# All Questions

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### 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 ...
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### 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 ...
671 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 ...
565 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 ...
289 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 ...
663 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 ...
788 views

### What is the mean and the standard deviation for Geometric Ornstein-Uhlenbeck Process?

I am uncertain as to how to calculate the mean and variance of the following Geometric Ornstein-Uhlenbeck process. $$d X(t) = a ( L - X_t ) dt + V X_t dW_t$$ Is anyone able to calculate the mean ...
1k 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 ...
702 views

### How to make the final Interpretation of PCA?

I have question regarding final loading of data back to original variables. So for example: I have 10 variable from a,b,c....j using returns for last 300 days i got return matrix of 300 X 10. ...
4k 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: ...
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### 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 ...
2k views

Does anyone know of a utility that can download historical Implied Volatility (IV) data from Interactive Brokers' Trader Workstation?
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### 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 ...
532 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 ...