# All Questions

10k views

### How do you explain the volatility smile in the Black-Scholes framework?

Does anyone have an explanation for the currently naturally forming volatility smile (and the variations) in the market?
20k 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: ...
2k views

### How to incorporate technical indicators into neural networks?

I plan to develop a neural network to trade commodities futures, but while messing around with some code, a question came up. If I understand correctly, people use various technical indicators with ...
13k views

### Why are GARCH models used to forecast volatility if residuals are often correlated?

The answers to this question on forecast assessment suggest that if the sequence of residuals from the forecast are not properly independent, then the model is missing something and further changes ...
5k views

### portfolio optimisation with VaR (or CVaR) constraints

I would like to optimize a portfolio allocation (maximizing the exposure or the expected return), but with VaR or CVaR contraints. (some parts of my portfolio cannot exceed a certain VaR) How can I ...
650 views

### Empirical or theoretical quant insights that have shaped your thinking?

What are some quant theoretical or empirical insights that have shaped your thinking or provided a deeper conceptual basis for explaining returns and risk?
4k views

### Why is the VIX futures market usually in a state of contango?

I'm a VIX newbie and I'm trying to understand why the VIX futures market is usually in a state of contango. All I can figure is that the sellers of VIX futures contracts demand high "prices" (because ...
791 views

### Approximately what proportion of a stock’s volatility is explained by market movement?

Assume we decompose the daily (log) returns of a stock as beta times market movement plus an idiosyncratic part. If this is done ex-ante, what proportion of the variance is explained by the market ...
5k views

### Is there an intuitive explanation for the Feynman-Kac-Theorem?

The Feynman-Kac theorem states that for an Ito-process of the form $$dX_t = \mu(t, X_t)dt + \sigma(t, X_t)dW_t$$ there is a measurable function $g$ such that g_t(t,x) + g_x(t, x) \mu(t,x) + ...
1k views

### Please give a step-by-step explanation on how to build a factor model

Factor models such as Fama-French or the other ones that are partially summarized here work on the cross-section of asset returns. How are the factors built, how are sensitivities/coefficients ...
2k views

### How to update an exponential moving average with missing values?

Say you have an Exponential Moving Average being continuously updated over a time series using 1-second-long time periods. What should happen if there is no value for the next second, e.g. there were ...
4k views

### Techniques to optimize the placement of orders in market making strategy?

Market making often requires placing and canceling a lot of orders. You have to buy and sell nearly simultaneously, so you need to move orders pretty often to beat other traders. But I would like to ...
1k views

### Is there a way to estimate (predict) the half life of a quantitative trading system?

Usually even good performing quant trading strategies work for a while and then return start to shrink. I see two reasons for that which would probably give rise to different analysis: The Strategy ...
4k views

### Which approach to estimating fundamental factor models is better, cross-sectional (unobservable) factors or time-series (observable) factors?

There are many approaches to estimating fundamental factor equity models. I would like to focus on two traditional methods: The time-series regression approach of Fama and French. Factors are ...
484 views

### Which interest rate model for which product

Given the multitude of existing interest rate models (ranging from simple to very complex) it would be interesting to know when the additional complexity actually makes sense. The models I have in ...
1k views

### Parameter estimation of Ornstein–Uhlenbeck and CIR processes

I would like to estimate Ornstein–Uhlenbeck process' parameters via Kalman filter. My process is the following one: $\text{d}x_{t}=\alpha(\theta-x_{t})\text{d}t+\sigma\text{d}W_{t}$ I'm interested ...
4k views

### What C++ math libraries are typically used by quants?

Before you mark question as off-topic, please read it - it is, actually, quant-related. Basically, I'm working on an app that spits out a lot of C++ math. When it comes to simple things like ...
4k views

### How are limit orders selected from the order book?

I'm sure there is a simple answer to this but I haven't had any luck with searches. I'm just wondering when someone places a market order which order(s) from the limit order book are selected to fill ...
23k views

### How to compute Implied Volatility Calculation?

We all know if you back out of the BS option pricing model you can derive and solve what the options is "implying" as its volatility. However, what is the formula used to derive Implied Volatility ...
24k views

### How to check if a timeseries is stationary?

I'm using KPSS Method to check if the series is stationary, but I would also like to use another test to confirm if the series is stationary or not, what method coudl I use?
3k views

### Should Sharpe ratio be computed using log returns or relative returns?

I am trying to reconcile some research with some published values of 'Sharpe ratio', and would like to know the 'standard' method for computing the same: Based on daily returns? Monthly? Weekly? ...
13k views

### Correlation between prices or returns?

If you are interested in determining whether there is a correlation between the Federal Reserve Balance Sheet and PPI, would you calculate the correlation between values (prices) or period-to-period ...
1k views

### What are the limitations of Gaussian copulas in respect to pricing credit derivatives?

The practice of using Gaussian copulas in modeling credit derivatives has come under a lot of criticism in the past few years. What are the major arguments against using the copula method in this ...
2k views

### Formal proof for risk-neutral pricing formula

As you know, the key equation of risk neutral pricing is the following: $\exp^{-rt} S_t = E_Q[\exp^{-rT} S_T | \mathcal{F}_t]$ That is, discounted prices are Q-martingales. It makes real-sense for ...
3k views

### Is there any good research on support and resistance?

Could somebody advise me on where to find good literature on the justification or motivation for using support and resistance lines - and also lines of maximums and minimums. In finance, it is ...
1k views

### Measuring liquidity

While liquidity is one of the key figure of financial markets, It seems to be very difficult to measure. Volume is sometime used as a proxy but can sometimes be completly irrelevant. Could you point ...
11k views

### Are there any good tools for back testing options strategies?

There are all kinds of tools for backtesting linear instruments (like stocks or stock indices). It is a completely different story when it comes to option strategies. Most of the tools used are ...
3k views

### How to cluster stocks and construct an affinity matrix?

My goal is to find clusters of stocks. The "affinity" matrix will define the "closeness" of points. This article gives a bit more background. The ultimate purpose is to investigate the "cohesion" ...
3k views

### When does delta hedging result in more risk?

There's a question in an interview book saying "when can hedging an options position make you take on more risk?" The answer provided is that "Hedging can increase your risk if you are forced to both ...
5k views

### Is there an all Java options-pricing library (preferably open source) besides jquantlib?

I am looking for an all-java implementation of black scholes, preferably open source. I found jquantlib and quantlib (C++). Any other recommendations? The jquantlib site seems to be down. I'd prefer ...
4k views

### What is a “coherent” risk measure?

What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in ...
976 views

### How to account for transaction costs in a simulated market environment?

I am simulating a market for my trading system. I have no ask-bid prices in my dataset and use adjusted close for both buy and sell price. To account for this I plan to use a relative transaction ...
266 views

### How reliable is Benford's Law in forecasting crises?

I was recently reading an article about how financial accounting has increasingly deviated from the ratios expected by Benford's Law. (Benford's Law and Decreasing Reliability). The author discusses ...
2k views

### What books should any quantitative portfolio manager or risk manager have as reference? [closed]

I'm interested to know what are the critical reference texts you rely on for portfolio or risk management? I mean those texts that you come back to because they are chock full of insight and know-how. ...
800 views

### Duality between constant rebalanced portfolio (CRP) and corresponding derivative

One of the greatest achievements of modern option pricing theory is finding corresponding dynamical trading strategies in linear instruments with which you can replicate and by that price derivative ...
1k views

### Quantitative Math required for Market-making?

I understand there is an awful lot of Quantitative Math required for statistical arbitrage/algorithmic trading. However, would someone "in the know" be able to tell me whether there is less ...
9k views

### What is a Heat Rate Option?

I tried a search with google but I can't find a clear definition of what a Heat Rate Option is. I would appreciate if someone could explain to me what this type of option is. My understanding is ...
5k views

### Free market data (delayed or snapshot)

I know there are similar questions but I don't think there are any identical ones. Basically, I'm looking for one of these two things. Delayed market data feed. A tick by tick feed, but delayed by ...
7k views

### Is statistical arbitrage on FX possible?

Do you know of any papers which consider pairs trading (or statistical arbitrage) on foreign exchange? I couldn't find any. I asked this question on several forums and got no reply. Thus I guess this ...
1k views

### Copula models and the distribution of the sum of random variables without Monte Carlo

There is a vast literature on copula modelling. Using copulas I can describe the joint law of two (and more) random variables $X$ and $Y$, i.e. $F_{X,Y}(x,y)$. Very often in risk management (credit ...
964 views

### How to forecast expected volatility from high-frequency equity panel data?

I'm wading through the vast sea of literature on realized volatility estimation and expected volatility forecasting (see, e.g. Realized Volatility by Andersen and Benzoni, which cites 120 other ...
1k views

### How does one analyze diversification if stock prices follow a Cauchy distribution?

How does diversification actually lead to less variance in a portfolio? I'm looking for a formal reason why this is the case. There are a number of explanations I have been able to find, but they make ...
1k views

### Cleansing covariance matrices via Random matrix theory

I am exploring de-noising and cleansing of covariance matrices via Random Matrix Theory. RMT is a competitor to shrinkage methods of covariance estimation. There are various methods expressed usually ...
414 views

### What should be considered when selecting a windowing function when smoothing a time series?

If one wants to smooth a time series using a window function such as Hanning, Hamming, Blackman etc. what are the considerations for favouring any one window over another?
2k views

### statistical arbitrage option overlay strategies / volatility trading

Here's an interesting trading puzzle that I would love to get the community's input on. Let's say there exists an alpha signal that does a good job of sorting equities expected excess returns over ...
2k views

### Why does the VIX index have *any* correlation to the market?

It appears that the log 'returns' of the VIX index have a (negative) correlation to the log 'returns' of e.g. the S&P 500 index. The r-squared is on the order of 0.7. I thought VIX was supposed to ...
34k views

I am preparing for the CFA level 2 exam, I got confused by the concept Z-spread and OAS. When a call option is added to a bond, since it is not favorable to the bond buyer, they would require more ...
2k views

### How to optimally allocate capital among trading strategies?

I'm trying to find an optimal way to allocate capital among trading strategies. "Quantitative Trading" by Ernie Chan claims on page 97 that the optimal fraction of capital to allocate to a given ...