# All Questions

217 views

### Min VaR and Min TE as second order cone program

The quadratic optimization (min variance) $$w^{T} \Sigma w \rightarrow \text{min},$$ where $w$ is the vector of portfolio weights and $\Sigma$ is the covariance matrix of asset returns, is a well ...
6k views

### How to simulate stock prices with a Geometric Brownian Motion?

I want to simulate stock price paths with different stochastic processes. I started with the famous geometric brownian motion. I simulated the values with the following formula: ...
916 views

### Optimizing a portfolio of ETFs

I am aware of how to do mean-variance or minimum-variance portfolio optimization with constraints like weights must add to 1.0 no short sells max weight in any ticker using basic quadratic ...
676 views

### How to simulate correlated assets for illustrating portfolio diversification?

I have seen multiple instances where people try to explain the diversification effects of having assets with a certain level of correlation, especially in the "most diversified portfolio" literature. ...
1k views

### How to extrapolate implied volatility for out of the money options?

Estimation of model-free implied volatility is highly dependent upon the extrapolation procedure for non-traded options at extreme out-of-the-money points. Jiang and Tian (2007) propose that the ...
759 views

### Recommendation for a library to calculate the local volatility surface?

I'd like a library to calculate the options local volatility surface, i.e. the options implied volatility surface for a collection of strikes and their bid/ask prices. Here are the libraries I've ...
1k views

### Quantmod: what's the difference between ROC(Cl(SPY)) and ClCl(SPY)

I feel like I'm missing something fundamental here, but I can't shake the feeling that these two series should be equivalent. /edit: there is also dailyReturn(Cl(SPY)). I've seen all 3 of these ...
506 views

### SKEW and VIX relations?

My question is about the CBOE published index VIX and SKEW. To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston ...
360 views

### Should cointegration be tested using close or adjusted close prices?

When doing cointegration tests should I use the adjusted close price or just close price for the time series? The dividend of each stock is on different dates and can cause jumps in the data.
19k views

### How to calculate unsystematic risk?

We know that there are 2 types of risk which are systematic and unsystematic risk. Systematic risk can be estimate through the calculation of β in CAPM formula. But how can we estimate the ...
1k views

### Drawdown calculation for strategies

I am developing a trading strategy for currencies. I am trying to find an indication for risk, something like Sharpe ratio or Sterling ration; for that, I thought of using the (maximum) drawdown ...
761 views

### Why isn't the Nelson-Siegel model arbitrage-free?

Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e. $$dX_t=\sigma dB_t-AX_tdt$$ and the spot interest rate evolves by the following equation: $$r_t=a+b\cdot X_t.$$ After solving for $X_t$ ...
1k views

### Why are options trades supposed to be delta-neutral?

I'm reading Natenberg's book, and he says that all options trades should be delta neutral. I understand that this prevents small changes in the underlying price from changing the price of the option, ...
349 views

### How to “uncluster” a set of financial data?

I am attempting to evaluate and compare the profit factor of different "test runs" of a FOREX trading strategy. My problem is that, despite an average time between orders of 2hr+, some of these runs ...
593 views

### Quantitative before/after or financial engineering studies of a bid or ask tax?

Has anyone in the quantitative finance or financial engineering community studied the effects of a bid or ask tax with actual or simulated data? If so, what were the quantitative results or ...
512 views

### What is a reasonable upper bound on the performance of a daily trading strategy?

I am backtesting an equity trading strategy which trades only once per day. Is there a general rule of thumb for the reasonable upper bound on the rate of return of such a strategy? For example, a ...
748 views

### What commercial financial libraries are available to outsource implementation risk?

During our daily jobs as quants, we tend to be willing to develop all the quantitative libraries ourselves. While I know that we need to develop specific algorithms which are the foundations of our ...
1k views

### Limit order book size

I am trying to write a highly optimised limit order book and I wondered what sort of size I can expect for: Range of limit prices Number of orders at each limit price I am developing custom ...
716 views

### Threshold calculation for buying a mean-reverting asset

I am trying to figure-out an optimal policy for buying a unit when its price follows a mean-reverting price process (Ornstein–Uhlenbeck), when I have a finite time deadline for buying the unit. I ...
649 views

### What are the steps to perform properly a risk factor analysis on a portfolio?

I have been asked to perform a factor analysis on a given portfolio, assume it's a Swiss portfolio in CHF. First step, I chose which factors I would like to see in my analysis. The first factors I ...
303 views

### How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?

I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
682 views

### Closed-form formula for approximate maximum duration of a bond?

In teaching myself about bonds, I am writing some software, one piece of which will calculate the maturity of a bond given the yield curve as a function and a requested duration. The tricky part is ...
1k views

### Cluster analysis vs PCA for risk models?

I built risk models using cluster analysis in a previous life. Years ago I learned about principal component analysis and I've often wondered whether that would have been more appropriate. What are ...
2k views

### Analyzing tick data

What are some of the commonly used techniques to analyze tick data? I am looking at tick data to see how the quotes/ mid-price evolves due to certain events in the market. Since tick data is ...
153 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 ...
122 views

### Good criteria to sort state-space $\beta_{t}$ according to Kalman filter output

Let the usual state-space linear model (without constant term for the sake of simplicity): $y_{t}=\beta_{t} X_{t}+\epsilon_{t}$ If we use Gaussian Kalman filter to estimate $\beta_{t}$ we get ...
365 views

### Why should there be an equity risk premium?

After years of mathematical finance I am still not satisfied with the idea of a risk premium in the case of stocks. I agree that (often) there is a premium for long dated bonds, illiquid bonds or ...
423 views

### Debunking risk premium via “hedging” argument? (or why even in the real world $\mu$ should equal $r$)

Since I began thinking about portfolio optimization and option pricing, I've struggled to get an intuition for the risk premium, i.e. that investors are only willing to buy risky instruments when they ...
3k views

### Utility to download historical Implied Volatility data from Interactive Brokers?

Does anyone know of a utility that can download historical Implied Volatility (IV) data from Interactive Brokers' Trader Workstation?
714 views

### How is historical data for forex collected or computed?

I'm looking at four sources of forex data, as compiled in the question, What data sources are available online? And I think I must be misunderstanding something, perhaps something fundamental, but I'm ...
2k views

### Data source for historical Share Outstanding totals for individual stocks?

Data is normally adjusted for splits/reverse splits, etc. The current shares outstanding is usually available. Is there a data repository that captures the shares outstanding for any point in the ...
860 views

1k views

### how do we estimate position of our order in order book?

how would you estimate your order in the exchange order book? The order of order events and acks is not deterministic or guaranteed. How could you write an algo to estimate accurately your position in ...
479 views

### What research is available on the performance of convertible bond arbitrage models?

The basic principles of convertible bond arbitrage have been clear at least since Thorp and Kassouf (1967). For those who are not familiar, the arbitrage entails purchasing a convertible bond and ...
267 views

### What is a cubature scheme?

Ideally an intuitive explanation with an example, please.
The Black-scholes formula typically has time as $\sqrt{T-t}$ or some such. My questions: What is the granularity of this? If we treat $t$ as the number of days, then logically on the day of expiry, ...