# All Questions

124 views

### Finding the dynamics of a dividend paying asset under arbitrary numeraire

Assuming I have a dividend paying asset $S$ with dividend process $D$. Now I would like to use the bank account process $B$ as numeraire and determine the dynamics of $S$ under the the corresponding ...
320 views

### Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
3k views

### Difference between S&P 500 index and S&P 500 Total Return index?

There's the standard S&P 500 index (SPX) and the rarer used S&P 500 Total Return index (SPTR). If you compare graphs, you'll find that the latter grows faster. Supposedly, SPTR assumes ...
266 views

### Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$w^T \Sigma w + w^T c \rightarrow Min$$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{R}^N$ and ...
177 views

### How can I introduce exogenous variables in the equation of the conditional variance?

Is it possible to introduce dummy variables or explanatory variables in the GARCH variance equation (garchset and garchfit).This is done in the mean (ARMAX) equation through the input 'Regress' in ...
529 views

### Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed ...
332 views

### Is this methodology to calculate Alpha using multi-factor regression model correct?

I am trying to find out Historical Alphas of a bunch of fund returns ${F_i}$ by Using Regression Model$(stepwise)$ with regressors as its underlying exposure-returns(risk-free rate subtracted) i.e. ...
537 views

### Testing Valuation, Size and Momentum (proprietary factors) from 1988-2013: No evidence of driving cross-sectional returns

I am currently testing whether three proprietary factors - Valuation, Size and Momentum - explain cross-sectional returns. A sample of 3000 securities was tested using Fama-MacBeth two-pass ...
89 views

### Risk neutral measure in exponential levy model

Is there a method of finding a risk-neutral measure for assets driven by the levy process? I understand there is the esscher transform but I think it tends to transform the processes into ...
152 views

### How to price an option with two volatilities?

Imagine you have two volatilities, the second which is "activated" when the stock crosses a barrier called $p_b$. The present price is $p_1$. ($p_b>p_1$). This can be used to price options after a ...
360 views

### Shrinkage Estimator for Newey-West Covariance Matrix

I like to apply the Newey-West covariance estimator for portfolio optmization which is given by $$\Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right),$$ where $\Sigma(i)$ is the lag ...
96 views

### Simple way to get the crossing probabilities of a moving barrier

Hello Quant Finance StackExchange, Is there a simple way to find the crossing probabilities of a moving barrier, namely a barrier written in the form $U(t)=\alpha_1t^2 + \beta_1t + \gamma_1$ and ...
157 views

### ERP and FF 3-factor model

In a more conservative estimate than a simple historical average, Fama & French estimate (US) equity risk premium at 3-4% (e.g., Equity Risk Premium, JF, 2002). This suggests that in an APT-like ...
148 views

### Is it random walk?

I would like to ask a question about random walk. Campbell, Lo & Mackinlay defined the random walk, in the following way (RW3): $$cov[f(r_{t}),g(r_{t+k})]=0,\qquad k\neq0$$ for all $f(\cdot)$ ...
315 views

### Rate Distortion Minimization in a Python Clustering Algorithm

I'm attempting to solve for $\hat{k}$ clusters, such that the rate distortion is minimized, as described here, however, the answers that I am getting from my algorithm are not following the "Jump" ...
267 views

### Quant/Stat Factor Performance Website/Distribution?

Does anyone know of a decent quant/stat factor website, distribution(public or private) or publication that tracks performance of "many" of traditional quant/stat factors? By that I mean would show ...
491 views

### How to determine ratios for mean-reverting basket

Suppose I have a basket of 3 securities A, B, and C. I believe that the basket is cointegrated and I want to create a mean-reverting trade. I fit the model: ...
359 views

### compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
198 views

### is there a mapping from Altman Z-score for private companies to bond ratings or probability of default?

On wikipedia, there is a formula to calculate the Altman Z-score for private companies: Z-score estimated for private firms: T1 = (Current Assets − Current Liabilities) / Total Assets T2 = Retained ...
186 views

### Estimation of ranks of log-returns via copula

I have successfully chosen and estimate a copula for the ranks of the log-returns of my actions. My question is, since I have worked with the ranks instead of directly the log-returns (in order to be ...
264 views

### Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
523 views

### Asymmetric Volatility Modeling (Interpretation)

I am currently writing a paper on asymmetric volatility modeling of brent, gold, silver, wheat, soybean and corn from 1986-2012 and divided them into 4 sub-sample periods (i.e. 1986-1991, 1991-1997, ...
506 views

### What makes IRC a market risk?

Since modeling leaves complete freedom we can assume both market and credit risks can enter the picture. However the minimum requirement is (migrations and) defaults simulation, how does this ...
163 views

### Discrete-time Jump-Diffusion Model

I am wondering if anybody could point me to any literature that talks about a discrete time version of the jump-diffusion model, I am aware that there is a paper by Amin (1993) that shows a discrete ...
153 views

### Rolling window Kendall's tau against APARCH(1,1) correlation

Assume you want to forecast the correlation matrix of a stocks' basket (say 15 ~ 20 stocks from different sectors); assume you need to forecast at $T$ days because you will use the forecast ouput with ...
189 views

### How to estimate CAViaR (Engle and Manganelli 2004) using non linear quantile regression?

I am trying to replicate results from Engle and Manganelli (2004). The following is one of their specifications, $q_t(\theta)=\gamma_0+\gamma_1q_{t-1}(\theta)+\alpha|r_{t-1}|$, $q$ is the quantile of ...
160 views

### Is it more accurate to analyze returns on a calendar day basis than a trading day basis?

I'm rather new to the actual practice of this kind of analysis, but it just seems wrong to me to throw Mondays' returns in with the rest without accounting for the passage of time on the weekend when ...
147 views

### Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time ...
175 views

### How companies choose earnings release dates, & effect on Implied Volatility

A company's earnings release date significantly affects weekly or monthly option prices/implied volatility. For companies that typically release earnings on the cusp of monthly options expiration, ...
475 views

### ATM volatility versus OTM volatility and directional standard deviation

The forward instrument vol curve is skewed to the downside (50 delta risk reversal, 25 put, 25 call) were trading several ticks to the put). Is there a smaller standard deviation (in price terms) to ...
712 views

### Help With Quant Modelling Software

Im a software developer (freelance) working in investment banking, and I'm looking to improve my CV by gaining a better understanding of the financial quant role and the software used by quants to ...
199 views

### Taking into account the correlation in Barrier options on a Basket

In a Barrier option (where the contract cancels when the underlying hits the barrier) I succesfully found the way to compute the probability of a single underlying touching the barrier (with constant ...
487 views

### Algorithms for predicting a couple points in the future

I'm familiar with supervised learning algorithms like regression and neural networks which look at a bunch of input points and learn a function which outputs a value (the value varying depending on ...
630 views

### Hasbrouck's information share

Given a cointegrated set of price series, I am trying to compute the Hasbrouck's information share, as described in page 12-13 of this article. page 7-8 of this article I have the vector error ...
169 views

### Use of Local Times in Option Pricing

I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
25 views

I'm trying to find the optimal portfolio of options and stock which minimizes the standard deviation of the portfolio returns but also taking into consideration the bid and ask prices of the assets. ...
78 views

### Bridgewater's Daily Observations

Bridgewater Associates send out Daily Observations to their clients, but I haven't found many traces of these publications online. The series started some 40 years ago by Ray Dalio, and there're just ...
39 views

### Reference Request: Horse Race for Portfolio Allocation

Probably the most popular horse race study for portfolio strategies is Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?, with DeMiguel, L. Garlappi and R. ...
78 views

### How can a beginner trader make use of 'volatility of volatility'

For a beginner option trader in equity options, how can he use this metric that is provided by his broker/data vendor? How can he use this metric to gain an added understanding of the option ...
43 views

### Which kind of normalization to prefer before PCA (generic solution for any factor analysis)

I have financial assets with totally different volatilities, thus I must standardize them before PCA, otherwise, assets with high variance may be considered as principle components, which is wrong. ...
53 views

### How to check that an interest rate curve is arbitrage free

I have 2 interest rate curves (LIBOR 3M and OIS). I want to create stress scenarios for those two curves. Is it possible that some scenarios will make my term structure arbitrageable? How can I test ...
73 views

### How to calculate the JdK RS-Ratio

Anyone have a clue how to calculate the JdK RS-Ratio? Let's say I want to compare the Relative strength for these: EWA iShares MSCI Australia Index Fund EWC iShares MSCI Canada Index Fund EWD ...
56 views

### pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
64 views

### Computing Value at Risk for portfolio in R

I know how to compute VaR with long positions using PerformanceAnalytics. What about a portfolio consisting in two equities A and B, 100 USD long positions in each, and 2 stock options for the same ...
36 views

### How to price lookback american option when its payment is distributed during its life

I would like to price a floating strike american lookback with a particular feature: I don't want to charge upfront the client, rather I would like to insert a "running fee", some sort of a dividend. ...
168 views

### Discrete Trading to reduce speculation

I recently read a paper by Terje Lensberg (2014) "Costs and benefits of financial regulation: Short-selling bans and transaction taxes" where he analyzed the effects of financial regulation (short ...
41 views

### Clarification of Saturation-Reset Regimes

I have worked my way through this article, waiting to get into school I have been self-learning a bit. I have a good grasp on most of the article, but the component strategy of Saturation and Reset ...
43 views

### Dynamic Hedging for a Bond

Sorry if this question is duplicate. Analyzing the scenario to hedge bond credit risk with CDS. but if Bond price changes CDS notional will not change. is there any way i can hedge this ?
Given a wealth process that evolves as $$d w_t = r w_t dt + \theta_t ( \sigma dW_t + (\mu-r) dt) - c_t dt.$$ where $\theta_t$ is the worth of holding at time $t$ and $c_t$ is the consumption stream. ...