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Why are there no securitized cash dividends? |
Sounds like you want a [Dividend Swap][1]?
These things trade OTC... there are quote windows in the BBG terminal.
[1]: https://en.wikipedia.org/wiki/Dividend_swap |
Some bond coupons are securitized and sold as strip bonds. Why can't stocks be similarly "stripped" to produce securitized dividend strips? Is it merely because there is no demand for such a product? |
Consider a American Option on a linear payoff i.e., if called at time $T$, it pays off $S(T)$, the stock price. Is the optimal call time of such an option determinsitc? Is there an intuition to the same; as in why linearity forces a deterministic call time? |
We could have the formula for `Heston` model for currency as (under the `Risk-neutral measure` for $r_d$) -
$dS_t = \left( r_d - r_f \right) S_tdt+S_t \sqrt{V_t}dW^S$
$dV_t = a(\bar{V}- V_t)dt + \eta \sqrt{V_t}dW_t^V$
Typically we estimate the model parameters observing the Call and Put options prices with dif... |
This is a *Structured Product*. Desks issuing these products make money by selling the product for X when it is really worth X-Y (where X is usually 100%, and Y will be some number of the order 1%, depending on the complexity and maturity of the product).
In the case you reference, you can see from the link that Y ... |
**The payoff**: you are missing one point. It's not only about the upside, it's also about the _downside_. Your performance $P_T$ at maturity $T$ (the Final Valuation Date) is basically:
$$P_T=P_0\left(1+1_{\left\{\max_{0\leq t\leq T}\left|\frac{I_t}{I_0}-1\right|\leq B\right\}}\left|\frac{I_T}{I_0}-1\right|\right)$$
... |
I need some help. \
I'm given $J$ different regimes, each one characterized by its own parameters $(r_i, \delta_i,\sigma_i,...)$ with $i\in \mathcal{J}= \{1,2,...,J\}$ ($r$ = risk-free interest rate, $\delta$ = continuous dividend yield). \
For instance, we can have regime $1$ under Black-Scholes model with paramete... |
I ran into a step in an argument that I can't quite figure out. It's basically how they use a limit that I don't seem to understand. The context is local-to-unity asymptotics in vector autoregressions, so I figured some people doing empirical work might know.
We have a $K \times K$ diagonal matrix $\Lambda := \text{... |
When arbitraging ETF holdings against the ETF, how does one manage the portfolio over time? Assume the strategy creates a long signal in pair A (stock X/ ETF) and a short signal in pair B ( stock Y / ETF). The hedge ratios are 0.5 for pair A and 2 for pair B so the following trades would get executed:
(+) 5 Shares S... |
I'm curious why things like PCA/ML aren't use frequently in trading? Is there an underlying philosophy that prevent this? What I was thinking, was that if PCA worked for making money, then everyone would do it, and so it effectively wouldn't work. |
Why is PCA/ML not used frequently in trading? |
ML is a very broad term. Do you mean linear regression? To you mean random forests? People use all of these approaches with various degrees of success. Bloomberg will have a story every few months about a big quant/ML fund starting or being shut down.
PCA specifically is used quite a bit in fixed income to mo... |
I was asked the following question in a recent interview: "**(i) Express a forward swap rate in terms of forward Libor rates. (ii) Apply Ito's lemma to this expression to derive the process for the forward swap rate. (iii) Finally, use this expression to price a swaption**". I couldn't quite figure out the full questio... |
Under one-factor Merton framework, like Basel, you use *unconditional* PDs as input of the portfolio model and this "*unconditional*" means it is a *TTC-PD*.
Given a *i-th* borrower, the default threshold is just the inverse cumulative standard normal distribution of the *unconditional* $PD_i$ and you will compare the... |
Please see the codes below
My question is about input parameters (a, b and sigma)and their calculation.
For the long term mean "b", do we use effective Fed Fund rates? or 3m T-bills?
Also, how do I calculate the mean reversion speed 'a'?
```
import numpy as np
import pandas as pd
import matplotli... |
>For the long term mean "b", do we use effective Fed Fund rates? or 3m T-bills?
I don't think so. For this particular short rate model, you have to provide 3 input parameters, namely: $a$, $b$ and $\sigma$ (using your notation).
I believe that $a$ and $b$ are obtained by fitting the current term structure of zer... |
I was asked the following question in a recent interview: "**(i) Express a forward swap rate in terms of forward Libor rates. (ii) Apply Ito's lemma to this expression to derive the process for the forward swap rate. (iii) Finally, use this expression to price a swaption**". I couldn't quite figure out the full questio... |
For example, lets say I own a bond issued by a company in Mexico that's denominated in USD and I want to hedge my duration exposure. I obviously need to hedge duration to the US yield curve. Do I also need to hedge my duration to the local Mexican gov yield curve? Even thought the MEX bond is denominated in USD, I f... |
To build a term structure I need different volatilities, as I dont get at every strike, I use interpolation technique to calculate the rest and plot. This is how I calculate the implied vols. Now how is newton-raphson method is used to calculate the implied vols, is it another way to calculate like I calculate with int... |
In the current, applied field of quantitative finance, the utility function has taken a back seat. Whether or not that is valid is a concerning issue.
If the Markowitz model and its children are correct, the utility function matters but is unnecessary to include in calculations, explicitly. In other words, people ... |
In the current, applied field of quantitative finance, the utility function has taken a back seat. Whether or not that is valid is a concerning issue.
If the Markowitz model and its children are correct, the utility function matters but is unnecessary to include in calculations, explicitly. In other words, people ... |
In the current, applied field of quantitative finance, the utility function has taken a back seat. Whether or not that is valid is a concerning issue.
If the Markowitz model and its children are correct, the utility function matters but is unnecessary to include in calculations, explicitly. In other words, people ... |
To build a term structure I need different volatilities, as I dont get at every strike, I use interpolation technique to calculate the rest and plot. This is how I calculate the implied vols. Now how is newton-raphson method is used to calculate the implied vols, is it another way to calculate like I calculate with int... |
Consider BS-model with parameters: Stock = 100, Strike = 100, Texp = 1 year, Vol = 13%, Rf Rate = 3%. For these parameters the BS put price is 3.76. Then consider the same parameters but with Texp = 20 years. The new BS put price is 3.29. Consider now Texp = 100 years. The put price is even lower still at 0.09.
Wha... |
Why does black scholes model give lower prices for puts with further time to expiry? |
Where can I find derivation of formula for portfolio skewness and kurtosis? I can find formulas everywhere, but not their derivations?
For example, the portfolio variance formula, $w^\top \Sigma w$ is well known and I can find the derivation of that formula in a lot of books, but I can't find anything on the formuals ... |
When computing the Sharpe for a strategy, should the shut down period be considered? I saw both. Theoretically, |
Should the strategy shut down period be considered when calculating Sharpe? |
I am not sure following funds' or advisors' white papers is a so great idea since they may be biased to promote one vision on the way the markets operate. For instance, remember that Blackrock has been vocal about the need for a standardisation of corporate bonds few years ago (see [FT in 2014][1]). It is (in my opinio... |
I am trying to estimate the cash flows of Mortgage Backed Security.
The example is present in the Fixed Income textbook written by Fabozzi.
The problem and the solution is as follows:-
Suppose there is a **$400 million** mortgage pass-through security with a **7.5%** pass-through rate, a weighted average coupon ... |
How to calculate scheduled mortgage payment of a mortgage pass-through security? |
When computing the Sharpe for a strategy, should the shut down period be considered? |
I am interested in the impacts of a debt crisis on the tracking ability of an ETF.
In particular I have read that the market makers for ETFs often take on large short-term loans in order to create or redeem large groups of shares of an ETF. This is conceivably necessary because purchasing the 50,000 shares of an ETF... |
I think your question can be split into two parts: (i) how to value a swap mathematically and (ii) how swaps actually work as a traded product.
**Part (i)**:
As noob2 pointed out, "theoretically", a swap is valued with the help of two curves: one "forward" curve and one "discounting" curve. Say you want to "value... |
A few years back in an interview I remember being asked to derive the Sharpe ratio from the correlation between a pre-open daily signal and the open-close returns. I think you had to make some assumptions regarding the risk/reward and accuracy but you could start with a correlation of say 0.05 and back out a sharpe rat... |
I think I understand the question, but maybe not.
In USD market, the most liquid IR swaps have floating leg reset quarterly from 3Mo LIBOR. (Ths will change when LIBOR is discountinued). (Market conventions differ for other currencies.) If you build your swap curve from such swap rates and ED futures (whose underlyi... |
Are copulas good tool to model the dependence between the two uncorrelated variables. I have X and Y datasets with 260 data points each with Pearson's correlation=-0.06 and Kendall rank correlation=0.1093. Will copulas be able to capture the dependence between the two variables? I tried fitting Arhimedian copulas and f... |
I have to price an american option on a daily basis and I have some questions regarding the CRR binomial tree model:
1. Is it correct to use implied volatility as an input? Or is it better to use historical vol? If I were to use implied vol, should I calculate one vol per node or just one vol using the time-to-expir... |
In the academic literature, I found that momentum returns are negatively skewed (e.g. Daniel and Moskowitz, 2002). As far as I understand, this usually happens when the "past losers" rebound causing heavy losses on the short leg of the strategy.
Nonetheless, I noticed that many CTA/trend-following funds exhibit retu... |
Are momentum returns negatively skewed? |
I’m trying to figure out the discretization of the Heston model. In the choice of `dt`, I have seen several ways that people specify this number. Would it not just be `1/n` where `n` is the number time steps? And the paper mentions that the wiener processes should be normally distributed with variance `dt`, but I often... |
By mixing multiple approaches I came up with algorithm that does not need guess as an input. I focused on custom precision and resiliency. Please take a look.
https://medium.com/@manchikanti/irr-internal-rate-of-return-calculator-15ec269bd8f5?source=friends_link&sk=21cc51cc485647cb73eb0a66c57522bd
https://chitb... |
Investors buy (and hold) more puts and pay up more for them for a few reasons. First, people fear downside more than they like upside as shown by Kahneman and Tversky (1979, 1992). Second, people may not be able to recover easily (or at all) from downside in the macroeconomy. In classical finance terms, if we think cri... |
Market makers may take loans out to create ETF shares or redeem shares to repay loans. In my experience working with an ETF desk, that activity usually does not affect index pricing much. However, in a crisis it could lead to mispricings versus index futures if creation or redemption is restricted.
What you also see... |
I was asked the following question in a recent interview: "**(i) Express a forward swap rate in terms of forward Libor rates. (ii) Apply Ito's lemma to this expression to derive the process for the forward swap rate. (iii) Finally, use this expression to price a swaption**". I couldn't quite figure out the full questio... |
In the academic literature, I found that momentum returns are negatively skewed (e.g. Daniel and Moskowitz, 2002). As far as I understand, this usually happens when the "past losers" rebound causing heavy losses on the short leg of the strategy.
Nonetheless, I noticed that many CTA/trend-following funds are convex (... |
I am trying to read some literature on Prime Brokerage. In context of prime brokerage, primarily we have 4 participants
Customer
Executing Broker (EB)
Prime Broker (PB)
DTC (it could be specific to the region)
Why would a customer go to an EB assuming that he already is availing services of PB ? In ot... |
Whats the need of Executing brokers if Prime brokers are the protagonist? |
Why they are only traded in OTC ? And why in general derivatives are all traded only in OTC ?
Why banks prefer to trade in OTC rather than exchange market ? |
Why forwards are not traded in exchange market? |
> In other words, is it too costly for PB to be an EB
> as well?
Answering your second question first, PB's are EB's; they just provide an entire suite of products and services beyond just trade execution that an EB would provide. If you have an account with a prime broker, they can undoubtedly execute trades, and... |
Why they are only traded OTC ? And why in general derivatives are all traded only OTC ?
Why do banks prefer to trade OTC rather than exchange market ? |
I have the following data for a fund. The contributions come from the GP, MV stands for market value.
[![enter image description here][1]][1]
The timing is **not regular** (makes me think I should use XIRR) and the **flows can be negative** (modified IRR, generalised IRR ? ) and I have to adjust for changes in t... |
internal rate of return ((M/X)IRR ?) of a fund |
I was asked the following question in a recent interview: "**(i) Express a forward swap rate in terms of forward Libor rates. (ii) Apply Ito's lemma to this expression to derive the process for the forward swap rate. (iii) Finally, use this expression to price a swaption**". I couldn't quite figure out the full questio... |
I am scrolling through the various metals on lme.com and some are in contango and some in backwardation. For example:
[Copper: contango][1]
[Aluminium: backwardation][2]
[1]: https://www.lme.com/Metals/Non-ferrous/Copper#tabIndex=0
[2]: https://www.lme.com/Metals/Non-ferrous/Aluminium#tabIndex=0
Fu... |
Why are some metals in contango (inverted) forward curve and some in backwardation (normal) forward curve? |
I was asked the following question in a recent interview: "**(i) Express a forward swap rate in terms of forward Libor rates. (ii) Apply Ito's lemma to this expression to derive the process for the forward swap rate. (iii) Finally, use this expression to price a swaption**". I couldn't quite figure out the full questio... |
I am scrolling through the various metals on lme.com and some are in contango and some in backwardation. For example:
[Copper: contango][1]
[Aluminium: backwardation][2]
[1]: https://www.lme.com/Metals/Non-ferrous/Copper#tabIndex=0
[2]: https://www.lme.com/Metals/Non-ferrous/Aluminium#tabIndex=0
Fu... |
I have the following data for a fund. The contributions come from the LPs (i.e., the investors in the fund), MV stands for market value.
[![enter image description here][1]][1]
The timing is **not regular** (makes me think I should use XIRR) and the **flows can be negative** (modified IRR, generalised IRR ? ) an... |
When the seller of a Call option hedges themselves, we know that they should buy $\Delta(t) = \mathcal{N}(d_1(t))$ amounts of the risky asset at time $t$.
But what about the riskless asset? My understanding is that they should buy $V(0) - \Delta(0)S_0$ at time $t = 0$ where $V(0)$ is the price of the option (ie the ... |
I have the following data for a fund. The **contributions come from the LPs** (i.e., the investors invest more in the fund, or withdraw money from the fund), MV stands for market value.
[![enter image description here][1]][1]
The timing is **not regular** (makes me think I should use XIRR) and the **flows can be... |
I am reading Wilmott's book, "Quantitative Finance" and try to understand the derivation that the variance of asset-returns, $V[\Delta S/S]$, is a linear function of the time step $\delta t$.
If we assume that the return distribution is gaussian, then he claims that the variance of asset-returns should $\in O(\del... |
Market makers may take loans out to create ETF shares or redeem shares to repay loans. In my experience working with an ETF desk, that activity usually does not affect index pricing much. However, in a crisis it could lead to mispricings versus index futures if creation or redemption is restricted.
What you also see... |
I am reading Wilmott's book, "Quantitative Finance" and try to understand the derivation that the variance of asset-returns, $V[\Delta S/S]$, is a linear function of the time step $\delta t$.
If we assume that the return distribution is gaussian, then he claims that the variance of asset-returns should $\in O(\del... |
I attached screenshot of US treasury yields from bloomberg today and try to understand it.
A few questions are below, taking the example of 2-year bond:
- Is maturity exactly 2-year later today? If not, how should I know exact date of the maturity.
- Is coupon semi-annual, i.e. the investor gains 13 cents every ... |
How can I use the binomial tree pricing method for American options to determine the expected time of exercise for the option (or "Fugit")? In particular, how would I modify the algirithm [here][1] to compute expected life?
[1]: https://en.wikipedia.org/wiki/Binomial_options_pricing_model |
I am scrolling through the various metals on lme.com and some are in contango and some in backwardation. For example:
[Copper: backwardation][1]
[Aluminium: contango][2]
[1]: https://www.lme.com/Metals/Non-ferrous/Copper#tabIndex=0
[2]: https://www.lme.com/Metals/Non-ferrous/Aluminium#tabIndex=0
Fu... |
I would like to point out some things that might be helpful.
>I’m trying to figure out the discretization of the Heston model. In the choice of `dt` ...
There exists many discretization schemes that could be implemented to simulate a system of stochastic differential equations (SDEs), such as your Heston model. O... |
Given the assumptions listed as 1,2 and 3 here https://www.investopedia.com/terms/t/technicalanalysis.asp
What do you think about the idea that old technical patterns/trends should definitely not work any longer given that central banks has taken an increasing place in the market?
The basic assumptions are that ... |
firstly I would like to say sorry for the title - its not the best. In fact its crap.
Here is my problem (I am new to coding btw - still learning)
I am using Python on my MacBook - using Terminal.
1) I have a portfolio of stocks with their weightings but at random periods. E.g. 2/Jan/2018 - Company X - 3%, C... |
I have missing data on my portfolio weightings but it can be solved through stock prices - how can I code to find this? |
There could be any number of explanations for copper to be backwardated and aluminum to be in contango right now.
The simplest (and most correct) explanation is the most vague: that these futures curves represent time-varying expectations of supply and demand over the next half year or so.
More helpful is to know... |
There could be any number of explanations for copper to be backwardated and aluminum to be in contango right now.
The simplest (and most correct) explanation is the most vague: that these futures curves represent time-varying expectations of supply and demand over the next half year or so.
More helpful is to know... |
Consider an overnight rate $r_{ON}$ and a one-week rate $r_{1W}$.A settlement period of 2 days is associated to the rate $r_{1W}$.
In order to compute the overnight discount factor, since the first rate has 0 settlement period, I apply the simple compounding formula $DF(t, t+1) = \frac{1}{1+\alpha_{0,1}r_{ON}}$, whe... |
How to bootstrap discount factor DF of the settlement period DF(today, today+settlement period)? |
I would like to point out some things that might be helpful.
>I’m trying to figure out the discretization of the Heston model. In the choice of `dt` ...
There exists many discretization schemes that could be implemented to simulate a system of stochastic differential equations (SDEs), such as the Heston model. On... |
I would like to point out some things that might be helpful.
>I’m trying to figure out the discretization of the Heston model. In the choice of `dt` ...
There exists many discretization schemes that could be implemented to simulate a system of stochastic differential equations (SDEs), such as the Heston model. On... |
Let's say I want to replicate an index like S&P500. People generally minimize a mathematical notion called tracking error which is nothing else than the standard deviation between the index's returns and our portfolio's returns. More precisely, let $r_{pf}$ be the returns of our portfolio and $r_{idx}$ be the returns o... |
I'm researching quant strategies suitable for retail traders, focusing on those beyond the typical 1-3 month holding period. Traditionally, retail strategies are influenced by insider information, market news, and analyst opinions, with quant approaches favoring timing-based methods like momentum, pairs trading, and me... |
1. The way to trade this is to put on a FOMC swap - where the start and end date is the meeting date, the underlying can be sofr or fedfunds(ff) and the notional can be the pv01 of risk you want to put on - say 100k/01.
Currently the market is pricing in a cumulative 25 bps of cut by June. Lets say you think this ... |
Assume the following:
- we are running a constant maturity bond fund (10yrs)
- all zero coupon bonds
- to maintain the maturity, we buy bonds of 10y and sell the 9y bonds 1y later
- price of 10y bond is 100, price of 9y bond is 99
Now..the bond fund consistently buys high and sells low, after a long time the fun... |
1. The way to trade this is to put on a FOMC swap - where the start and end date is the meeting date, the underlying can be sofr or fedfunds(ff) and the notional can be the pv01 of risk you want to put on - say 100k/01.
Currently the market is pricing in a cumulative 25 bps of cut by June. Lets say you think this ... |
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