# All Questions

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### What is the ideal ratio of in-sample length to out-of-sample length?

Suppose you are running a portfolio of quantitative strategies and that you develop a new potential strategy to be added to the mix. Assume for simplicity that the new strategy is independent of the ...
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### Drawbacks & Caveats of using (N)Esper for ESP/CEP in trading systems?

Esper and its .NET port NEsper are components that enable Complex Event Processing (CEP) and Event Stream Processing (ESP) engines. They are especially suitable for trading applications. They can, ...
1k views

### 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 ...
363 views

### How to account for market movement when some exchanges are closed?

Daily data, such as open and close prices, is often available for much longer periods than high-frequency data. However, whenever backtesting any strategy that examines instruments traded in different ...
2k views

### Is there a standard method for quantifying mean-reversion for use in directional trading?

Assuming a directional strategy (no pairs or spread trades) is there a "standard" method for quantifying mean-reversion? Should auto-correlation, variance ratios, hurst exponent, or some other measure ...
232 views

### 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 ?
382 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 ...
1k views

### Where to find Greeks for futures to form delta-hedged futures portfolio of S&P 500 index/futures

I can't find S&P 500 index (SPX) futures data with Greeks to create delta-hedged portfolios. Do these data exist? I have access to most of the common data sources. In the meantime, I am trying to ...
694 views

### Intuitive explanation of the Hansen-Jagannathan bound

The Hansen-Jagannathan bound states that the maximum Sharpe ratio of a portfolio can't exceed the ratio of the standard deviation of a stochastic discount factor to its mean. I more or less understand ...
733 views

### 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 ...
443 views

### Exploiting breakdowns in correlation of estimated volatility

In the attached image I have a plot of the rolling correlation of 90-day historic volatility (using the Garman Klass estimator based on Sinclair's Volatility Trading) of JPM v. the S&P. As can be ...
1k views

### Simulating Returns

I'll start this off with a rather broad question: I am trying to simulate returns of a large number of assets within a portfolio of different classes - equity and fixed income in a first step, say 100 ...
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### How do you characterize dividends for equity options?

While many systems like to treat dividends as a continuous yield when pricing equity options, it works quite poorly for short-dated options. In the short run, deterministic dividends are clearly the ...
1k views

### How to use macroeconomic indicators for long/short trading strategies?

I am trying to understand how to use macroeconomic data in my trading. I understand that using such data could be used to gauge an overall view of the market and how it's doing as a whole. I have been ...
342 views

### What are the major characteristics of natural gas volatility and options?

Seasonality is a big deal in the natural gas markets. My understanding is that they are broadly divided into summer and winter, with seasonality in both price and the volatility. What does this ...
659 views

### Strictly local martingales: what is the intuition behind them?

A process $X_t$ is a local martingale if for each increasing sequence of stopping times $\{\tau_k,k=1,2,...\}$ the stopped process is a martingale. All true martingales are local martingales, but the ...
307 views

### Portfolios from Sorts

Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios ...
407 views

### How to estimate the following model?

Suppose I have the following model: $$r_t=\sigma_t * \epsilon_t$$ where $r_t$ is the return at time t, $\sigma_t$ is the volatility, the model used to model this volatility is an exponentially ...
423 views

### Stochastic modelling of derivatives on dividends

I consider pricing and risk analysis of derivatives on dividends of the members of equity indices (such as Dow Jones EuroStoxx). There are options but I focus on futures. What are common stochastic ...
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### A non parametric study of VaR with kernel density

I'm working in order to compare the calculation of the VaR between the methodology of copulas and kernel density, all this by using the software r. The process that I follow is: Obtain a sample ...
384 views

### Is Arithmetic Return Bias Basis of Low Vol Anomaly?

An observation in capital markets is that the connection between return and risk (measured as volatility) is not that straightforward (at least not as modern portfolio theory assumes). One interesting ...
423 views

### Creating an n-factor Certainty Equivalent Discounting Formula

Brealey & Myers provide a certainty-equivalent version of the present value rule, using CAPM, as follows: $$PV_0=\frac{C_1 - \lambda_m *cov(C_1, r_m)}{1 + r_f}$$ $PV_0$ - Present Value of cash ...
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### What weights should be used when adjusting a correlation matrix to be positive definite?

I have a correlation matrix $A$ for an equity market that is not positive definite. Higham (2002) proposes the Alternating Projections Method, minimising the weighted Frobenius norm $||A-X||_W$ where ...
388 views

### performance of historical VaR parameters

An historical VaR measure is parameterized in terms of the confidence level and also number of periods. Specifically, the $\alpha$% T-period VaR is defined as the portfolio loss x in market value over ...
1k views

### When to shut down a trend following strategy?

Suppose I have trend following strategy(on close to close data) that is not getting acceptable returns for some time. When should I start thinking about shutting it down?
3k views

### When to use Monte Carlo simulation over analytical methods for options pricing?

I've been using Monte Carlo simulation (MC) for pricing vanilla options with non-lognormal underlyings returns. I'm tempted to start using MC as my primary option-valuating technique as I can get ...
1k views

### Why Ito calculus?

Coming from physics, I am used to the fact that the Ito interpretation of most natural stochastic equations is wrong, and one should be using Stratonovich calculus instead (of course they are ...
3k views

### Why do we use GARCH(1,1) to predict volatility?

What makes GARCH(1,1) so prevalent in modeling especially in academia? What does this model has that is significantly better than the others?
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### What tools are used to numerically solve differential equations in Quantitative Finance?

There are a lot of Quantitative Finance models (e.g. Black-Scholes) which are formulated in terms of partial differential equations. What is a standard approach in Quantitative Finance to solve these ...
708 views

### What are the risk factors in analysing strategies?

What do you think of strategies displayed on timelyportfolio.blogspot.com? I really like the fact that there is some code to reproduce the strategies, but they seem very elementary because he does ...
2k views

### Why is the first principal component a proxy for the market portfolio, and what other proxies exist?

Let's say that I have a universe of stocks from a certain sector. I want to compute the market portfolio of this sector. Beta is the covariance between each stock and the market. But how do you ...
9k views

### Why would an investor trade a variance swap over a volatility swap?

Why would an investor trade a variance swap over a volatility swap? Is it simply related to the leverage involved in a Var (i.e. sigma-squared) or is there something else to it?
2k views

### Order submission strategies of a rational market maker?

Consider a market maker that has decided to try to make a round-trip trade in stock A in order to capture the bid-ask spread. Assume furthermore that he has no current inventory in the stock A. To ...
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### How does volatility affect the price of binary options?

In theory, how should volatility affect the price of a binary option? A typical out the money option has more extrinsic value and therefore volatility plays a much more noticeable factor. Now let's ...
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I am looking for academic articles which model the p&L of market makers. I have read the Ho-Stoll (1984) article. Is there any recent article on this subject?
1k views

### Maximization of CARA utility function: unique solution with an unbounded parameter?

An investor at time $t_0$ can invest his wealth $w_0$ in a risky asset $x$ for an amount $a$ and the remain part in the riskless asset $w_0-a$. At the end of the period $t_1$, the investor will ...
741 views

### 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 ...
2k views

### 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 ...
711 views

### Are e-mini markets manipulated?

Are the prices of e-minis such as S&P 500, Russell 2000, EUROSTOXX, etc. manipulated? That is, are there traders who trade large enough positions to make the price go in the direction they want, ...
540 views

### What is the fair price of this option?

Without having to use Black-Scholes, how do I price this option using a basic no-arbitrage argument? Question Assume zero interest rate and a stock with current price at \1\$ that pays no dividend. ...
2k views

### How to solve for the implied stock lending rate given equity options prices?

When market makers price options on hard-to-borrow equities, they include the cost to borrow the underlying equity that their broker is going to charge them to sell the security short to hedge. I'm ...
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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 ...
3k views

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 ...
3k views

### How to calibrate Hull-White from zero curve?

I am interested in calibrating a Hull-White model to the market. I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to ...
485 views

### How do you estimate the volatility of a sample when points are irregularly spaced?

I was looking again at this question which basically haunts every quant I believe, and I was thinking about the effect of these gaps when computing volatility of the series. Let's define the problem ...
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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 ...
472 views

### Effective Euro-USD (EURUSD) Exchange Rate Prior to Euro's Existence

Motivation: I am running a quantitative analysis that requires long-term, exchange rate data. Problem: Does anyone have methods for dealing with the EURUSD exchange rate prior to the Euro's ...
636 views

### Is Walk Forward Analysis a good method to estimate the edge of a trading system?

Do you think Walk Forward Analysis is a good method to estimate the predictability or edge of a trading system? Are there similar methods to know (estimate) how much alpha can capture an algo (in the ...