevant factor in driving FX market players from pricing currency pairs. I dowloaded US inflation percentages and data for the price of the USD/CNY currency pair. I have used this data... |
We need to offer an estimated return of a non-hold-to-maturity strategy. Essentially, we borrow money from the market and buy a bond. Instead of holding the bond to mauturity and locking in a return equal to YTM, we will sell the bond before maturity. How should we provide an estimated return/quote for such strategy?
... |
How accurate is YTM as a reference measure of non-holding-to-maturity return? |
We need to offer an estimated return of a non-hold-to-maturity strategy. Essentially, we borrow money from the market and buy a bond. Instead of holding the bond to mauturity and locking in a return equal to YTM, we will sell the bond before maturity. How should we provide an estimated return/quote for such strategy?
... |
We need to offer an estimated return of a non-hold-to-maturity strategy. Essentially, we borrow money from the market and buy a bond. Instead of holding the bond to mauturity and locking in a return equal to YTM, we will sell the bond before maturity. How should we provide an estimated return/quote for such strategy?
... |
I am trying to understand the pricing of barrier options, and have considering the Brownian motion $\mathrm{d}X_t=a\mathrm{d}t+b\mathrm{d}W_t$, $a$ and $b$ constant. I am trying to:
1. derive the distribution of $X_{T/2}$ given $X_T$ and $X_0$; and
2i. prove that the probability $\mathbb{P}\left(\inf_{[t_1,t_2]}X_t<... |
The shadow rate is what the interest rate would be if money did not behave like an option.
The concept was [created by Fischer Black][1] and his insight was that money acts like an option. Someone with a dollar can either (1) buy something today or (2) not spend the dollar and have a dollar tomorrow. When the eco... |
Adding to the answer of @BobJansen there are some additional *worries* with *complex* machine learning models (eg. Neural Networks of any kind and complex tree-based approaches) that you can encounter, **within the setting of volatility forecasting (or forecasting in general)**.
1. **The mechanisms behind the result... |
I am trying to understand the pricing of barrier options, and have considering the Brownian motion $\mathrm{d}X_t=a\mathrm{d}t+b\mathrm{d}W_t$, $a$ and $b$ constant. I am trying to:
1) derive the distribution of $X_{T/2}$ given $X_T$ and $X_0$; and
2i) prove that the probability $\mathbb{P}\left(\inf_{[t_1,t_2]}X_t<... |
I have come across people calculating parametric VaR who scaled the standard deviations by say square root of 10 to scale up to a 10 day horizon.
Elsewhere I have seen textbooks suggesting that it is the whole VaR figure which should be multiplied by the square root of 10.
Which is correct, and are both equivalent?... |
There are a couple of point here. This:
>If we consider VaR = z-score * portfolio variance (assuming >mean is zero)
is not quite right. In a Gaussian model
>(**)
>VaR = z-score * **sqrt**(portfolio variance) = z-score * (standard deviation of the portfolio)
So your math actually works out. And in a Gaus... |
Suppose I have the following problem:
> We have data on three bonds: a one-year zero-coupon bond (bond A), a twoyear zero-coupon bond (bond B), and a three-year bond with an annual coupon equal to 5% of its face value (bond C). All three bonds have face values of 100 USD. The price of bond A is $90, the price of bon... |
How to compute the yield to maturity on a zero-coupon 3 year bond in this case? |
I am trying to understand the pricing of barrier options, and have considering the Brownian motion $\mathrm{d}X_t=a\mathrm{d}t+b\mathrm{d}W_t$, $a$ and $b$ constant. I am trying to:
1) derive the distribution of $X_{T/2}$ given $X_T$ and $X_0$;
2i) prove that the probability $\mathbb{P}\left(\inf_{[t_1,t_2]}X_t<L\Bi... |
I am investigating the suitability of using deep learning for pricing and calibration for the full implied volatility surface. Such examples of their application are in papers [here][1] and [here][2]. During examples, the latter achieved the calibration task in mere milliseconds, which were orders of magnitude faster t... |
There are many ways to short term rates like `Ho-lee` process, `HW` process. However I failed to understand how this information can be used to simulate the process for Overnight rate like `EONIA` etc.
Can you please refer to any online technical papers to simulate such Overnight process? Any software implementation... |
I have around 5 years of data of an index containing many features on a daily basis. I want to classify whether the index will move up or down the next trading day (up or down movement is determined by next day open/close price). I am using an SVM classifier for this classification. What could be some essential steps w... |
I am trying to understand the pricing of barrier options, and am considering the Brownian motion $\mathrm{d}X_t=a\mathrm{d}t+b\mathrm{d}W_t$, $a$ and $b$ constant. I am trying to:
1) derive the distribution of $X_{T/2}$ given $X_T$ and $X_0$;
2i) prove that the probability $\mathbb{P}\left(\inf_{[t_1,t_2]}X_t<L\Big|X... |
the following is causing a bit of confusion...
In some countries, e.g. Brazil, I saw the bonds are quoted in "Unitary prices" (PU).
If we pick an example where:
Unitary price = 10,400 (Market price)
Par value = 1,000
What is the math behind to convert the market price to a "% of par price"? I saw... |
There are many ways to short term rates like `Ho-lee` process, `HW` process. However I failed to understand how this information can be used to simulate the process for Overnight rate like `EONIA` etc.
Can you please refer to any online technical papers to simulate such Overnight process?
Just to explain more, l... |
the following is causing a bit of confusion...
In some countries, e.g. Brazil, I saw the bonds are quoted in "Unitary prices" (PU).
If we pick an example where:
Unitary price = 10,400 (Market price)
Par value = 1,000
What is the math behind to convert the market price to a "% of par price"? I saw... |
I'm testing (out-of-time) my machine learning (ML) based strategy against a strong benchmark. As a performance metric, I'm using a custom rolling metric $M(t)$ which takes into account the portfolio value at time $t$ as well as other variables (inventory, time, etc). Visually, it is clear that the ML strategy is beatin... |
I am experimenting with an implementation of the Black-Scholes valuation for call options, and ran into the following questions:
1. Black-Scholes pricing requires a risk-free interest rate. What is 'best practice', i.e. if I were writing a finance paper, where exactly would I get these rates over different time period... |
I am a student and trader. I was recently interested in f&o trading recently, so I decided to enter with a hedge strategy. I saw the market go in my favour as the clock reached 3:30 and Nifty was at 15582. But when it was 3:31, Nifty50 was at 15557. Can someone please tell me what price will be excercised when the cont... |
Why did Nifty50 close at 15557 when it was at 15582 at 3:30 pm IST? |
I would like to use geometric brownian motion (gbm) in order to generate artificial asset prices. I know that gbm has constant volatility, therefore I somehow converted it to stochastic in a very crude way which result in something different than gbm. Other than gbm, is there any algorithm or method for such purpose?
... |
How can I find the distribution function of the following random variables? |
Let us say I have a Bermudan option which I can terminate at 3 possible dates. When can I expect the discrepancy between a local vol and a stochastic vol model to be highest (assuming both are calibrated to vanillas)?
Intuitively, If the probability of exercise at any point is virtually 1, it is like a call option w... |
When is the effect of skew most potent for an early exercise option? |
So let me begin with why both of these models concern me.
In the first model, the Frequentist Markowitzian model, Ito's method assumes that all parameters are known. No estimators are needed.
That is a big deal because White in 1958 proved that models with $\tilde{w}=Rw+\varepsilon, R>1$ have no solution if $R$ ... |
In the colloquial sense of the word "justified," it is not justified. I will describe why it is justified mathematically and under what circumstances and in what case it is not justified.
Let me begin with the simplest of equations $$\tilde{w}=R\bar{w}+\epsilon,\epsilon\sim\mathcal{N}(0,\sigma^2).$$ Let us assume ... |
I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?
Since as inflation occurs, the face value would also increase which is ultimately returned to you at t... |
This is more a theoretical problem rather than a technical one.
I am looking for a clear definition of corner portfolios and I like to understand more precisely their relation with the mean-variance/minimum variance frontier.
I noticed divergent views while reading about this topic and the related two-funds theor... |
This is more a theoretical problem rather than a technical one.
I am looking for a clear and rigorous definition of corner portfolios and I like to understand more precisely their relation with the mean-variance/minimum variance frontier.
I noticed divergent views while reading about this topic and the related tw... |
This is more a theoretical problem rather than a technical one.
I am looking for a clear and rigorous definition of corner portfolios and I like to understand more precisely their relation with the mean-variance/minimum variance frontier.
I noticed divergent views while reading about this topic and the related tw... |
This is more a theoretical problem rather than a technical one.
I am looking for a clear and rigorous definition of corner portfolios and I like to understand more precisely their relation with the mean-variance/minimum variance frontier.
I noticed divergent views while reading about this topic and the related tw... |
As I understand it, an algorithmic trading strategy could lose profitability, if, for example:
* it's rediscovered by others
* employee turnover leaks the strategy to others
* market conditions change somehow
Is there a typical "half-life" of a strategy? Is it different for HFT vs non-HFT? |
How long do algorithmic trading strategies typically remain profitable? |
*"where does the idea of a bonds carry = forward yield - spot yield tie into all of this?"*
I'd refer to that as rolldown rather than carry. |
Couple of basic questions:
1- I'd like to calculate the implied of VIX options intraday, without access to intraday VIX futures.
In the absence of VIX futures as underlyings, what would be the pitfalls of backing out the underlying forward prices using Calls - Puts + strike, and using these synthetics in my IV cal... |
As I understand that after 2023 the `Libor` will be discontinued and `OI rates` like `SOFR` will replace its place as `RFR`. My question is, that scenario how exactly we would discount the expected future payoff of a contingent claim to the time zero.
So, this question boils down to: How we can construct a Risk free... |
As I understand that after 2023 the `Libor` will be discontinued and `OI rates` like `SOFR` will replace its place as `RFR`. My question is, in that scenario how exactly we would discount the expected future payoff of a contingent claim to the time zero.
So, this question boils down to: How we can construct a Risk f... |
There is question from 2017 [here][1] but the answer given doesn't really go into any detail.
How correlated is volume with price impact? Especially with regard to wash trading; For example, wash trading is extremely prevalent in crypto markets and yet, despite this, one can still a clear correlation between volume ... |
To what degree is volume correlated with price impact? |
I am trying to reproduce the **bid** EUR implied yield I see in the screenshot below for 1y tenor which is -0.6226%.
EUR implied yield bid = spot_bid/fwd_bid *(1+i_USD_bid) - 1
Inputs from BBG terminal:
1y USD yield bid = 0.1962%
1y fwd_bid = 1.204757
spot bid = 1.1949
EUR implied yield bid = 1.... |
I'm trying to code in C++ Rebonato's formula for swaption volatilities
$$ v_{\alpha,\beta}^2=\frac{1}{T_\alpha} \sum_{i,j=\alpha+1}^{\beta} \frac{w_i(0)w_j(0)F_i(0)F_j(0)}{S_{\alpha\beta}^2(0)}\rho_{i,j}\int_{0}^{T_\alpha}\sigma_i(t)\sigma_j(t)dt$$
where the forward rate volatility is a piecewise-constant functio... |
## There are very many finance papers using machine learning
- One the of the top finance journals is the Review of Financial Studies (RFS). [You find **87 published and peer-reviewed papers** if you look up machine learning][1]. You find a lot more recent research (working papers) 'published' by the National Bure... |
I have implemented a very simple limit order book in c++ . 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 |
> Is there a typical "half-life" of a strategy?
This is a really subjective question, and I don't think any singular answer will generalize well. That being said, I will give some examples from personal experience.
I have made hundreds of trading models in my career. I have only deployed 9 into live trading in t... |
> Is there a typical "half-life" of a strategy?
This is a really subjective question, and I don't think any singular answer will generalize well. That being said, I will give some examples from personal experience.
I have made hundreds of trading models in my career. I have only deployed 9 into live trading in t... |
Suppose given implied volatility quotations $\widehat{\sigma}(T_i,K_j)$ of call options on an underlying $S$ for various expiries $T_i$'s and strikes $K_j$'s. I am interested in the following problem : what is the "optimal" method to calculate numerically the familly of densities $(\varphi_{T})_T$ where $\varphi_{T}$ i... |
I am studying the Heston model. I have not had time to read the detailed derivation of the formula to compute option prices. The formula is given according to this thread: https://quant.stackexchange.com/questions/18684/heston-model-option-price-formula
I want to compute the delta of the option priced under Heston m... |
I'm trying to code in C++ Rebonato's formula for swaption volatilities
$$ v_{\alpha,\beta}^2=\frac{1}{T_\alpha} \sum_{i,j=\alpha+1}^{\beta} \frac{w_i(0)w_j(0)F_i(0)F_j(0)}{S_{\alpha\beta}^2(0)}\rho_{i,j}\int_{0}^{T_\alpha}\sigma_i(t)\sigma_j(t)dt$$
where the forward rate volatility is a piecewise-constant functio... |
## EDIT 2021-03-19:
We have now moved to discounting using OIS-SOFR swaps on cleared products and SOFR products in general have picked up in liquidity since last time this question was asked. I'd therefore like to additionally ask (if anyone here is knowledgeable about the exact mechanics of the currently traded US... |
We have now moved to discounting using OIS-SOFR swaps on cleared products and SOFR products in general have picked up in liquidity since last time this question was asked. I'd therefore like to additionally ask (if anyone here is knowledgeable about the exact mechanics of the currently traded USD OIS-SOFR swaps):
**... |
## EDIT 2020-11-17: ##
thank you to @user42108 for the link to OpenGamma conventions PDF in his answer below. The PDF is comprehensive and explains the mechanics of USD OIS Swaps based on **Effective Federal Funds Rate (EFFR)** well, I paste an extract from the PDF here:
*"Federal Fund swaps are a USD particulari... |
## EDIT 2020-11-17: ##
thank you to @user42108 for the link to OpenGamma conventions PDF in his answer below. The PDF is comprehensive and explains the mechanics of USD OIS Swaps based on **Effective Federal Funds Rate (EFFR)** well, I paste an extract from the PDF here:
*"Federal Fund swaps are a USD particulari... |
Hey guys I'm pretty new here, not sure how to code my question so I'll include a picture reference instead. I'm a bit confused on how the standard deviation of F (commodity price) would affect the already existing matrix. Is each vector's standard deviation a combination of both risk and F? How would the covariance mat... |
## Bad news: Your calculation is not quite correct
As you say, the initial price of a European call option is
$$C(S_0;K,T)= S_0e^{-qT}\Pi_1-Ke^{-rT}\Pi_2. \tag{$\star$}$$
However, the exercise probabilities $\Pi_1$ and $\Pi_2$ depend on the stock price $S_0$ too! Thus, you need the product rule and the chain rule to... |
What's the intuition behind there being a perfect linear relationship between option value and expected volatility? |
what does the cover page of Guyon and Labordere's Nonlinear Option Pricing represent? |
I know 3-month Eurodollar future prices and need to convert it to 6-month LIBOR.
I calculated the 3-month LIBOR as : (100 - ED price) / 100
How to continue from here?
Thanks for the help.
Billy
|
How to convert 3-month ED to 6-month LIBOR? |
I know 3-month Eurodollar future prices and need to convert it to 6-month LIBOR.
I calculated the 3-month LIBOR as : (100 - ED price) / 100
How to continue from here?
Thanks for the help.
Edit: I can do the assumption that there's no difference basis between swaps that have 3- or 6-month libor as the floati... |
> I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?
Absolutely. Let's consider two scenarios:
### 1. You are *not* holding the bond to maturity:
In... |
> I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?
Absolutely. Let's consider two scenarios:
### 1. You are *not* holding the bond to maturity:
In... |
Since algorithmic trading strategies often [stop being profitable after a while](https://quant.stackexchange.com/questions/61834/), I wonder if any such formerly profitable strategies have been made public, and if so, where can I find them? |
Formerly profitable algorithmic trading strategies? |
> I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?
Absolutely. Let's consider two scenarios:
### 1. You are *not* holding the bond to maturity:
In... |
> I've recently been learning about TIPS and their role as an inflation protection instrument. If you buy a TIP even when it has a negative real yield-to-maturity, is it still possible to have a profitable position?
Absolutely. Let's consider two scenarios:
### 1. You are *not* holding the bond to maturity:
In... |
There is an active `spread option` traded in ICS as described here - https://www.theice.com/products/28881205/Crude-Future-Brent-1-Month-Calendar-Spread-Options
I am interested to know the `Delta` and `Gamma` profile of such `Calendar spread option` w.r.t. various possible underlying spread values.
Is there any e... |
Is there any method/module/library to directly solve an SDE in python? Especially if it's just geometric brownian motion |
I am working with a Heston model discretization through truncation, given by the following code:
```
(for (i in 1:Nsteps){
X<-log(S)
X<-X+(R-0.5*pmax(V,0))*dt+sqrt(pmax(V,0))*dW1
S<-exp(X)
V<-V+kappa*(theta-pmax(V,0))*dt+sigma*sqrt(pmax(V,0))*dW2
}))
```
I am trying to simulate several paths let's say 10 or ... |
I am in the following continuous time market:
- $S_t^0 = rS_t^0dt$
- $S_t^1 = (\mu - \delta) S_t^1dt + \sigma S_t^1 dB_t$
where $r, \mu, \delta$ and $\sigma$ are constant values in $\mathbb{R}$. $\delta$ is the dividend yield. I want to recover the risk neutral price of a future written on $S^1$ with delivery ... |
Please could someone explain how the greeks (especially the delta) of a multi-underlying autocallable product (i.e. an autocall on a basket) change when the correlation of the underlyings fluctuates?
Thanks |
I am working with a Heston model discretization through truncation, given by the following code:
```
(for (i in 1:Nsteps){
X<-log(S)
X<-X+(R-0.5*pmax(V,0))*dt+sqrt(pmax(V,0))*dW1
S<-exp(X)
V<-V+kappa*(theta-pmax(V,0))*dt+sigma*sqrt(pmax(V,0))*dW2
}))
```
I am trying to simulate several paths let's say 10 or ... |
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