instruction stringlengths 15 26.1k |
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Theoretically, this is a more difficult problem than it looks like at first glance. Unfortunately, existing literature taking into account a proper dividend consideration is rare (at least from a practical viewpoint). There are several options:
1) Use what is called "De-Americanization": In this case, based on your ... |
Consider a model defined by 2 geometric Brownian motions
$$dY_{1}(t) = \sigma_{2} Y_{1}(t)dW_{1}(t)$$
$$dY_{2}(t) = \sigma_{2} Y_{2}(t)dW_{2}(t)$$
with $Y_{1}(0) = y_{1}$, $Y_{2}=y_{2}$ and $dW_{1}(t)dW_{2}(t)=\rho$. By performing a Monte Carlo simulation I want to compute
$$\mathbb{E}[\log(Y_{1}(T))|\log(Y... |
This is a post which serves as a follow-up question to https://quant.stackexchange.com/questions/38514/nature-of-short-vix-strategies. I am trying to understand where the change in value in a synthetic strategy constructed from futures comes from:
- Roll-over;
- Roll yield.
Below I display a simplified framework... |
One bitcoin exchange isn't directly connected to another. So price in bitcoin can vary from one exchange to another. The price differences are not usually huge.
One bitcoin exchange is only weakly connected with another bitcoin exchange. If price in one exchange is higher than price at another, people can buy where... |
How exactly money moves from one forex to another so prices are the same across exchanges? |
I have a binary classification model that predicts BUY (1) and SELL (-1) with an out of sample F1 score of 71% (precision is 65% and recall is 80%). The model's output is a probability of a BUY label occurring, which is then used in a bet sizing formula to bet cash (similar to the kelly criterion). The model was also t... |
To answer your questions in turn:
> What happens to me, the other party, and the futures contract?
Nothing happens to you initially. The other party is the *exchange* - nothing happens to exchange initially. Nothing happens to the contract - it's still valid.
> Do I default on my obligations?
If the contra... |
Define two correlated stock price- and interest rate (Vasicek) processes, governed by the Wiener processes $W^{S}(t)$ and $W^{r}(t)$
$$dS(t)=r(t)S(t)dt+\sigma S(t)dW^{S}(t)$$
$$dr(t)=\kappa(\theta-r(t))dt+\gamma dW^{r}(t)$$
with constant scalars $S_{0}>0$, $T>0$, $r_{0}>0$, $\sigma>0$, $\theta>0$, $\gamma>0$, ... |
In order to create a synthetic FRA position of 30-day FRA on 90-day LIBOR, the diagram below shows that we can enter into positions by going long a 120-day Eurodollar contract and short a 30-day Eurodollar contract.
Here is a section from Basic of Derivative Pricing and Valuation, Reading 57, a part of CFA curriculum ... |
Yesterday and today, some kinds of oil have been traded for negative prices.
Does it mean that I can take oil from seller and at the same time I get money? Or is the negative price connected only with derivatives and not physical delivery? |
In portfolio management, it is assumed that the assets and the weights in the portfolio are static and do not change in time. By the help of this static structure of the portfolio, we can talk about the standard deviations and returns of the portfolio in order to quantify risk and return. Am I correct?
If so, I have... |
How can we quantify time varying portfolios? |
A double call option allows the holder to either exercise at time $T_{1}$ or time $T_{2}$, where $T_{2}$>$T_{1}$. With corresponding strike prices $K_{1}$ and $K_{2}$, it can be shown that it is never optimal to exercise at $T_{1}$ if $K_{1}e^{-rT_{1}}>K_{2}e^{-rT_{2}}$. This is shown by the idea that, at $T_{1}$ you h... |
In the Black-Scholes model they consider that the stock follows this stochastic differential equation: $$ dS = \mu S dt + \sigma S\ dW $$
I was wondering, was it common at the time they work on this to use $\log S$ with Itô lemma to solve this kind of equation, or do they discover it ?
Or do they use it because ... |
For some background information, I am a PhD student in econonomics. Although I did not study in finance previously, I took a course on stochastic calculus and a course on asset pricing in incomplete markets at the PhD level. We're mostly talking about option pricing models and their applications (think, GARCH models, s... |
I want to value an **uncollateralized** cross-currency swap to exchange **EURIBOR 6M** for **JIBAR 3M**.
I have a few questions:
1. What discount curves should I use?
2. From which curve should I infer forward rates for each leg?
Thanks for your help.
|
For some background information, I am a PhD student in economics. Although I did not study in finance previously, I took a course on stochastic calculus and a course on asset pricing in incomplete markets at the PhD level. We're mostly talking about option pricing models and their applications (think, GARCH models, sto... |
Hi can a market practitioner explain how par par asset swap work. I understand the swap fixed leg has the same details as the bond ie fixed rate is equal to the bond coupon rate. The way i look at it The notional of the swap is the par value of the bond otherwise fixed payments wouldnt match and the investor wants expo... |
I want to value an **uncollateralized** cross-currency swap to exchange **EURIBOR 6M** for **JIBAR 3M** (Johannesburg Interbank Average Rate).
I have a few questions:
1. What discount curves should I use?
2. From which curve should I infer forward rates for each leg?
Thanks for your help.
|
I'm looking for a proxy (or some rule of thumb) that can create a link between the implied volatility, the realized volatility and the frequency of Delta hedging required to keep the Delta as close as possible to zero.
For example, let me short a straddle: it's likely I will have to Delta hedge it more frequently th... |
$$\text { What is the conditional distribution of } ( X_t = \int_0^t W_s ds) \text{ with respect to } W_t = x ? $$ |
$$\text { The conditional distribution of } ( X_t = \int_0^t W_s ds) \text{ with respect to } W_t = x ? $$ |
What is the conditional distribution of $$X_t = \int_0^t W_s \mathrm{d}s$$with respect to $W_t = x$? |
I just wanted to clarify a few things around implied volatility which I've read in the Hull/Natenberg books, which I find quite confusing.
Both books refer to implied volatility in the context of a European option on a non-dividend paying underlying, and they calibrate the BS 1973 model to observed option prices and... |
I want to buy some stocks and short future contract instead. I wonder whether I can calculate the hedge ratio? |
I 'm trying to get the theta of a Call in the classical Black Scholes model.
We have (classical result with usual notations) :
$$C_t = S_tN(d_1) - Ke^{r(T-t)}N(d_2)$$
When deriving according to time, I get, among others terms, this one :
$$N(d_1)*\partial{S_t}/\partial{t}$$
But I can't find anywhere this ter... |
i am seeing different formulas at different places on stack exchange, so not sure!
eg if denominator has a term y^2/w^2, or y/w^2 or
1/w or -1/w
and also, whatever formula i use, i get a negative denominator for the following (which has no arbitrage), so i wonder why it doesnt work?
T=1,F=100,K1=95,K2=100,VOL1=2... |
what is the formula for local vol , as a function of implied vol, AND why am i getting a negative denominator? |
i am seeing different formulas at different places on stack exchange, so not sure!
eg if denominator has a term y^2/w^2, or y/w^2 or
1/w or -1/w
and also, whatever formula i use, i get a negative denominator for the following (which has no arbitrage), so i wonder why it doesnt work?
T=1,F=100,K1=95,K2=100,VOL1=2... |
Look at this trade:
Sequence Side Quantity @ Price
1. Buy 1000 @ 1000
2. Sell 1000 @ 1250
The calculation of the realized PnL:
**version 1:**
realizedPnL = (1000-1250)*1000 = 25000$
But looking at other PnL-formulas, for example:
- https://www.bitmex.com/ap... |
Look at this trade:
Sequence Side Quantity @ Price
1. Buy 1000 @ 1000
2. Sell 1000 @ 1250
The calculation of the realized PnL:
**version 1:**
realizedPnL = (1000-1250)*1000 = 25000$
But looking at other PnL-formulas, for example:
- https://www.bitmex.com/ap... |
Look at this trade:
Sequence Side Quantity @ Price
1. Buy 1000 @ 1000
2. Sell 1000 @ 1250
The calculation of the realized PnL:
**version 1:**
realizedPnL = (1000-1250)*1000 = 25000$
But looking at other PnL-formulas, for example:
- https://www.bitmex.com/ap... |
Look at this trade:
Sequence Side Quantity @ Price
1. Buy 10 @ 1,0 (with leverage of 50)
2. Sell 10 @ 1,2 (sell with leverage of 30)
Imagine that this trade is a CFD or a forex with USDEUR. I use a leverage of 50 for buy and a leverage of 20 for sell. How should I in... |
I want to value an **uncollateralized** cross-currency swap to exchange **EURIBOR 6M** for **JIBAR 3M** (Johannesburg Interbank Average Rate).
I have a few questions:
1. What discount curves should I use?
2. From which curve should I infer forward rates for each leg?
Thanks for your help.
For the first q... |
I am running a super simple code in Python to price European Call Option via Monte Carlo, and I am surprised at how "bad" the convergence is with 10,000 "simulated paths". Usually, when running a Monte-Carlo for this simple problem in C++ or even VBA, I get better convergence.
I show the code below (the code is tak... |
I'm building a little system for myself that helps me make trade decisions, essentially downloading daily OHLC prices for a few hundred stocks once a day, running various sizes of crossing averages on them and sending me a push notification when something interesting pops up.
Right now, I'm using stock data from Yah... |
How to deal with unreliable data sources? |
Look at this trade:
Sequence Side Quantity @ Price
1. Buy 10 @ 1,0 (with leverage of 50)
2. Sell 10 @ 1,2 (inherits the leverage of 50?)
Imagine that this trade is a CFD or a forex with USDEUR. I use a leverage of 50 for buy. How should I include this leverage within... |
Look at this trade:
Sequence Side Quantity @ Price
1. Buy 10 @ 1,0 (with leverage of 50)
2. Sell 10 @ 1,2 (inherits the leverage of 50?)
Imagine that this trade is a CFD or a forex with USDEUR. I use a leverage of 50 for buy. How should I include this leverage within... |
Let assume 2 parties agree a plain vanilla swap with the following terms:
- Notional: $100,000
- Length/Tenor: 3 year
- Payment/Settlement Periods:
- Annual Start Date: 01/01/2021
- Floating Rate on Start Date: 4% Fixed
- Rate on Start Date: 5%
- Payment Terms: 10 days in arrears
Would the valua... |
In an interest rate swap, is the first payment based on the floating and fixed values set at inception? |
Using zero coupon Treasury curve, I discounted a 10% coupon bond. Using the same curve, I discounted a 5% coupon bond. Both these bonds have the same maturity. Since I discount both these bonds using the same curve, I should get two yields where the difference reflects the coupon effect.
I put in these two yields in... |
i am seeing different formulas at different places on stack exchange, so not sure!
eg if denominator has a term y^2/w^2, or y/w^2 or
1/w or -1/w
and also, whatever formula i use, i get a negative denominator for the following (which has no arbitrage), so i wonder why it doesnt work?
T=1,F=100,K1=95,K2=100,VOL1=2... |
Assuming that your value at risk model is based on normality assumptions, e.g. using a Delta-Gamma normal model does the approximation hold perfectly for a portfolio of stocks and options? What about other instruments? |
The Black-Scholes-Merton model assumes that the prices of the underlying asset at maturity are log-normally distributed. I understand that this assumes that the prices can never go below 0.
However, there are cases where the underlying asset's price can go below zero. For example:
* With unlimited liability compa... |
Should a normal distribution be used instead of a log-normal distrubution for valuing options on unlimited liability companies? |
Should a normal distribution be used for valuing options on assets that can potentially have negative value? |
The Black-Scholes-Merton model assumes that the prices of the underlying asset at maturity are log-normally distributed. I understand that this assumes that the prices can never go below zero.
However, there are cases where the underlying asset's price can be negative. For example:
* With unlimited liability comp... |
Should a normal distribution be used for valuing options on assets that can potentially have negative prices? |
The Black-Scholes-Merton model assumes that the prices of the underlying asset at maturity are log-normally distributed. I understand that this assumes that the prices can never go below zero.
However, there are cases where the underlying asset's price can be negative. For example:
* With (hypothetical) unlimited... |
**Edited to include VBA code for comparison**
**Also, we know the analytical value of the simple Call option, which is 8.021, towards which the Monte-Carlo should converge, which makes the comparison easier.**
**Excel VBA gives 8.067 based on averaging 5 Monte-Carlo simulations (7.989, 8.187, 8.045, 8.034, 8.075)... |
Let's assume I have a 2-year fixed-floating swap, the floating leg has a quarterly reset.
Does this mean the valuation is done every 3 months for the floating leg? (and the total value of these 4 quarters paid once at the end of year 1)
Does this mean the valuation and payments are due every 3 months for the floa... |
What are reset periods/dates in relation with interest rate swaps? |
**Edited to include VBA code for comparison**
**Also, we know the analytical value of the simple Call option, which is 8.021, towards which the Monte-Carlo should converge, which makes the comparison easier.**
**Excel VBA gives 8.067 based on averaging 5 Monte-Carlo simulations (7.989, 8.187, 8.045, 8.034, 8.075)... |
Calculating risk-reward ratio R is easy when trading a straight forward strategy which has its entry and exit points clear:
```python
risk = entry - stop
reward = take_profit - entry
R = reward / risk
```
But what if I have dynamic exit points? For example in a trend following strategy, which after the price mo... |
I am having a hard time understanding what "EDSF" represents as a bond pricing benchmark. I have seen bonds quoted as spreads to EDSF with maturities < 2 years instead of treasury notes, and this seems to be a common convention in the ABS market.
Here is a footnote from a recent Wells Fargo consumer ABS report
> ... |
I am having a hard time understanding what "EDSF" (Eurodollar Synthetic Forward Curve) represents as a bond pricing benchmark. I have seen bonds quoted as spreads to EDSF with maturities < 2 years instead of treasury notes, and this seems to be a common convention in the ABS market.
Here is a footnote from a recent ... |
I am having a hard time understanding what "EDSF" (Eurodollar Synthetic Forward Curve) represents as a bond pricing benchmark. I have seen bonds quoted as spreads to EDSF with maturities < 2 years instead of treasury notes, and this seems to be a common convention in the ABS market.
Here is a footnote from a recent ... |
I'm googling all over the internet but seems no luck. Just curious, if anyone knows, what did the formula look like for USDX before euro was adopted? And on which day did ICE change the formula ? Jan 1st, 1999 or sometime in 2002?
Much appreciated |
I am currently working through the paper [*The Myth of Long-Horizon Predictability*](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=862285) [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of length 75 years (with each year corresponding to one sam... |
Could somebody help me understand if the VIX is a leading or lagging indicator.
From the CBOE whitePaper ( https://www.cboe.com/micro/vix/vixwhite.pdf). I've understood that the VIX tries to calculate the 30 day expected volatility.
[![enter image description here][1]][1]
This would make me assume that i... |
In the book *Investments* (Bodie, Kane, Marcus), in chapter 8, the authors discuss index models (page 247) and, in its context, systematic risk. The authors state, without explanation, that the market factor **m** of the unanticipated part of the realized return will have a mean of zero because, over time, "surprises w... |
Why do surprises in macroeconomic variables average out to zero? |
I am currently working through the paper [*The Myth of Long-Horizon Predictability*](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=862285) [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of length 75 years (with each year corresponding to one sam... |
In the book *Investments* (Bodie, Kane, Marcus), in chapter 8, the authors discuss index models (page 247) and, in its context, systematic risk. The authors state, without explanation, that the market factor **m** of the unanticipated part of the realized return will have a mean of zero because, over time, "surprises w... |
In the construction of an index model, we often use the expected return of a security, including surprises, for analysis. To calculate this, we must estimate the risk premium of the index.
Since we only have one data point for each index at each point in time, we only have one of the risk premium, so the only option... |
How is the risk premium of the index estimated? |
Is there any website for a detail chronological description of U.S. index futures market development? I have searched online for some time but unable to locate particular focus on index futures market development... A lot of them regard the general futures market as a whole...
Thank you in advance. |
Is there any website for a detail chronological description of U.S. index futures market development? |
Hope you're doing great! I'm struggling to develop the code for the Third Order Greeks.
In all places I have searched, the development is missing.
For example:
[![enter image description here][1]][1]
But I don't know how to develop it, in order to code it in VBA.
Could you help me or know where I can sea... |
I do have a panel data set on North American companies from Compustat covering balance sheet and income information. I am wondering if there is a possibility to use a balance sheet variable as an indicator how much and if a company is hedged against uncertainty. I mean is it possible to see on a balance sheet level, fo... |
I am trying to compute shocks on the forward swap rates based on shocks to the swap rate curve (aiming at repricing consistently a set of swaps and swaptions based on a shock to the swap curve):
- It seems that I cannot deduce forward swap rates by treating the swap curve as any other discount curve and computing "... |
How to compute forward swap rates? |
I am currently working through the paper [*The Myth of Long-Horizon Predictability*](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=862285) [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of length 75 years (with each year corresponding to one sam... |
The solution to [Merton's portfolio problem](https://en.wikipedia.org/wiki/Merton%27s_portfolio_problem) suggests that an investor invest $\frac{\mu - r}{\sigma^2 \gamma}$ percent of their wealth in the stock market, where $\mu$ is the rate of return of the stock mareket, $r$ is the risk free interest rate, $\sigma$ th... |
Why does Merton's fraction give unintuitive quantities using real world data? |
I wonder if the $FTP\%$ term for loans in the following formula
$FTP\%=\text{Baserate} + \alpha
*\text{liquiditypremium}_{1y}+(1-\alpha)*\text{liquiditypremium}_{6m}$.
is a measure for the bank's profit? |
I am struggling to find an arbitrage in the following configuration. I know how to prove that there is an arbitrage (using the fundamental theorem of asset pricing). So I ve proven there is an arbitrage. But how to find it?
I have two assets and a bond in a market where, the risk free asset has as interest $r$, and ... |
arbitrage, 2 assets in a market. How to find an arbitrage when the solution is not obvious? |
I am struggling to find an arbitrage in the following configuration. I know how to prove that there is an arbitrage (using the fundamental theorem of asset pricing). So I ve proven there is an arbitrage. But how to find it?
I have two assets and a bond in a market where, the risk free asset has as interest $r$, and ... |
I am a newbie to fixed income quant side and I am trying to understand in the **curve building process**, why do we need **funding curve** and **projected curve** and what are they exactly in current industry?
Could someone please give me some simple introduction about the curve building procedure ?
Much appreci... |
In the curve building process, why do we need funding curve and projected curve and what are they exactly in current industry? |
Trying to understand what being in a short position of a currency forward means.
For example, given a 60-day currency forward at `0.92154 pounds/euro` where euro is the base currency, does the short position of this contract mean I will be selling pounds for euros? And the long position is I will be buying 0.92154 p... |
I am currently working through the paper [*The Myth of Long-Horizon Predictability*](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=862285) [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of length 75 years (with each year corresponding to one sam... |
How to find an arbitrage when the solution is not obvious (2 assets in a market)? |
I wonder if the $FTP\%$ term for loans in the following formula
$$FTP\%=\text{BaseRate} + \alpha
\,\text{LP}_{1y}+(1-\alpha) \,\text{LP}_{6m},$$
where $\text{LP}$ is a liquidity premium, is a measure for the bank's profit? |
I am struggling to find an arbitrage in the following configuration. I know how to prove that there is an arbitrage (using the fundamental theorem of asset pricing). So I ve proven there is an arbitrage. But how to find it?
I have two assets and a bond in a market where, the risk free asset has as interest $r$, and ... |
Let $S_t^k$ be the price of the $k^{th}$ risky asset at time $t$.
Let $x$ be your position in $S_t^0$ (risk-free bank account), $y$ your position in $S_t^1$ and $z$ your position in $S_t^2$.
You need to check two things to find an arbitrage strategy.
1. Normally arbitrage strategies have zero initial cost, th... |
Disclaimer: Am a software engineer by training, diving into finance. Am still a noob xD
Hey team, I have been reading one of Spitznagel's whitepapers:
https://www.universa.net/UniversaResearch_SafeHavenPart2_NotAllRisk.pdf
Here, Spitznagel explains how adding an asset that has 0% overall return, when combined... |
I understand that $f$ continuous $\Rightarrow Q(f) = 0$ where this is defined over a bounded interval [0,T] as then we may use uniform continuity and the mean value theorem. But I am not sure how the converse implication can be shown? |
Proof that $f$ is continuous if and only if it has 0 quadratic variation? |
I have a data set which looks as following:
Y
1 2
1 1.5
1 2.5
2 5
2 3
3 5.2
3 6
3 6.8
4 6
4 7
And the corresponding plot is:
[![enter image description here][1]][1]
What kind of regression is appropriate for the above kind of data ?
[1]: https://i.... |
This perhaps is an over simplification of calculating trading returns while including trading costs. I've made some assumptions - the commission for investing in a extract investment is 1% and 2% respectively and does not change over the trading period which in this case is 5 time steps. I've used python code to perfor... |
Figure 2 of the 2019 paper "[Celebrating Three Decades of Worldwide Stock Market Manipulation][1]" shows that 29 Jan 1993 to 31 Oct 2019, overnight returns (from close to open) of SPY were 1232% while intraday returns (from open to close) were –14%.
Surprisingly, the opposite holds for the S&P500 index i.e. intraday... |
I am currently working through the paper [*The Myth of Long-Horizon Predictability*](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=862285) [1] and I got stuck in reproducing the empirical results in Section 1.4.
It is my understanding that time series of length 75 years (with each year corresponding to one sam... |
I have a question related to accessing historical data. My first attempt to grab historical data for a few companies was using google sheets and the GOOGLEFINANCE function. Unfortunately, it seems to be fairly limited.
Running this function works very well and I could not be happier:
=GOOGLEFINANCE("AAPL", "price... |
When building an ERC portfolio given covariance $S$, I am familiar with the approach in [optimalPortfolio][1]. It takes the risks of a given weight vector $(w_i * (S w)_i)$, divides it by total risk to get the vector of current budget $Rb = (w_i * (S w)_i) / w^T S w$ and it minimizes the objective $\sum (Rb - b)^2$ whe... |
Equivalent constructions of risk budgeted portfolios? |
Are probabilities of certain events (e.g. amount of rainfall over a period, probability of a Fed rate hike) inferred from derivatives on non-tradeable random variables (e.g. Weather Futures, Fed Funds Futures) stated in the risk-neutral measure (with the money market numeraire) or real-world measure? |
Measure for probabilities inferred from prices of derivatives on non-traded random variables? |
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