# All Questions

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### 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 ...
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### How does left tail risk differ from right tail risk?

How does left tail risk differ from right tail risk? In what context would an analyst use these metrics?
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### 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 ...
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### 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 ...
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### Cross Currency Swap Pricing in nowadays environment

Multicurve setting has now become the new paradigm for vanilla swap valuation. For the record I give here (without getting into too much details) the methodoloy for pricing Euribor3M swaps in this ...
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### 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 ...
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### What is a good topic on financial time series analysis for master thesis?

Can someone suggest a topic or some reasonably narrow area in financial time series analysis (e.g. statistical, machine learning, etc.) which can make a good topic for a master thesis? By 'good' I ...
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### Value-at-Risk of the sum of two dependent lognormal random variables

Hy I posted this question first at mathflow.net they suggested me this page, which I was not aware of. Question: Let $(X_1,X_2)$ be a multivariate normal random vector ($X_1$ and $X_2$ need not be ...
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### Are BSDE's used in practice?

In the academic applied probability/math finance community, Backwards Stochastic Differential Equations (BSDE's) are extremely popular, and they provide a single framework for several different ...
761 views

### Modelling with negative interest rates

For a project, I am interested to model the impact of recently negative interest bonds on the portfolio. The literature on modelling negative interest rates is limited, and the only theory I could ...
611 views

### Quantitative Analysis Games on Investing?

I have been playing a quantitative investing game (instructions here) that is actually quite interesting, teams have some time to decide their next moves. It requires all kind of knowledge such as ...
306 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 ...
913 views

### How do I price OANDA box options?

How do I price OANDA box options without using their slow and machine-unfriendly user interface?: http://fxtrade.oanda.com (free demo account) sells "box options": If you already know what a ...
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### 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 ...
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It is known (see for example Joshi-Chan "Fast and Accureate Long Stepping Simulation of the Heston SV Model" available at SSRN) that for a CIR process defined as : $$dY_t= \kappa(\theta -Y_t)dt+ ... 8answers 5k views ### Is “eoddata” a good data source? Not sure if this is a relevant question for site, but I am looking to move to www.eoddata.com as my data source. If anyone has used it, can you tell me how the data quality is ? I am currently ... 7answers 757 views ### Keeping a track record honest I want to start a blog/newsletter and maintain a track record of trades I recommend. I have a never-expiring demo account for this purpose. How do I keep this track record "honest"? Three months ... 5answers 3k views ### What exactly is meant by “microstructure noise”? I see that term tossed around a lot, in articles relating to HFT, and ultra high frequency data. It says at higher frequencies, smaller intervals, microstructure noise is very dominant. What is ... 8answers 4k views ### Why does implied volatility show an inverse relation with strike price when examining option chains? When looking at option chains, I often notice that the (broker calculated) implied volatility has an inverse relation to the strike price. This seems true both for calls and puts. As a current ... 6answers 2k views ### References for developing an automated trading system? I am looking for references on the architecture of automated trading systems and the trading algorithms behind them. I am more interested in system development than analysis. A couple of books I ... 3answers 1k views ### Hedging stocks with VIX futures It seems that VIX futures could be a great hedge for a long-only stock portfolio since they rise when stocks fall. But how many VIX futures should I buy to hedge my portfolio, and which futures ... 3answers 1k 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 ... 5answers 1k views ### Is it possible to use a series of option prices to predict the most likely path of an asset? I've always wondered about this. If you have a series of options, with the expires spaced let's say one week between them, and you search for each expiration date the option with the smallest ... 4answers 733 views ### Resources for finding scholarly research on topics in quantitative finance? A friend and I have taken up an interest in quantitative finance, and we're pretty much starting from scratch—neither of us have backgrounds in finance, but rather electrical engineering and ... 6answers 1k 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 ... 5answers 879 views ### Monte carlo methods for vanilla european options and Ito's lemma. I understand that by applying Ito's lemma to the following SDE$$dX=\mu\,X\,dt+\sigma\,X\,dW$$one obtains a solution to the above SDE which is as follows:$${X}\left( t\right) =\mathrm{X}\left( ...
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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 ...
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### How high of a Sharpe ratio is implausibly high for a low-frequency equity strategy?

I am looking to convince someone that an annualized Sharpe Ratio of 7 is 'extremely high' for a low frequency (daily rebalancing, say) long-short technical strategy on U.S. equities. I was hoping for ...
4k views

### Using linear regression on (lagged) returns of one stock to predict returns of another

Suppose I want to build a linear regression to see if returns of one stock can predict returns of another. For example, let's say I want to see if the VIX return on day X is predictive of the S&P ...
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### 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 ...
14k 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?
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### Why is the ratio of Hi-Low range to Open-Close range close to 2?

I tried it in several symbols and timeframes with the same result: $$\frac {mean(HIGH-LOW)}{mean(|CLOSE-OPEN|)}$$ ...
1k 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.
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### How to group timeseries showing similar curve

I am trying to classify similar looking curves of a timeseries and was wondering what is the best algorithm to research. Reading R, it looks like k-means clustering could be applied - but I don't know ...
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### 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 ...
371 views

### 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 ...
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### Is it ever possible that---because of illiquidity---exercising an out-of-the-money option is better than directly buying the stock?

Is there a case, where due to illiquidity, exercising out-of-the-money options could be better than directly buying the stock? When a stock is too illiquid, there are some costs because of this ...
1k 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. ...
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### How to combine multiple trading algorithms?

Is it possible to combine different algorithms so as to improve trading performance? In particular, I have read that social media sentiment tracking, digital signal processing and neural networks all ...
3k 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 ...
873 views

### Rate interpolation in Libor Market Model

Libor Market Model (LMM) models the interest rate market by simulating a set of simply compounded, non-overlapping Libor rates which reset and mature on predefined dates. How do I obtain from them a ...
2k 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 ...