# All Questions

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### R code for Ornstein-Uhlenbeck process

Can any one help me with some R code to run Ornstein-Uhlenbeck process?
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### Best way to store hourly/daily options data for research purposes

There are quite a few discussions here about storage, but I can't find quite what I'm looking for. I'm in need to design a database to store (mostly) option data (strikes, premiums bid / ask, etc.). ...
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### Has spectrum analysis ever been used successfully to analyse historical price data?

Spectrum analysis is often used to analyse waveforms. A common configuration, for example, is to create a graph where X is time, Y is frequency, and the brightness of each position represents ...
21k views

### What is the Swap Curve?

What is the so-called Swap Curve, and how does it relate to the Zero Curve (or spot yield curve)? Does it only refer to a curve of swap rates versus maturities found in the market? Or is it a swap ...
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### Fundamental Theorem of Asset Pricing (FTAP)

In the spirit of canonical questions please state here versions of the FTAP in the following form (please only one theorem by answer) : Necessary definitions (or a direct link to definitions) ...
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### Why are there still manual market makers in options

Why are manual market makers still predominant in options markets? Why haven't algorithms replaced these market makers, as they have for liquid stocks for example?
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### Optimal execution strategy

Can someone shed some light on optimal ways to execute medium sized orders ~2000 shares in the market? Unfortunately the execution algo I have access to is very dumb. It follows the top-of-book ...
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### Can you fully hedge an option in the presence of counterparty risk?

The derivation of the Black-Scholes model assumes no counterparty risk. Does the presence of counterparty risk invalidate the argument behind the model? EDIT: The question is about options in general,...
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### How can higher co-moments be applied to portfolio optimization in an asset allocation context?

Traditional portfolio optimization involves mean variance optimization, where only the mean and covariance matrix of returns are estimated. What asset allocation and portfolio optimization techniques ...
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### robust portfolio optimization re-balancing with transaction costs

The optimal re-balancing strategy takes account of factors including i) objective function, ii) current portfolio weights, iii) expected return vector containing updated views/alpha forecasts, iv) ...
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### better estimator of volatility for small samples

One commonly used sample estimator of volatility is the standard deviation of the log returns. It is indeed a very good estimator (unbiased, ...) when the sample is large. But I don't like it for ...
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### What is a commonly accepted econometric model for volume?

What is the gold standard econometric model for volume? For example, a common model for price is the autoregressive (AR) model with GARCH(1,1) innovations. Do you know of any good survey articles ...
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### How to interpolate gaps in a time series using closely related time series?

I am trying to construct a daily time series of prices and returns for some large universe of securities. However, all I have available are a monthly time series of the prices/returns (as well as ...
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### What is the precision of standard deviation estimates with small samples?

I was asked today to "quantify" the precision of an estimated the standard deviation from a small sample, I was not sure how to answer. The case is quite simple, I have a sample of $n=25$ measures (...
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### How do I calculate the skewness of a portfolio of assets?

I need to calculate the skewness of a portfolio consisting of 6 assets. I know that for that I would need the co-skewness matrix between the assets. Does anybody know the formula for co-skewness or ...
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### How can one compute the Greeks on VIX Futures

I am guessing the short answer to this question is "use the chain rule and linearity of the derivative," but I am looking for more specific advice on how to compute the derivatives of a VIX futures ...
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### Deterministic interpretation of stochastic differential equation

In Paul Wilmott on Quantitative Finance Sec. Ed. in vol. 3 on p. 784 and p. 809 the following stochastic differential equation: $$dS=\mu\ S\ dt\ +\sigma \ S\ dX$$ is approximated in discrete time by ...
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### So many volatility models. Any comparisons of them?

Are there any papers that make an explicit contrast/comparison of the following (or other) vol models in terms of the suitability for addressing some empirical problem? Wavelet multiresolution ...
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### How does one measure the effect of latency on potential returns?

I am looking to evaluate the hypothetical advantage one trading system has over another in terms of the possible returns given their latency. Irene Aldridge wrote a piece (How Profitable Are High-...
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### What is an efficient data structure to model order book?

What is an efficient data structure to model order book of prices and quantities to ensure: constant look up iteration in order of prices retrieving best bid and ask in constant time fast quantity ...
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### What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?

Is there any relationship between the risk aversion coefficient in an individual's utility function (commonly used in portfolio optimization) and the preference for higher moments such as skewness and ...
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### How can I learn about the quantitative aspects of market making in illiquid single stock options?

I would like to learn more about the possible ways of doing quantitative research regarding option market making. In particular, while the mainstream index option market may be very liquid, the ...
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Using total return calculations is critical in developing security selection models. The standard way to measure total return is to develop a series of price-adjusted data. Investopedia describes the ...
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### How to detect structural breaks in variance?

I'm looking for a method to automatically detect structural breaks, I tried Chow test, It works good but it doens't work for breaks in variance. Do you know a test to check strucutural break in ...
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### How to simulate slippage

I'm backtesting a trading strategy, using free OHLC data from yahoo or google. I'm simulating friction by lopping a flat percentage (say 0.5%) off my returns for each day that I make a trade. Whats ...
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### When is the LIBOR market model Markovian?

The question is inspired by a short passage on the LMM in Mark Joshi's book. The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. ...
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### Estimation of Geometric Brownian Motion drift

One can find many papers about estimators of the historical volatility of a geometric Brownian motion (GBM). I'm interested in the estimation of the drift of such a process. Any link on this topic ...
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### Literature on generating synthetic time series for testing

I have some market data (daily time series) for bond prices and CDS indices and I would like to generate synthetic versions of these which are statistically "similar" for testing trading strategies. ...
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Are there any free c++ libraries that would have some of the functions that would be used in developing a trading strategy. For instance, calculating drawdown, Volatility Forecasting, MAE, MFE....etc. ...
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### How would you test the hypothesis “There are no idiosyncratic returns available in the market”?

A commentary attributed to Matt Rothman had recently (in the past six months) been making the rounds of the internet echo chamber claimed "There are no idiosyncratic returns available in the market". ...
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### Discrete returns versus log returns of assets

There have been similar posts here already but nevertheless I find the question worth posting: why do some people claim that log returns of assets are more suitable for statistics than discrete ...
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### What benchmark/index to use for backtesting a portfolio of stock options?

What benchmark should I use for backtesting a model for when I should buy an option of a particular stock? For equities, one could say their portfolio outperformed the S&P 500. I would like to ...
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### How do I eliminate developed currency funding cross rate risk in an EMFX position?

Back in the "old days" (ie 5-10 years ago) when we wanted to be long or short an emerging currency (say the ZAR, BRL, or TRY) we simply did everything against the pre-eminent currency of the day, the ...
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### Solving Path Integral Problem in Quantitative Finance using Computer

I've asked this question here at Physics SE, but I figured that some parts would be more appropriate to ask here. So I'm rephrasing the question again. We know that for option value calculation, path ...
455 views

### Is there a website that lists replication code of financial papers?

There are lot of questions on this website related to the replication of the empirical part of financial papers. I noticed that some (honest) authors provide on their personal website some ...
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### What mathematical models did Harry Markopolos run to prove that Bernie Madoff 1% a month gain was a Ponzi scheme?

http://www.cbsnews.com/news/the-man-who-figured-out-madoffs-scheme-27-02-2009/ Asked how long it took him to figure out something was wrong, Markopolos said, "It took me five minutes to know ...
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### How to generate synthetic FX data for backtesting?

I want to generate synthetic forex data for the purpose of backtesting my trading algorithms. I have some rough ideas in mind on how to do this: Start with a curve representing a trend, then randomly ...
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### Easiest and most accessible derivation of Black-Scholes formula

I am preparing a QuantFinance lecture and I am looking for the easiest and most accessible derivation of the Black-Scholes formula (NB: the actual formula, not the differential equation). My favorite ...
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### What are some computational bottlenecks that quants face? [closed]

What are the current computational (non-network) bottlenecks now in a quant's workflow? What computational tasks would be revolutionary with a 10-100x improvement in performance using general purpose ...
6k views

### Earnings and valuation data sources online

Are there any free/cheap sources for historical data on company earnings and valuations? I can get historical price data from Google and Yahoo, and it looks like I can get about five years of ...
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### Enhancing Monte-Carlo convergence (crude method)

I am currently doing a project involving Monte-Carlo method. I wonder if there is papers dealing with a "learning" refinement method to enhance the MC-convergence, example : Objective : estimate of \$...
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### Does entropy pooling apply to distributions with time-varying drift?

I have a returns process that is drawn from a normal distribution with a nonlinear time-varying drift, so I was wondering if the entropy pooling method still applies or if I need an invariant ?
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### How to estimate probability of default from bond prices?

How do you use bond prices/yields to infer probabilities of default? I would think of it as follows: Create a relationship between default free (e.g., Germany) and defaultable (e.g., Greece) bond ...
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### Currency Hedged ETFs

At work we were talking about currency hedging our equity index exposures but I am struggling to understand how this happens in a typical iShares ETF. If we take the Japan ETF IJPN then we see this ...
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### Correctly applying GARCH in Python

Problem: Correct usage of GARCH(1,1) Aim of research: Forecasting volatility/variance. Tools used: Python Instrument: SPX (specifically adjusted close prices) Reference material: On Estimation of ...
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### What is the best live options data API?

What is the best/cheapest service to get real-time (as real-time as you can get) on stock options? I'm looking for the fastest update on the ENTIRE market, with a few stocks prioritized, so I need ...
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### Quantitative Derivatives Trading vs. Time

Most quantitative investment strategies focus on the changing prices of a commodity or equity over time. Derivatives, however, make this more complicated. How can I apply quantitative strategies to ...