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271
votes
30answers
202k views

What data sources are available online?

What sources of financial and economic data are available online? Which ones are free or cheap? What has your experience been like with these data sources?
29
votes
4answers
22k views

How to derive the implied probability distribution from B-S volatilities?

The general problem I have is visualization of the implied distribution of returns of a currency pair. I usually use QQplots for historical returns, so for example versus the normal distribution: ...
4
votes
1answer
729 views

Black Scholes differential

I'm studying a BS derivation and I don't understand one part .We have a portfolio consisting of $\Delta(t)S(t)+B(t)$ where the first term is risky and the second is a riskless bond. The part i don't ...
28
votes
4answers
20k views

Integral of Brownian motion w.r.t. time

Let $$X_t = \int_0^t W_s \,\mathrm d s$$ where $W_s$ is our usual Brownian motion. My questions are the following: Expectation? Variance? Is it a martingale? Is it an Ito process or a Riemann ...
50
votes
8answers
54k views

What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate $...
33
votes
6answers
7k views

How to estimate real-world probabilities

In the world of finance, Risk-neutral pricing allow us to estimate the fair value of derivatives using the risk free rate as the expected return of the underlyings. However, the behavior of ...
36
votes
5answers
70k views

A simple formula for calculating implied volatility?

We all know if you back out of the Black Scholes option pricing model you can derive what the option is "implying" about the underlyings future expected volatility. Is there a simple, closed form, ...
38
votes
4answers
15k views

What are the quantitative finance books that we should all have in our shelves?

Which books/papers should we all have in our shelves? There are a couple that I use regularly such as: An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation Asset ...
6
votes
1answer
3k views

Extended Hull White Interest Rate Model for Zero Coupon Bond

Let's take the following three SDEs: $$dr=u(r,t)dt + w(r,t)dX$$ $$u(r,t)=a(t)-br$$ $$w(r,t)=c$$ where $b$ and $c$ are constants and $a(t)$ an arbitrary function of time $t$. If Zero Coupon Bond $Z(...
34
votes
13answers
18k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
10
votes
1answer
2k views

Variance replication using options

I would like to understand the intuition behind the following question: Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying? A variance swap ...
96
votes
16answers
12k views

What concepts are the most dangerous ones in quantitative finance work?

There are a few things that form the common canon of education in (quantitative) finance, yet everybody knows they are not exactly true, useful, well-behaved, or empirically supported. So here is the ...
28
votes
17answers
87k views

What programming languages are most commonly used in quantitative finance?

What programming languages are the most common in quantitative finance, and why are these languages used? Note: I do not mean, what languages are used to develop the accounting system at a hedge fund:...
45
votes
4answers
5k views

How much data is needed to validate a short-horizon trading strategy?

Suppose one has an idea for a short-horizon trading strategy, which we will define as having an average holding period of under 1 week and a required latency between signal calculation and execution ...
50
votes
8answers
68k views

How to annualize Sharpe Ratio?

I have a basic question about annualized Sharpe Ratio Calculation: if I know the daily return of my portfolio, the thing I need to do is multiply the Sharpe Ratio by $\sqrt{252}$ to have it annualized....
27
votes
2answers
22k views

Transformation from the Black-Scholes differential equation to the diffusion equation - and back

I know the derivation of the Black-Scholes differential equation and I understand (most of) the solution of the diffusion equation. What I am missing is the transformation from the Black-Scholes ...
12
votes
3answers
4k views

Carr-Madan Formula

Really new to financial Maths. I am currently having problems with the Carr-Madan Formula. $$f(S_T)=f(F_t) + f'(F_t) (S_T - F_t) + \int_0^{F_t} f''(K) (K-S_T)^+ \ d K + \int_{F_t}^{\infty} f''(K)...
3
votes
3answers
483 views

Derivation of BS PDE problem using Delta hedging

I've always been confused with Delta hedging. It is well-known that for a (smooth enough) function of $(S,t)$ we have, due to Ito's lemma, that: \begin{eqnarray*} dC = \left(\frac{\partial C}{\partial ...
52
votes
6answers
86k views

Where to download list of all common stocks traded on NYSE, NASDAQ and AMEX?

I have a very basic data question: how to get a list of all common stocks traded on NYSE, NASDAQ and AMEX? I would need to be able to get the approximate list of common stocks as is available in ...
28
votes
7answers
35k views

How to calculate historical intraday volatility?

Sorry for what must be a beginner question, but when I went to write code I realized I didn't understand exactly how historical volatility, or statistical volatility, is defined. Wikipedia tells me "...
42
votes
8answers
35k views

How does the “risk-neutral pricing framework” work?

I've struggled for a long time to understand this - What is this? And how does it affect you? Yes I mean risk neutral pricing - Wilmott Forums was not clear about that.
16
votes
3answers
15k views

Is there a step-by-step guide for calculating portfolio VaR using monte carlo simulations

I am trying to determine a step-by-step algorithm for calculating a portfolio's VaR using monte carlo simulations. It seems to me that the literature for this is extraordinarily opaque for something ...
29
votes
9answers
15k views

Any known bugs with Yahoo Finance adjusted close data ?

Yahoo Finance allows you to download tables of their daily historical stock price data. The data includes an adjusted closing price that I thought I might use to calculate daily log returns as a ...
18
votes
1answer
6k 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 ...
11
votes
4answers
2k views

Understanding $N(d_1)$ and how to use the stock itself as the numeraire?

Assume the stock price follows a geometric Brownian motion Then in Black-Scholes pricing model, $N(d_2)$ is the risk-neutral probability that the option expires in-the-money. However, it is said that $...
14
votes
3answers
13k views

Daily returns using adjusted close

I want to chart the daily returns of a stock, and I'm using Yahoo finance data to download historic data. I was told to use Adjusted Close, but there seems to be an issue with this. For ANTO.L, you ...
8
votes
3answers
3k views

Why discounted derivative price is a martingale?

Usually after showing that discounted stock price process is martingale under the risk-neutral measure, most authors say that this implies that the discounted derivative price process is a martingale ...
76
votes
9answers
32k views

Efficiently storing real-time intraday data in an application agnostic way

What would be the best approach to handle real-time intraday data storage? For personal research I've always imported from flat files only into memory (historical EOD), so I don't have much ...
31
votes
9answers
23k views

How should I store tick data?

How should I store tick data? For example, if I have an IB trading account, how should I download and store the tick data directly to my computer? Which software should I use?
23
votes
8answers
4k views

What are some good technical and non-technical books for a math lover to get in to quantitative analysis? [closed]

To get the ball rolling... I will answer this question this evening For people aware & unaware I think it would be a great way to introduce the group, resources for fundamental knowledge & ...
29
votes
6answers
16k views

What is the intuition behind cointegration?

What is the intuition behind cointegration? What does the Dickey-Fuller test do to test for it? Ideally, a non-technical explanation would be appreciated. Say you need to explain it to an investor ...
35
votes
9answers
4k views

Has high frequency trading (HFT) been a net benefit or cost to society?

Various studies have demonstrated the very large and growing influence of high frequency trading (HFT) on the markets. HFT firms are clearly making a great deal of money from somewhere, and it stands ...
27
votes
5answers
52k 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: $$R_i=\frac{S_{i+1}-...
23
votes
5answers
10k views

Is there a standard model for market impact?

Is there a standard model for market impact? I am interested in the case of high-volume equities sold in the US, during market hours, but would be interested in any pointers.
13
votes
12answers
128k 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 ...
11
votes
3answers
5k views

Black-Scholes under stochastic interest rates

I'm trying to implement the Black-Scholes formula to price a call option under stochastic interest rates. Following the book of McLeish (2005), the formula is given by (assuming interest rates are ...
17
votes
6answers
3k views

How to generate a random price series with a specified range and correlation with an actual price?

I want to generate a mock price series. I want it to be within a certain range and have a defined correlation with the original price series. If I choose, say, oil, I want as many time series which ...
15
votes
3answers
21k views

Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?

I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ ...
8
votes
5answers
2k views

Estimate probability of limit order execution over a large time frame

I have a negligible amount of money (\$5000) that I would like to invest in a stock. I would like to buy the stock at some point in the next year, and get the lowest possible price. I would like to ...
14
votes
3answers
9k views

What is Ito's lemma used for in quantitative finance?

Further to my question asked here: prior post and which left some points unanswered, I have reformulated the question as follows: What is Ito's lemma used for in quantitative finance? and when is it ...
9
votes
2answers
3k views

How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?

I have $\frac{dS_t}{S_t} = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs $$(S_T f(S_T))^+$$ How do I express the stock dynamics using the ...
10
votes
2answers
2k views

How to derive the price of a square-or-nothing call option?

At maturity $T$, the holder of a "square-or-nothing" call option written on an underlying $S_t$ receives a payoff of the form $$ \phi(S_T) = \frac{S_T^2}{K} \pmb{1}_{\{S_T \geq K\}} = \begin{cases}\...
7
votes
1answer
829 views

Ho and lee derivation for short rates model

A silly question that is bugging me. I am working my way through Baxter and Rennie (again) and I am getting my wires crossed on the short rate models in particular the straight forward Ho and Lee ...
6
votes
1answer
4k views

Understanding Yang-Zhang Volatility Estimator

I am using TTR in R and I am trying to understand the Yang Zhang volatility estimator (without drift). The following equations seem to imply a single value: $$ \sigma = \sqrt{{\sigma_o^2}+k\sigma_c^2+...
51
votes
6answers
23k views

How are correlation and cointegration related?

In what ways (and under what circumstances) are correlation and cointegration related, if at all? One difference is that one usually thinks of correlation in terms of returns and cointegration in ...
49
votes
5answers
3k views

What are the key risks to the quantitative strategy development process?

Prompted in part by this question on data snooping, I would be interested to know: What are the key risks that should be considered when developing a quantitative strategy based on: (a) historical ...
29
votes
5answers
15k views

How should I calculate the implied volatility of an American option in a real-time production environment?

There are many models available for calculating the implied volatility of an American option. The most popular method, employed by OptionMetrics and others, is probably the Cox-Ross-Rubinstein model. ...
31
votes
5answers
5k views

Why aren't econometric models used more in Quant Finance?

There is a big body of literature on econometric models like ARIMA, ARIMAX or VAR. Yet to the best of my knowledge practically nobody is making use of that in Quantitative Finance. Yes, there is a ...
23
votes
10answers
46k views

Strategy of Renaissance Technologies Medallion fund: Holy Grail or next Madoff?

Renaissance Technologies Medallion fund is one of the most successful hedge funds - ever! Yet it is very secretive. Do you have information on the strategy used that is not yet mentioned in the ...
44
votes
4answers
17k views

What is the best way to “fix” a covariance matrix that is not positive semi-definite?

I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix). I am ...

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