instruction stringlengths 15 26.1k |
|---|
So I've been studying the paper ["Learning To Trade via Direct Reinforcement" Moody and Saffell (2001)][1] which describes in detail how to use exponential moving estimates (EMAs) of returns at time t (`r_t`) to approximate both the Sharpe and Sortino ratios for a portfolio or security.
Note: in the paper he refers... |
I'm a retail trader not a pro and my experience is with equity options not futures so take this with a grain of salt.
You have the right idea to defend when the underlying's price touches a strike price but I would adjust before that, even long before that if these are wide strangles.
With equities, you can delta... |
So I've been studying the paper ["Learning To Trade via Direct Reinforcement" Moody and Saffell (2001)][1] which describes in detail how to use exponential moving estimates (EMAs) of returns at time t (`r_t`) to approximate both the Sharpe and Sortino ratios for a portfolio or security.
Note: in the paper he refers... |
So I've been studying the paper ["Learning To Trade via Direct Reinforcement" Moody and Saffell (2001)][1] which describes in detail how to use exponential moving estimates (EMAs) of returns at time t (`r_t`) to approximate both the Sharpe and Sortino ratios for a portfolio or security.
Note: in the paper he refers... |
I'm not a pro and my experience is with equity options not futures so take this with a grain of salt.
You have the right idea to defend when the underlying's price touches a strike price. However, I would adjust before that, even long before that if these are wide strangles.
With equities, you can delta neutral... |
I can calculate the fair price of a European Option using `Quantlib` as below -
import QuantLib as ql
maturity_date = ql.Date(15, 1, 2016)
spot_price = 127.62
strike_price = 130
volatility = 0.20
dividend_rate = 0.0163
option_type = ql.Option.Call
risk_free_rate = 0.00... |
I've a very basic question:
Assume, as time $t_0$, I started a algorithmic trading strategy with initial capital $X_0$. My strategy on subsequent $N$ time frames generated returns $r(t_1), r(t_2),..r(t_N)$. Now at time step $t_{N+1}$, I added an additional $X_{N+1}$ capital to my algorithm for trading and also incre... |
So I've been studying the paper ["Learning To Trade via Direct Reinforcement" Moody and Saffell (2001)][1] which describes in detail how to use exponential moving estimates (EMAs) of returns at time t (`r_t`) to approximate both the Sharpe and Sortino ratios for a portfolio or security.
Note: in the paper he refers... |
I heard that VWAP slippage (relative difference between the VWAP and the initial mid-price, $\varepsilon \ . \ \frac{P_{VWAP}-P_{arrival}}{P_{arrival}}$ with $\varepsilon = +1 \ or \ -1 $ the trade sign) could be modelled as a function of volume, spread and volatility. Have you ever had experience for that?
Thank yo... |
I know the basics about options greeks, but I heard traders extrapolating the concept to portfolios composed not just of options.
For instance, providing liquidity on [Uniswap](http://uniswap.exchange/), an automated market maker (AMM) built on top of the Ethereum blockchain, is said to have [negative gamma](https:/... |
What does {positive,negative} gamma mean? |
This a reference request for any python notebooks, packages or blogs that teach how to do mean-variance asset allocation using multivariate copulas. How can copula portfolio optimization actually be implemented in code rather than in theory? |
How to implement copula portfolio optimization? |
Is there any other impact of securities litigation on firms other than the direct cost of litigation and damages? |
First of all you need to understand how to model **Implementation Shortfall** (IS), i.e. the difference between your average price between $t_0$ and $T$ and the price at $t_0$.
They are a lot of references to do this, just cite these two ones:
* [Market Impacts and the Life Cycle of Investors Orders][1], by Bacry, ... |
There is more than one way to approach this. Given your comment that this is a small strategy in a larger account, I assume that you are testing it and, if it bears enough fruit, you may want to scale it up. You should assume some starting value. I'm going to assume a number that's equal to your initial nominal value... |
> The instability and high sensitivity of optimisation results can be augmented by adding another layer of quantitative methodology in the form of Monte Carlo Simulation. The name Monte Carlo alludes to the nature of the simulation procedure, which, in essence, involves drawing random numbers from a distribution, and t... |
Why is this investment strategy negative gamma? |
What are the *exact* components of VXN -- the [volatility index for NASDAQ-100](http://www.cboe.com/index/dashboard/vxn#vxn-overview)?
The CBOE page links to the document for VIX, which clarifies the exact set of front-month near-the-money SPX options used for VIX calculation and how weights are assigned (basically ... |
What are the components of VXN? |
Recently I found myself reading more about Monte Carlo approach in m.v. portfolio optimization framework.
I already discuss the topic on this forum (if interested please consider the following links - [Monte Carlo (resampling) in m.v. portfolio optimization
][1], [Quasi Random Monte Carlo in m.v. portfolio optimiz... |
I have a number of individual securities that each have a Net Asset Value time-series. For example:
NAV1 NAV2 NAV3
30/10/2014 100.00 100.00 100.00
31/10/2014 100.09 100.34 99.20
03/11/2014 100.98 99.96 98.55
04/11/2014 100.76 100.94 99.55
05/11/2014 99.99 100.04 ... |
I'm reading Option Volatility and Pricing by Sheldon Natenberg who in the chapter on Risk Management is trying to explain the effect of interest rates on options.
He says
> The value of a stock option will also depend on whether the trader has a long or short stock position. If a trader's option also includes a shor... |
How do short stock positions lower the value of calls and raise the value of puts? |
We know how to calculate the theoretical forward price of a stock. But what is the theoretical forward price of a futures contract? |
What is the forward price of a futures contract? |
Recently I found myself reading more about Monte Carlo approach in m.v. portfolio optimization framework.
I already discuss the topic on this forum (if interested please consider the following links - [Monte Carlo (resampling) in m.v. portfolio optimization
][1], [Quasi Random Monte Carlo in m.v. portfolio optimiz... |
How to compute yield from the price for a sonia bond. Example XS 1848770407 issued by ecB maturity 29th June 2023. semi annual cpn. Floating base SONIA compound +35 Bp. Traded price on 21st Aug 2020 100.3961 - Yield computed is 0.0907%. can some one pls help me to solve this ? |
This a reference request for any python notebooks, packages or blogs that teach how to do asset allocation using multivariate copulas. How can copula portfolio optimization actually be implemented in code rather than in theory? |
I know the basics about options greeks, but I heard traders extrapolating the concept to portfolios composed not just of options.
Providing liquidity on [Uniswap](http://uniswap.exchange/), an automated market maker (AMM) built on top of the Ethereum blockchain, is said to have [negative gamma](https://twitter.com/t... |
The short answer? In the absence of a dividend, call premium exceeds put premium by the carry cost (look at the explanation of conversions and reversals).
If you're short the stock, your receive interest on the proceeds. However, you pay a borrow cost to the lender of the stock, thereby "reducing the interest rate ... |
I'm looking for books/research papers that would have information on systematic strategies used in the Credit Securitized products space (specifically RMBS, CLO, etc.), if there are any? I've been looking for a while but haven't been able to find anything so far. Given the number of factors that go into these products,... |
If you look at the original paper of Roll (1984), he explains that part of the transaction costs borne out by investors would be the bid-ask spread and that it was "fraught with measurement problems" and that trading mostly occurred within the quoted spread anyways.
So, I would have a trivia questions on this:
1. D... |
What would be the point of Roll (1984) on measuring the effective bid-ask spread? |
I have a few options strategies Id like to back test and I am some familiarity with Python. In particular Id like to backtest a dynamic long vol. strategy putting on $0$ cost backspreads in the direction of the market after a say $5 $% movement within a month.
Any ideas? Packages and so on.
Also feel free do run ... |
I have a few options strategies Id like to back test and I am some familiarity with Python. In particular Id like to backtest a dynamic long vol. strategy putting on $0$ cost backspreads in the direction of the market after a say $5 $% movement within a month.
Any ideas? Packages and so on.
Also feel free do run ... |
How does one calculate the below two-year par yield given the zero rate curve:
Assume the following two-year zero rate curve, with continuous compounding:
2.0% @ 0.5 years, 2.5% @ 1.0 year, 3.0% at 1.5 years, and 3.5% at 2.0 years. What is the two year PAR YIELD?
I know we can use the zero rate curve to derive a t... |
Consoder the following maximization problem $$\max_{\{\tau(\cdot),q(\cdot)\}}\int_{\underline{\theta}}^{\bar{\theta}}\left(\theta q(\theta)-\dfrac{\gamma\sigma^{2}}{2}q^2(\theta)-\tau(\theta)\right)f(\theta)d\theta$$
subject to $$\int_{\underline{\theta}}^{\bar{\theta}}\left(\tau(\theta)-v(\theta)q(\theta)\right)f(\t... |
Consider the following maximization problem $$\max_{\{\tau(\cdot),q(\cdot)\}}\int_{\underline{\theta}}^{\bar{\theta}}\left(\theta q(\theta)-\dfrac{\gamma\sigma^{2}}{2}q^2(\theta)-\tau(\theta)\right)f(\theta)d\theta$$
subject to $$\int_{\underline{\theta}}^{\bar{\theta}}\left(\tau(\theta)-v(\theta)q(\theta)\right)f(\t... |
I know the basics about options greeks, but I heard traders extrapolating the concept to portfolios composed not just of options.
Providing liquidity on [Uniswap](http://uniswap.exchange/), an automated market maker (AMM) built on top of the Ethereum blockchain, is said to have [negative gamma](https://twitter.com/t... |
How does one calculate the below two-year par yield given the zero rate curve:
Assume the following two-year **zero rate curve**, with continuous compounding:
2.0% @ 0.5 year
2.5% @ 1.0 year
3.0% @ 1.5 years
3.5% @ 2.0 years
What is the two year **par yield**?
I know we can use the zero rate curve to d... |
How to compute par yield from zero rate curve? |
I have a number of individual securities that each have a Net Asset Value (NAV) time-series. For example:
NAV1 NAV2 NAV3
30/10/2014 100.00 100.00 100.00
31/10/2014 100.09 100.34 99.20
03/11/2014 100.98 99.96 98.55
04/11/2014 100.76 100.94 99.55
05/11/2014 99.99 10... |
Any books on systematic investing in credit securitized products (RMBS, CLO)? |
As per the Wikipedia, the `SABR` model looks like below -
$dF_t = \sigma_t \left(F_t\right)^{\beta} dW_t$
$d \sigma_t = \alpha \sigma_t d Z_t$
I have 3 questions -
1) Let us assume that we know all the parameters. Then what does it mean when we are told that, estimate the Black volatility using `SABR`? T... |
May I request for research paper recommendations, if any, on existing models that study how the presence of ETFs affect equilibrium prices of the underlying assets?
I am exploring a project on a similar topic, but I would like to better understand current literature to refine the model I'm using.
The framework ... |
I'm building a machine learning model with the aim of learning a daily strategy of buy or sell the stock.
I was wondering if I should use adjusted close price or something else to calculate returns (I was thinking about considering open price/close price the day before) and to evaluate the strategy. I know that adju... |
What kind of returns shuld I use for my model? |
May I request for research paper recommendations, if any, on existing models that study how the presence of ETFs affect equilibrium prices of the underlying assets?
I am exploring a project on a similar topic, but I would like to better understand current literature to refine the model I'm using.
The framework ... |
There are a few papers out there.
A good starting point os the (always relevant) Grossman and Stiglitz (1980) "[On the Impossibility of Informationally Efficient Markets][1]" which shows that markets cannot be perfectly efficient without analysts being rewarded for their efforts (and is mentioned by many of the foll... |
We have two LIBOR contracts:
contract 1 pays $L\left(T_{1},\:T_{2}\right)-K$ at time $T_{1}$
contract 2 pays $L\left(T_{1},\:T_{2}\right)-K$ at time $T_{2}$.
Now, $F_{1}$ is the par strike such that if $K=F_{1}$ then contract one has 0 value at today $t$
$F_{2}$ is the par strike such that if $K=F_{2}$ th... |
Usually the the difference between your average price between $t_0$ and $T$ and the price at $t_0$ is called the **Implementation Shortfall** (IS).
They are a lot of references to do this, just cite these two ones:
* [Market Impacts and the Life Cycle of Investors Orders][1], by Bacry, Iuga, Lasnier and L
* [Mode... |
I have a few options strategies Id like to backtest and I am some familiarity with Python. In particular Id like to backtest a "semi-dynamic" long vol. strategy putting on $0$ cost backspreads in the direction of the market after a say $5 $% movement within a month.
Any ideas? Packages and so on.
Also feel free d... |
I have a portofolio with 30 indexes and I want to calculate the annulised returns and volatility because I want to compare it with another portofolio with different number of indexes (but same time period)
My data are time series with 3 month frequency from 2009-12-31 to 2020-3-31.
I know that the general formula i... |
Since electricity prices involve strong seasonality, jump components as well as negative prices and can not be modelled by the GBM, what models/distributions exist, which would allow for modelling these processes. If I remember correctly the Variance-Gamma Process allows for negative prices? |
I'm looking at the chapter, "The Greek Letters" in Hull's book (Options and derivatives...) and in particular the paragraph "Dynamic Aspects of Delta Hedging". He demonstrates two examples of how dynamic hedging works (within the Black-Scholes framework), for a **short position on a European call option** with expiry 2... |
I have a few options strategies Id like to backtest and I have some familiarity with Python. In particular Id like to backtest a "semi-dynamic" long vol. strategy putting on $0$ cost backspreads in the direction of the market after a say $5 $% movement within a month.
A backspread is a option combo where one sells a... |
I have a few options strategies Id like to backtest and I have some familiarity with Python. In particular Id like to backtest a "semi-dynamic" long vol. strategy putting on $0$ cost backspreads in the direction of the market after a say $5 $% movement within a month.
A backspread is an option combo where one sells ... |
Recently I came across the VVIX index (also known as VIX of VIX), which represents the 30 day implied (expected) Volatility of the VIX Index. I studied CBOE's Whitepaper for the VIX, which explains the methodology used for calculating the VIX and VVIX. While I think to have understood the calculations for the two indic... |
Recently I came across the VVIX index (also known as VIX of VIX), which represents the 30 day implied (expected) Volatility of the VIX Index. I studied CBOE's Whitepaper for the VIX, which explains the methodology used for calculating the VIX and VVIX. While I think to have understood the calculations for the two indic... |
What kind of returns should I use for my model? |
Should a corporation that receives quarterly royalty income, on products sold in different currencies than the one in which royalties are paid, specify the relevant fx rate as the quarterly average or end of quarter rate? Intuitively the monthly average rate has a lower variance so it should be preferred. Am I missing ... |
I often see it quoted that the M2 measure offers an advantage over the sharpe, as sharpe is 'difficult to interpret' for negative returns.
eg: https://en.wikipedia.org/wiki/Modigliani_risk-adjusted_performance#:~:text=The%20M2%20measure%20is,to%20the%20risk%2Dfree%20rate.
However, consider the following returns:
... |
I am wondering why the effective duration of a floating rate note is the time to the next payment. Effective duration is is defined as
$$\frac{V_{-\Delta y}-V_{+\Delta y}}{2V_0\Delta y},$$
for a small $\Delta y$. Why will this value be the time to the next payment for a floating rate note? |
Why is the effective duration of a floating rate bond the time to the next payment? |
I am currently trying to price swaptions under QuantLib/Python using a **volatility cube** using ```ql.SwaptoinVolCube2```. From the documentation:
```
optionTenors = ['1y', '2y', '3y']
swapTenors = [ '5Y', '10Y']
strikeSpreads = [ -0.01, 0.0, 0.01]
volSpreads = [
[0.5, 0.55, 0.6],
[0.5, 0.55, 0.6],
... |
Hi All: I looked in the search icon for questions related to Sharpe Ratio but I couldn't find what I was looking for. My question is about how to calculate it. I will explain the scenario and then ask my 2 part question.
Suppose I have, during some month, M, daily returns $X_i$. So, roughly 20 returns.
I want to ca... |
Hi All: I looked in the search icon for questions related to Sharpe Ratio but I couldn't find what I was looking for. My question is about how to calculate it. I will explain the scenario and then ask my 2 part question.
Suppose I have, during some month, M, daily returns $X_i$. So, roughly 20 returns.
I want to ca... |
The answers to your questions vary -- not because the answers are not precise but because Sharpe ratios are often used for marketing.
**The Correct Estimator of a Sharpe Ratio**
If we are trying to be correct (and not trying to fool ourselves), the expected Sharpe ratio $S_P$ for portfolio $P$ would be simply $E(... |
If I want to estimate Realized Kernel for 1 min bins, is there a way to compute the optimal bandwidth?
In the reference paper: [Realised Kernels in Practice: Trades and Quotes][1] (Olee Barndoff-Nielsen et al.), it provides the following formula for the optimal bandwidth $H^*$:
$$ \hat{H}^* = c^* \hat{\xi}^{4/5} n^... |
If I want to estimate Realized Kernel for 1 min bins, is there a way to compute the optimal bandwidth?
In the reference paper: [Realised Kernels in Practice: Trades and Quotes][1] (Ole Barndoff-Nielsen et al.), it provides the following formula for the optimal bandwidth $H^*$:
$$ \hat{H}^* = c^* \hat{\xi}^{4/5} n^{... |
The answers to your questions vary -- not because the answers are not precise but because Sharpe ratios are often used for marketing.
**The Correct Estimator of a Sharpe Ratio**
If we are trying to be correct (and not trying to fool ourselves), the expected Sharpe ratio $S_P$ for portfolio $P$ would be simply $E(... |
In chinese stock market , every stock's traded volume and amount (price * volume) data was disclosed.
![source from sina finance][1]
Why in us stock market no amount data disclosed?
![source from yahoo finance][2]
There must be such 7 fields as `date`,`open`,`high`,`low`,`close`,`volume`,`amount` for every... |
Why no stock's amount data on us stock market? |
In chinese stock market , every stock's traded volume and amount (price * volume) data was disclosed.
![source from sina finance][1]
Why in us stock market no amount data disclosed?
![source from yahoo finance][2]
There must be such 7 fields as `date`,`open`,`high`,`low`,`close`,`volume`,`amount` for every... |
To compute the price of an American option or a callable instrument in general, at each potential exercise date, one is required to compare its continuation value (discounted risk-neutral expectation of what the option would pay off if it was not exercised) to the relevant exercise value/early redemption price.
By c... |
When I was using Monte Carlo to calculate the gamma of a vanilla call option by finite difference method, I stuck in this weird situation as below.
Consider this,
$$
Gamma = \frac{CallPrice(S_{up}) - 2 * CallPrice(S) + CallPrice(S_{down})}{dS^2}
$$
And we can choose dS small enough such that when
$$
S>K \text... |
When I was using Monte Carlo to calculate the gamma of a vanilla call option by finite difference method, I stuck in this weird situation as below.
Consider this,
$$
Gamma = \frac{CallPrice(S^{up}_{T}) - 2 * CallPrice(S_{T}) + CallPrice(S^{down}_{T})}{dS^2}
$$
And we can choose dS small enough such that when
$... |
When I was using Monte Carlo to calculate the gamma of a vanilla call option by finite difference method, I stuck in this weird situation as below.
Consider this,
$$
Gamma = \frac{CallPrice(S^{up}_{T}) - 2 * CallPrice(S_{T}) + CallPrice(S^{down}_{T})}{dS^2}
$$
And we can choose dS small enough such that when
$... |
Please refer to the approach described in the PRIIP-RTS annex iv p10-13
https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32017R0653&from=en |
Is there a formula for Black and Scholes when we have $\mathbb{E}[max(se^{X}-K,0)]$ for $X$ having any normal distribution? |
Is there a formula for Black and Scholes when we have expected payoff $\mathbb{E}[\max(se^{X}-K,0)]$ for $X$ having any normal distribution? |
If I would want to use a different type of distributions (i.e. to allow for negative prices) f.e. a beta distribution how would I have to start to proceed to apply it f.e. to a SDE of the type of a Geometric Brownian Motion. The classic way would be to apply the log transformation followed by Itos Lemma, but since thi... |
I am looking for methods and papers on forecasting SPX option at-the-money implied volatility or realized volatility within its expiration day. What are some stylized facts and forecasting methods? |
Don't all the variables used have to be of the same order of integration in VAR models ?
In this paper [*Bayesian VAR Forecasts, Survey Information and Structural Change in the Euro Area*][1] Gergely Ganics and Florens Odendah are using $\Delta$loglevel, loglevel and level data as we can see on page 28 (31).
Thank ... |
Why is Banque de France using BVAR with different orders of integration? |
Should a corporation that receives quarterly royalty income, on products sold in different currencies than the one in which royalties are paid, specify the relevant fx rate as the quarterly average or end of quarter rate? Intuitively the monthly average rate has a lower variance so it should be preferred. Am I missing ... |
Hi All: I looked in the search icon for questions related to Sharpe Ratio but I couldn't find what I was looking for. My question is about how to calculate it. I will explain the scenario and then ask my 2 part question.
Suppose I have, during some month, M, daily returns $X_i$. So, roughly 20 returns.
I want to ca... |
Interest rate derivatives indexed on [SOFR][1] use USGS as the fixing calendar, which is defined in the [FpML specs][2] as:
> U.S. Government Securities Business Day (as defined in 2006 ISDA Definitions Section 1.11 and 2000 ISDA Definitions Section 1.11)
Indeed, Section 1.11 of the 2006 ISDA Definitions defines ... |
(I'm not an english native speaker, neither an expert of finance, so for me it's quite hard to express myself in a proper way. If you want to correct me I really appreciate.)
In the graph below you can see an irregular cash flow. The graph is cumulative, on the y axes there are moneys, on the x the dates.
[![ent... |
Which relation stands between IRR and the cumulative profits? |
The answers to your questions vary -- not because the answers are not precise but because Sharpe ratios are often used for marketing.
**The Correct Estimator of a Sharpe Ratio**
If we are trying to be correct (and not trying to fool ourselves), the expected Sharpe ratio $S_P$ for portfolio $P$ would be simply $E(... |
I found on some articles that in order to place a stop loss and a take profit at the same time for a long order, one should buy a market order and sell a stop limit order (with the stop loss value for the stop price and price) in a ddition to sell a limit order (with the take profit value as a limit) but it’s not worki... |
Hi All: I looked in the search icon for questions related to Sharpe Ratio but I couldn't find what I was looking for. My question is about how to calculate it. I will explain the scenario and then ask my 2 part question.
Suppose I have, during some month, M, daily returns $X_i$. So, roughly 20 returns.
I want to ca... |
There is two ways to see it:
* The first one is as noob2 mentionned, do you want to reduce your currency risk exposure? In that case, the rate should be fixed when the royalties are earned (presumably through the month, but typically even before if the amounts can be estimated).
* The second one is if a very theore... |
I'm studying these codes from Mathworks https://www.mathworks.com/help/finance/plotting-sensitivities-of-an-option.html
The output is a 3D image. Is it possible to get a video that shows the creation of the mesh? |
Is there anything infeasible or ethically wrong about optimizing portfolios like this?
$$\min_w \enspace w' \Sigma w - w' C w$$
where $\Sigma$ is the asset return covariance matrix, and $C$ is the asset return correlation matrix. subject to the individual portfolio weights in vector $w$ summing to 1.
It says, ... |
Is there anything infeasible or ethically wrong about optimizing portfolios like this?
$$\min_w \enspace w' \Sigma w + w' C w$$
where $\Sigma$ is the asset return covariance matrix, and $C$ is the asset return correlation matrix. subject to the individual portfolio weights in vector $w$ summing to 1.
It says, ... |
There is nothing wrong mathematically (nor ethically) with this objective function. However, this objective is weird in a couple of ways.
First, there is no weighting on these which implies you prefer to minimize these terms in accordance with their orders of magnitude. As has been pointed out, the correlation term ... |
Typically asset return distributions are bell-shaped with most mass occurring in and around the center, 0% returns, and less so in the tails, with the left tail representing the probability of large losses, and the right tail representing the probability of large gains. Despite the tails being small compared to the cen... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.