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I know Yahoo has stock quote data (OHLCV). But it contains errors.
tdameritrade API have 1- and 5-minute data. But it only starts at 7AM ET, instead of 4AM ET. It is only limited to 182 trading days, which is rather limited.
Is there an alternative free quote data source that contains the 1- or 5-minute data from... |
I know Yahoo has stock quote data (OHLCV). But it contains errors.
tdameritrade API have 1- and 5-minute data. But it only starts at 7AM ET, instead of 4AM ET. It is only limited to 182 trading days, which is rather limited.
Is there an alternative free quote data source that contains the 1- or 5-minute data from... |
A trading strategy is defined as follows: starting capital $v_0 = 5$ and 1 risky asset holdings $\varphi_t = 3W_t^2-3t$ where $W$ is a Wiener process.
The problem is to find the probability of the value of the strategy at the end of period 1 is greater than zero, $\mathbb{P}(V_1>0)$
Now, $V_1=v_0+\int_0^13W_s^2-3t\... |
Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of the option as cheaply as possible so that I can keep as much of that spread as possible.
I’m content with hedging delta... |
How do we hedge option vega practically? |
I would like to use tick data (especially order book data; but also trade) to backtest my strategies, can anyone offer a recommendation? Personally, I've written my own backtesting scripts couple of times, and also tried out `backtrader`. I'm aware of other Python backtesting tools out there, but typically they deal wi... |
Most data providers I find online offer historical market data in time resolutions of 1 minute bars or longer (which is too long), or tick resolution (which is too short). Of course one could get tick data and construct 1 second bars from this information. However, the price for tick data is very excessive.
Is there... |
Where to get 1 second bar intraday historical market data? |
The following formulation is from Vasicek and refers to the cond. probability of the loss of a loan (equ. 3 in the reference):
$$p(Y)=\Phi\left(\frac{\Phi^{-1}(p)-\sqrt{\rho}\,Y}{\sqrt{1-\rho}}\right).$$
Vasicek also states that the variables in his outlined asset value formula (equ. 1 in the reference) are jointly... |
We are using a SABR model to interpolate the implied volatility surface.
The model yields a formula for implied volatility that contains the following term:
$\ln \left(\frac{K}{F}\right)$
It is proposed to take into account cash dividends by modifying this part of the equation to:
$\ln \left(\frac{K+D}{F+D}\r... |
In studying skew I've been advised to focus on understanding on components that affect it. One such component that's been recommended to me is the relationship btwn RV-IV and realized skew. Allegedly, there should be a strong correlation btwn the 2 (skew steepens when RV exceeds implied), but when I regress one on th... |
Reference book is 'Steven Shreve: Stochastic Calculus and Finance'
What I don't understand is $F_3$ below picture
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/nY8c2.png
I understand that 'filteration' have accumulative information.
So when we tossed the coin one time($F_1$), if ... |
The concept of momentum in trading is a bit weird to me.
It seems to me to be measuring a first derivative or first difference of price, or something in that ballpark depending on the exact formulae used. I would describe this as the velocity of a security's price. I would expect momentum to require some concept o... |
I'm using a well-known SABR model in order to build an implied volatility surface of caps/floors on a very illiquid market which is entirely missing OTM quotes. What happens to SABR implied smile/surface calibrated only on ITM and ATM quotes? I think that it's going to somehow underestimate/overestimate the real volati... |
I am currently studying Merton's Problem Portfolio from the slides here:
https://stanford.edu/~ashlearn/RLForFinanceBook/MertonPortfolio.pdf
Where they stated the optimal solution are:
[![enter image description here][1]][1]
I tried to do a simple Monte Carlo simulation using the optimal solutions and the SD... |
I wonder if there is an agreed market convention on a discount margin formula for the new style frn's with overnight-compounded rates paid in arrears i.e. sofr/sonia/estr/etc frn's?
This question is not about the specific details regarding lockback/lockout/pmt-lags etc. but about the simplified (i.e. no curve from w... |
I am looking for a metric for measuring "the expectation of the tightness of monetary policy." I know this is a super vague concept.
My ideal metric is something I can do a "spot price / avg price of past year" to gauge the "expectation" of the tightness of monetary policy. It should ideally also be "forward loo... |
I'm getting into pairs trading (statistical arbitrage), but I keep finding different instructions on how it's done.
Some sources (like [this][1]) run the linear regression (to find hedge ratio) on the log **prices** of the two assets. Other sources (like [this][2]) run the linear regression on the log **returns** of... |
Pairs trading - is regression done on log prices or log returns? |
I am looking into a data provider which provide the `credit loss` data from different banks - https://globalcreditdata.org/interactive-dashboard/
They also provide data on something called `Discounted Recovery Rate`. Does anyone know what exactly is `discounted` RR? I know the Loss given default i.e. `LGD` hence the... |
As an example of what I am looking for, here is one tentative high-level classification of the various ways that the book value, or shareholders' equity, of a company may change over a given financial reporting period:
1. The company can post a positive or negative net income.
2. The company can issue a dividend ... |
Can we construct a complete classification of the ways that shareholders' equity of a company can change? |
How can I reproduce the implied volatility curve (plotted against the strike price) in the Heston model (i.e. the blue line in the graph below)?
>What's the equation that I have to set up and solve?
I have a function that evaluates the price of a Heston call:
heston_call$(S_0, v_0, \theta, \kappa, \eta, r, \r... |
The main result of [this paper][1] is equation (16) on page 63, that states that:
In the limit $\tau \rightarrow 0$, the implied volatility is the harmonic mean of the local volatility, namely
$$\lim_{\tau \rightarrow} \frac{1}{\phi(x,\tau)}=\int_{0}^{1}\frac{ds}{\sigma(sx,0)}$$
where $\phi(x,\tau)$ is the imp... |
I'm looking for a bit more background on a question that came up here: Our traders use some sort of Longstaff-Schwartz to calculate the optimal point when to call an issuer-callable bond.
My question is: Does anyone know whether a) it' s possible and b) how to exactly locate the optimal exercise point by systematica... |
How to spot optimal exercise level of issuer-callable bonds with autocallable bonds call level? |
As an example of what I am looking for, here is one tentative high-level classification of the various ways that the book value, or shareholders' equity, of a company may change over a given financial reporting period:
1. The company can post a positive or negative net income.
2. The company can issue a dividend ... |
Can we construct a complete classification of the ways that the shareholders' equity of a company can change? |
The main result of [this paper][1] (*Asymptotics and Calibration in Local Volatility Models*, Berestycki, Busca, and Florent. Quantitative Finance, 2002) is equation (16) on page 63, that states that:
In the limit $\tau \rightarrow 0$, the implied volatility is the harmonic mean of the local volatility, namely
$$... |
One of the most straightforward approaches to investing involves predicting how the book value, or shareholders' equity, of a company will change over time. This in turn requires that we know the various way that this value _can_ change.
For example, here is one tentative high-level classification of the various wa... |
Is there a closed form solution for the vector weight $w$ for the following mean-variance optimization problem?
$\max_w w'\mu - \frac{\gamma}{2}w'\Sigma w $
s.t.
$w'\boldsymbol{1}=1$
$w'z\geq \bar{z}$
where $w, z$ are N x 1 vectors, $\bar{z}$ is a constant.
If I write the following Lagrangian:
$... |
Is there a closed form solution for the vector weight $w$ for the following mean-variance optimization problem?
$\max_w w'\mu - \frac{\gamma}{2}w'\Sigma w $
s.t.
$w'z\geq \bar{z}$
where $w, z$ are N x 1 vectors, $\bar{z}$ is a constant. It assumes the existence of risk-free asset with $r_f=0$, that's why ... |
I am trying to demonstrate the famous result that states that when $T \rightarrow 0$, the Implied Volatility is the harmonic average of Local Volatility.
I am st the final stage, and I have the following equation:
$$I(0,k)=\sigma(0,k)\left(1-\frac{k}{I}\frac{\partial I}{\partial k}\right)^2$$
This differentiat... |
I have to derive several things for my thesis, however, I have the following expression:
$$
\int^{t}_{0} \exp\{\sigma W_{t}\}.dW_{t}
$$
Does anyone know what the solution for this is?
Kind regards. |
I read on https://www.reuters.com/markets/europe/russia-etf-draws-meme-stock-like-trading-frenzy-2022-03-02/ ([mirror](https://archive.ph/ZYb6b)):
> The ETF's tumble has been a boon for bearish investors. RSX shorts are up $299 million in year-to-date mark-to-market profits, according to financial analytics firm S3 ... |
How do financial analytics firms estimate the earnings from short sellers on an ETF or stock? |
I'm after returns of the Value factor (book-to-market) from [Ken French's library][1]. Based on the description, I'm guessing it's this one: `Portfolios Formed on Book-to-Market`. The [csv][2] has the following headings:
- SMALL LoBM
- ME1 BM2
- SMALL HiBM
- BIG LoBM
- ME2 BM2
- BIG HiBM
I'm guessing S... |
When conduction principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4? |
When conducting principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4? |
Suppose a SABR model framework (with $\beta=1$)
$$dF_t=\sigma_t S_t dW^{S}_{t}$$
$$d\sigma_t=\alpha \sigma_t dW^{\sigma}_{t}$$
$$dW^{S}_{t}dW^{\sigma}_{t}=\rho dt$$
I know that the Implied Volatility induced by SABR model can be expressed in a very readable way, by the following equation:
$$\sigma^{SAB... |
Is there a closed form solution for the vector weight $w$ for the following mean-variance optimization problem?
$\max_w w'\mu - \frac{\gamma}{2}w'\Sigma w $
s.t.
$w'z\geq \bar{z}$
where $w, z$ are N x 1 vectors, $\bar{z}$ is a constant, $\Sigma$ is a variance-covariance matrix, that is symmetric and posit... |
I like the ideas above but I am wondering why the obvious approach, likelihood, hasn't been mentioned in these answers?
I benchmark dozens of approaches and also the portfolio implications, and I'm finding that likelihood isn't a bad predictor of utility for the latter.
I mean the posterior gaussian likelihood ... |
A more apples to apples comparison would be between (i) Fama-Macbeth procedure and (2) clustering standard-errors by date. Adding fixed-effects is somewhat different.
### Problem: cross-sectional correlation causes naively computed standard errors to be understated
Let $r_{it}$ denote the return of firm $i$ in mon... |
I am seeing two formulas:
1. $gamma = 0.5 * gamma * (stock price ^ 2)
2. $gamma = gamma * (stock price ^ 2)
Not sure where this 0.5 term is coming from.
And also, what is the correct definition of dollar gamma?
1. Change in dollar delta for 1% move in the underlying price move.
2. Additional dollar am... |
I am seeing two formulas:
1. $gamma = 0.5 * gamma * (stock price ^ 2)
2. $gamma = gamma * (stock price ^ 2)
Not sure where this 0.5 term is coming from.
And also, what is the correct definition of dollar gamma?
1. Change in dollar delta for 1% move in the underlying price move.
2. Additional additiona... |
The most dangerous concept is hidden in the underlying rules of mathematics, not economics or finance. Many of the other posts only exist because this concept exists. I know because it took me forever to figure out why it was the real problem.
In the underlying rules of calculus, there is a non-hidden, but not wel... |
I am trying to understand the cross-sectional regression methology of Fama MacBeth in the setting of monthly returns with time lags. I was reading "Seasonality in the cross-section, Steven L. Heston and Ronnie Sadka". On page 4 they write: We apply the cross-sectional regression methodology (Fama and MacBeth, 1973; Fam... |
If the var-covar matrix for equities takes the return on equity prices, what should the var-covar matrix for credit derivatives (like a CDS) take?
Should it be the probability of default, since that usually determines the prices of the credit derivatives?
I'm not sure on what would be the equivalent of equity re... |
I am trying to understand the cross-sectional regression methology of Fama MacBeth in the setting of monthly returns with time lags. I was reading "Seasonality in the cross-section, Steven L. Heston and Ronnie Sadka". On page 4 they write: We apply the cross-sectional regression methodology (Fama and MacBeth, 1973; Fam... |
Here is how I remember it: In the famous paper by Carr and Madan *Towards a theory of volatility trading* the term $\frac{\Gamma S^2}{2}$ is referred to as "half the dollar gamma" so the dollar gamma is $\Gamma S^2$. Carr was the world's foremost expert on volatility trading (RIP) and the main result in that paper is w... |
I am reading the book Machine Learning for Algorithmic Trading by Stefan Jansen. And there is a file called filing_index.csv, which contains index information of some SEC filings. It can be accessed via the following link.
https://github.com/stefan-jansen/machine-learning-for-trading/blob/main/data/sec-filings/filin... |
What is the possible source of this filing_index.csv? |
I am reading the book Machine Learning for Algorithmic Trading by Stefan Jansen. And there is a file called filing_index.csv, which contains index information of some SEC filings. It can be accessed via the following link.
https://github.com/stefan-jansen/machine-learning-for-trading/blob/main/data/sec-filings/filin... |
Where can I download a complete list of US OTC stocks? https://www.nasdaqtrader.com/trader.aspx?id=symboldirdefs only has lists of exchange-listed stocks, not OTC stocks. There is FINRA's OTC [Symbol Directory][1] and OTC Markets' [Company Directory][2], but these lists are not available for download.
[1]: https... |
For any time $t$ I did an OLS so that for any $t$ I got $\gamma_{1,t}$. After doing this for all times I computed
$$\hat{\gamma}_1 = \frac{1}{T}\sum_{t=1}^T \gamma_{1,t}.$$
I can do the same computation for several monthly time lags. Do they give me some kind of interpretation, so if I plot $\hat{\gamma}_1$,...,$\... |
The primary quant skill needed to make the market is **optimal control** (a typical paper is [Guéant, O., L, and J. Fernandez-Tapia (2013, September). Dealing with the inventory risk: a solution to the market making problem. Mathematics and Financial Economics 4 (7), 477-507][1]), because you need to control your inven... |
I have a correlation matrix that I wanted to convert into a variance covariance matrix. I also have the weights in a column in excel along with each assets standard deviation. What excel function can I use to get a variance covariance matrix or portfolio standard deviation if I only have the correlation matrix with wei... |
The first step in the Black-Litterman method is to find the "implied market returns" (the prior). Usually this is calculated as: PI = lambda * SIGMA * w, where PI is the vector of returns "implied by the market", w is the vector of market weights (each element = security market cap / total market cap), SIGMA is the cov... |
I am looking to run weight portfolio simulations, but I would like to fixed the weight of one asset and set lower/upper bound limits for the remaining assets.
I have only been using Python for a couple of months.
Below is the standard code I found to run simulated asset weights. It works great; but I want to see... |
I am looking to run weight portfolio simulations, but I would like to fix the weight of one asset and set lower/upper bound limits for the remaining assets.
I have only been using Python for a couple of months.
Below is the standard code I found to run simulated asset weights. It works great; but I want to see h... |
I bought put options on RSX expiring March 11 2022. I want to sell them for cash and profit! I don't want RSX shares!
6 hours ago, my brokerage emailed me that I cannot sell or exercise my puts. What will happen on expiration, if trading on RSX is still halted? Will my puts expire 100% worthless at $0?
If I rec... |
If RSX is still halted on expiration, what shall happen to my puts on RSX? |
Based on Merton model of credit risk, I understand that investing in a risky debt is the same as buying a treasury bond and writing a put option on the firm's assets with a strike price equal to the face value of the debt. And the the equity is a call option on the assets of the borrowing firm with a strike price equal... |
By formla (14) in Merton (1974) the difference of the yield to maturity $R(\tau)$ of the firms risky debt and the riskless rate $r$ is
$$\tag{14}
R(\tau)-r=\frac{-1}{\tau}\log\Big\{\Phi[h_2(d,\sigma^2\tau)]+\frac{1}{d}\Phi[h_1(d,\sigma^2\tau)]\Big\}
$$
where $\tau$ is the time to maturity, and
\begin{align}
d&=Be... |
By formula (14) in Merton (1974) the difference of the yield to maturity $R(\tau)$ of the firm's risky debt and the riskless rate $r$ is
$$\tag{14}
R(\tau)-r=\frac{-1}{\tau}\log\Big\{\Phi[h_2(d,\sigma^2\tau)]+\frac{1}{d}\Phi[h_1(d,\sigma^2\tau)]\Big\}
$$
where $\tau$ is the time to maturity, and
\begin{align}
d&=... |
I'm reading a book that states that PO mortgages go up when interest rates go down as the prepayment happens faster.
I'm confused whether prices go up on PO bonds or yields go up?
|
PO (Principal only) mortgages - Does Price or yield go up when interest rates go down? |
By formula (14) in Merton (1974) the difference of the yield to maturity $R(\tau)$ of the firm's risky debt and the riskless rate $r$ is
$$\tag{14}
R(\tau)-r=\frac{-1}{\tau}\log\Big\{\Phi[h_2(d,\sigma^2\tau)]+\frac{1}{d}\Phi[h_1(d,\sigma^2\tau)]\Big\}
$$
where $\tau$ is the time to maturity, and
\begin{align}
d&=... |
Assume we have a system that is built on the CDS spread values. If we want to shock the system, how can we define the shock? For instance, we can define it as the increase in the spread. Of course a threshold should be decided for this. What are other ways to define the shock? |
By formula (14) in Merton (1974) the difference of the yield to maturity $R(\tau)$ of the firm's risky debt and the riskless rate $r$ is
$$\tag{14}
R(\tau)-r=\frac{-1}{\tau}\log\Big\{\Phi[h_2(d,\sigma^2\tau)]+\frac{1}{d}\Phi[h_1(d,\sigma^2\tau)]\Big\}
$$
where $\tau$ is the time to maturity, and
\begin{align}
d&=... |
I am currently in the process of developing an interest rate model that would be used to price mortgage-backed securities and develop an OAS estimate. Referring to Brigo and Mercurio (2006) I'm focusing on two-factor models instead of one-factor to overcome the 'basic' assumption that all rates on the term structure ar... |
Is the G2++ model apt to use when one needs estimates of longer term refinance rates for mortgages and can the model be created with Monte Carlo? |
I'm reading a book that states that PO mortgage bonds go up when interest rates go down as the prepayment happens faster.
I'm confused whether prices go up on PO bonds or yields go up?
|
PO (Principal only) mortgage bonds - Does Price or yield go up when interest rates go down? |
[![enter image description here][1]][1]
[![enter image description here][2]][2]
The reference is Fixed Income Securities by Pietro Veronesi.
As you can see, In Table 20.5 when the maturity is 1.25, the LIBOR Discount is 96.7402
However In Table 20.3 with same maturity, the continuous compounding discount is 96.... |
Why LIBOR discount and continuous compounding discount are different? |
The answer lies in the derivation of the VIX, as implemented by the CBOE.
The basic derivation of the VIX was done by Demeterfi et al. ([1999][1]), where they used a "basket" of options to replicate expected future variance. This yields the formula:
$$\begin{aligned}
\mathbb{E}[\mathbb{V}] =& \frac{2}{T} \left[ rT... |
The answer lies in the derivation of the VIX, as implemented by the CBOE.
The basic derivation of the VIX was done by Demeterfi et al. ([1999][1]), where they used a "basket" of options to replicate expected future variance. This yields the formula:
$$\begin{aligned}
\mathbb{E}[\mathbb{V}] =& \frac{2}{T} \left[ rT... |
I am trying to connect some dots in my understanding between 2 concepts.
Utility function: I can see there there are different utility functions and I can draw them at different levels until I find one that is touching the efficient frontier, call it point A. That will define a portfolio that is optimal for a given ... |
Here is an interview question:
>For a double knock out barrier option (ITM), which model gives higher price? local vol or stochastic vol model?
The answer is that local vol gives the higher price. However I only know that stochastic vol is the correct model to price barrier option to control the forward vol (vol of... |
Please have a look at this image, which I have copied from [here](https://people.duke.edu/~charvey/classes/ba350_1997/capm/capm.htm):
[![enter image description here][1]][1]
Here, the point **M** is the tangency portfolio of the capital market line.
As you can see, the investor A (left hand side) can attain hi... |
This is an interview question:
Imagine you have a double knock-out barrier option: the current spot is 100, the lower barrier is 80, and upper barrier is 120. The barrier is continuous, meaning that once the spot goes out side the range of 80-120 anytime before time to maturity, you got nothing. If the spot stays with... |
I am trying to do a standard realized volatility calculation in python using daily log returns, like so:
```
window = 21
trd_days = 252
ann_factor = window/trd_days
rlz_var = underlying_df['log_ret'].rolling(window).var() * ann_factor
rlz_vol = np.sqrt(rlz_var)
```
I am essentially getting a realized vol ... |
I am trying to do a standard realized volatility calculation in python using daily log returns, like so:
```
window = 21
trd_days = 252
ann_factor = window/trd_days
rlz_var = underlying_df['log_ret'].rolling(window).var() * ann_factor
rlz_vol = np.sqrt(rlz_var)
```
I am essentially getting a realized vol ... |
Assume $(X_t)_{t\geq 0}$ follows an SDE of the form:
$$dX_t = a(t, X_t) dt + b(t, X_t) dW_t$$
where $W$ is a standard $n$-dimensional Brownian motion, $a$ and $b$ are mappings from $\mathbb{R}_+\times\mathbb{R}^n$ to respectively $\mathbb{R}^n$ and $\mathcal{M}_{\mathbb{R}}(n,n)$ with all the usual regularity conditi... |
Assume $(X_t)_{t\geq 0}$ follows an SDE of the form:
$$dX_t = a(t, X_t) dt + b(t, X_t) dW_t$$
where $W$ is a standard $n$-dimensional Brownian motion, $a$ and $b$ are mappings from $\mathbb{R}_+\times\mathbb{R}^n$ to respectively $\mathbb{R}^n$ and $\mathcal{M}_{\mathbb{R}}(n,n)$ with all the usual regularity conditi... |
I'm more of a rates person than equities, but i'll give it a shot: first of all one assumes that both models have been calibrated so that vanilla options at all strikes and maturities are aligned, otherwise the question doesn't make sense. Since European digital options are the limit of European call spreads, it must ... |
Assume $(X_t)_{t\geq 0}$ follows an SDE of the form:
$$dX_t = a(t, X_t) dt + b(t, X_t) dW_t$$
where $W$ is a standard $n$-dimensional Brownian motion, $a$ and $b$ are mappings from $\mathbb{R}_+\times\mathbb{R}^n$ to respectively $\mathbb{R}^n$ and $\mathcal{M}_{\mathbb{R}}(n,n)$ with all the usual regularity conditi... |
I'm more of a rates person than equities, but i'll give it a shot: first of all one assumes that both models have been calibrated so that vanilla options at all strikes and maturities are aligned, otherwise the question doesn't make sense. Since European digital options are the limit of European call spreads, it must ... |
I would recommend to have a look at: https://www.youtube.com/channel/UC9RbRnYPhO9lpiY-6wWNHWg
It is quite long but worth it. It covers exactly the topic you are looking for.
More precisely, this playlist: https://www.youtube.com/playlist?list=PLJ9XZsVSloaTwgPWr4k0iYH7ahdM5WtEr
from video 23 onwards. |
I would like to sort companies according to the Fama-French 48 industry levels. For that, I need the Compustat Standard Industrial Classification (SIC) code. In the web interface of WRDS, I could simply select the field SIC. However, I need to get the compustat data via an SQL query but comp.funda does not have an entr... |
I have a set of 7 assets, and I have run an ADF test on all possible pair-spreads to find possible pair strategies. I am creating the spreads using a rolling window in which I run linear regression to find the hedge ratio.
It seems that when the rolling window is large/long, few spreads are stationary. But as I dec... |
Pairs Trading - isn't any spread stationary if your rolling lin-reg window is small enough? |
I have a set of 7 assets, and I have run an ADF test on all possible pair-spreads to find possible pair strategies. I am creating the spreads using a rolling window in which I run linear regression to find the hedge ratio.
It seems that when the rolling window is large/long, few spreads are stationary. But as I dec... |
I'm learning about copulas and their applications in finance. When used to assess the dependence structure between two indices for example, can the copula models be estimated directly on the log-returns or should they undergo, that is the log-returns, some transformation then estimating the copula models on the said tr... |
The Kelly criterion for the discrete case is:
$$\tag{1}f=\frac{pW-(1-p)L}{LW}$$
where $f$ is the fraction of wealth to invest, $p$ the probability of winning, $(1-p)$ the probability of losing, $W$ the return if win, $-L$ the return if loss.
The continuous case is:
$$\tag{2}f=\frac{E[r]}{V(r)}$$
where $E[r]$ is ... |
If asset allocation decisions were made prior to the news of unanticipated inflation, how should asset allocators incorporate the fact the inflation is now 5% higher than the 2% inflation target?
It seems that a 60:40 Equity:Bonds allocation was miraculously persistent during the 40 year period of declining interest... |
Given that the price of market risk (or market price of interest rate risk) is $\lambda(r_t, t)=0$ and that we have the following dynamics of the interest rate (under the physical measure $P$.
$$dr_t = \sigma dW_t^P \quad , \quad \sigma \in \mathbb{R}, \; W_t \text{ is a Wiener Process}.$$
If we furhter more hav... |
I have been wondering how the following situation is / should be implemented.
Consider some kind of surface $z = f(x,y)$ which has to be pre-calculated; the shape of this surface would not have a closed-form solution, but would instead be calibrated by some time-consuming numerical methods, which are updated asynchr... |
How do people 'lookup' values from calculated surfaces? |
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