# All Questions

5k views

### What is the implied volatility skew?

I often hear people talking about the skew of the volatility surface, model, etc... but it appears to me that a clear standard definition is not unanimously in place among practitioners. So here is ...
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 ...
885 views

### When hiring a quant, how can I protect my IP?

I am a one-man operation, and would like to hire a quant for around 4 weeks or work. I am worried that the person I hire might copy my data or the indicators that I have him work on. What have ...
596 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

### 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) ...
820 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 ...
2k views

### Categories of systematic trading strategies?

What are the main categories of systematic trading strategies (e.g. momentum, mean reversion), as might be considered by an index or fund-of-fund analyst? Are there any common sub-strategies?
1k 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 ...
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 ...
2k views

### 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 ...
392 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 ...
741 views

### 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 ...
275 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 ...
585 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 ...
5k views

### Rationale for OIS discounting for collateralized derivatives?

Can someone explain to me the rationale for why the market may be moving towards OIS discounting for fully collateralized derivatives?
244 views

### Is a linear combination of GARCH processes also a GARCH process?

If two time series follow a GARCH process, and a third is a linear combination of them, is the third also GARCH process?
170 views

### Are there any valuation models of securities that use hyperbolic discounting?

To quote Wikipedia: In hyperbolic discounting, valuations fall very rapidly for small delay periods, but then fall slowly for longer delay periods. This contrasts with exponential discounting, in ...
1k views

### 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 ...
453 views

### 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". ...
2k views

### Skewness and Kurtosis under aggregation

Returns possess non-zero skewness and excess kurtosis. If these assets are temporally aggregated both will disappear due to the law of large numbers. To be exact, if we assume IID returns skewness ...
626 views

### How to compute performance attribution between daily rebalanced strategies?

I have a daily rebalanced portfolio of several strategies. After one month, I now want to attribute the performance to the different strategies. There are several ways to do it. For instance one ...
491 views

### 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. ...
966 views

### Is there a popular curve fitting formula of options skew vs strike price or vs Delta?

I was trying to build a options trading/optimization system. But it often gets more inaccurate as it scans through the far from ATM options because, you know, options skews. That is because I did ...
608 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, ...
551 views

### One dimensional analog of cleansing a correlation matrix via random matrix theory

The general idea of cleansing a correlation matrix via random matrix theory is to compare its eigenvalues to that of a random one to see which parts of it are beyond normal randomness. These are then ...
314 views

### When is it rational to exercise a bond option early?

Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?
468 views

### Is it possible to understand financial theory without mathematics?

I am trying to develop a short course on financial theory, covering the fundamentals of forward and options pricing, and 'efficient market' theory. I want to reduce the amount of mathematics to a ...
526 views

### VaR for portfolio of funds

Let's assume we need to calculate a 1-day VaR for a portfolio of funds. Funds are traded, they can be bought and sold every day. We know exactly what the assets in each fund are. What is the right way ...
468 views

### What to ask for in a good prototyping framework?

Reading up on quantitative methods, model development, and back-testing, one obvious question springs to mind: What should one ask of a prototyping (model testing) framework? I know a lot of people ...
1k views

### 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 ...
2k views

### 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 ...
3k views

### How to calculate future distribution of price using volatility?

I want to create a lognormal distribution of future stock prices. Using a monte carlo simulation I came up with the standard deviation as being $\sqrt{(days/252)}$ $*volatility*mean*$ $\log(mean)$. ...
380 views

### copula-marginal algorithm

has there been any interesting work or advances on the copula-marginal algorithm (CMA) as proposed by Attilio Meucci. I am unable to find anything on the web other then the original article, here is ...
1k views

### Is the risk-free rate really limited by inflation?

In all the classic texts on equities derivatives, there is an assumption of the risk-free rate r. We can immediately dismiss the concept of a fixed rate; all interest rates are variable (and ...
2k 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 ...
334 views

### Appropriate measure of Volatility for economic returns from an asset?

I am doing research on uncertainty analysis and risk assessment for oil field development. For doing economic forecast and valuation I use Real Options theory, which is almost similar to theory used ...
871 views

### Implementing a Fast Fourier Transform for Option Pricing

So, I'm in need of some tips regarding a small project I'm doing. My goal is an implementation of a Fast Fourier Transform algorithm (FFT) which can be applied to the pricing of options. First ...
344 views

### local price return and volume relationship

I wanted to see how the stock price and volume relationship is locally. So I tried ranking both the daily return (at day t) and volume (at day t) base on a 30 day rolling window with historical daily ...
463 views

### Links to the risk model methodologies of the major providers?

There is quite a bit of art in constructing an equity risk model. This paper summarizes some of the key decisions: choice of factors, horizon matching, cross-sectional vs. time-series method, and ...
1k views

### Is QuantLib more trouble than it's worth?

I'm just starting to work with QuantLib and wonder if I'm going down a very wrong path. I'm working on a site that presents the visitor with a table of streamed real-time options data, including ...
173 views

### Breaking Transactions Down into Derivatives

We were talking about merger arb in a class I had last night, and when we got do deal construction it was mentioned that the different ways can be viewed as different options. For instance a fixed ...
179 views

### St Petersburg lottery pricing & short investing horizons

I am a statistician (no solid background in finance). Please forward me to a book \ chapter \ paper to resolve the following general question. Suppose we have a stock with the following monthly return ...
577 views

### How are Expected Shortfall and Variance related?

I would like to know how Expected Shortfall $SF_\alpha$ and variance $\sigma^2$ are related. If I follow what Aaron Brown answered in this post, when the underlying distribution is Normal with ...
306 views

### What drives changes in implied volatility on ETFs/ETNs?

I thought implied volatility, as well as the VIX, primarily increase due to increases in the underlying asset's volatility, as well as the options themselves being bid up because more people were ...
630 views

### Models for measuring insurance risk exposure

I've recently begun working as a quant for a large bank, and one of my first tasks will be to improve the model determining the risk exposure of their insurance portfolio. The portfolio is fairly ...
525 views

### Can VIX be interpreted as a proxy for instantaneous volatility?

BJO06 (Table 2) estimate the following Cox-Ingersoll-Ross model for market variance, $\sigma^2_t$: \$\mathrm{d}\sigma^2_t = (\alpha_0 + \alpha_1\sigma^2_t)\mathrm{d}t + ...
254 views

### Could banks move to continuous (rather than overnight) funding?

The dominant frequencies for Money Market and FX instruments were 6m and 3m for a long time, and banks slowly moved to commercial trades at those frequencies but funding overnight. If this is a step ...