# All Questions

3k views

### 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 ...
259 views

### What approaches are there for stress testing a portfolio?

Wikipedia lists three of them: Extreme event: hypothesize the portfolio's return given the recurrence of a historical event. Current positions and risk exposures are combined with the historical ...
1k 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 ...
902 views

### Why do expected return models and risk models use different factors?

This is a question responding to weekly topic challenge. I happen to see an interesting question from SYMMYS by Michael Kapler. I always approached expected return and risk modeling as separate ...
2k views

### What is a martingale?

What is a martingale and how it compares with a random walk in the context of the Efficient Market Hypothesis?
1k views

### Are there comprehensive analyses of theta decay in weekly options?

Are there comprehensive analyses of how much theta a weekly options loses in a day, per day? I know what the shape of theta decay looks like, in theory, where the decay towards zero happens more ...
4k views

Are there any free c++ libraries that would have some of the functions that would be used in developing a trading strategy. For instance, calculating drawdown, Volatility Forecasting, MAE, MFE....etc. ...
369 views

### Comparing MVO with Resampled Efficient Frontier

My question: How can I compare the Resampled Frontier (REF) to the standard MVO frontier when I have been provided with $\mu$, $\Omega$, and don't have access to true future data to test real out of ...
511 views

### How to simulate correlated assets for illustrating portfolio diversification?

I have seen multiple instances where people try to explain the diversification effects of having assets with a certain level of correlation, especially in the "most diversified portfolio" literature. ...
795 views

### How to extrapolate implied volatility for out of the money options?

Estimation of model-free implied volatility is highly dependent upon the extrapolation procedure for non-traded options at extreme out-of-the-money points. Jiang and Tian (2007) propose that the ...
561 views

### Recommendation for a library to calculate the local volatility surface?

I'd like a library to calculate the options local volatility surface, i.e. the options implied volatility surface for a collection of strikes and their bid/ask prices. Here are the libraries I've ...
936 views

### Quantmod: what's the difference between ROC(Cl(SPY)) and ClCl(SPY)

I feel like I'm missing something fundamental here, but I can't shake the feeling that these two series should be equivalent. /edit: there is also dailyReturn(Cl(SPY)). I've seen all 3 of these ...
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### SKEW and VIX relations?

My question is about the CBOE published index VIX and SKEW. To start with, I consider working on the variance dynamics. I calibrate the market data (such as VIX and VIX futures) into the Heston ...
850 views

### Recommendation for a book on CVA/Credit Risk and PD/LGD/EAD modeling?

I need suggestions for some good books on the following topics: Credit Value Adjustment (CVA) / Credit Risk Probability of Default / Loss-Given-Default / Exposure-At-Default modeling Any pointers ...
248 views

### How to detect and adjust for stock splits?

I am using a large daily data panel for over 250 companies and over several years. I am concerned about adjusting for stock splits. Is there any program in SAS to detect stock splits? How do I adjust ...
2k 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 ...
560 views

### Quantitative before/after or financial engineering studies of a bid or ask tax?

Has anyone in the quantitative finance or financial engineering community studied the effects of a bid or ask tax with actual or simulated data? If so, what were the quantitative results or ...
591 views

### 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 ...
550 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?
409 views

### Is this a common variation of sharpe ratio?

As an aside on his answer on another question Freddy said: Sharpe ratio is an often cited metric, though I do not like it too much because you are penalized for out-sized positive returns while ...
523 views

### What commercial financial libraries are available to outsource implementation risk?

During our daily jobs as quants, we tend to be willing to develop all the quantitative libraries ourselves. While I know that we need to develop specific algorithms which are the foundations of our ...
773 views

### Limit order book size

I am trying to write a highly optimised limit order book and I wondered what sort of size I can expect for: Range of limit prices Number of orders at each limit price I am developing custom ...
492 views

### Threshold calculation for buying a mean-reverting asset

I am trying to figure-out an optimal policy for buying a unit when its price follows a mean-reverting price process (Ornstein–Uhlenbeck), when I have a finite time deadline for buying the unit. I ...
361 views

### What are the steps to perform properly a risk factor analysis on a portfolio?

I have been asked to perform a factor analysis on a given portfolio, assume it's a Swiss portfolio in CHF. First step, I chose which factors I would like to see in my analysis. The first factors I ...
241 views

### How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?

I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
510 views

### Closed-form formula for approximate maximum duration of a bond?

In teaching myself about bonds, I am writing some software, one piece of which will calculate the maturity of a bond given the yield curve as a function and a requested duration. The tricky part is ...
1k views

### Cluster analysis vs PCA for risk models?

I built risk models using cluster analysis in a previous life. Years ago I learned about principal component analysis and I've often wondered whether that would have been more appropriate. What are ...
289 views

### What is the mean and the standard deviation for Geometric Ornstein-Uhlenbeck Process?

I am uncertain as to how to calculate the mean and variance of the following Geometric Ornstein-Uhlenbeck process. $$d X(t) = a ( L - X_t ) dt + V X_t dW_t$$ Is anyone able to calculate the mean ...
683 views

### Optimizing a portfolio of ETFs

I am aware of how to do mean-variance or minimum-variance portfolio optimization with constraints like weights must add to 1.0 no short sells max weight in any ticker using basic quadratic ...
384 views

### How to make the final Interpretation of PCA?

I have question regarding final loading of data back to original variables. So for example: I have 10 variable from a,b,c....j using returns for last 300 days i got return matrix of 300 X 10. ...
1k 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: ...
10k 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 ...
359 views

### Debunking risk premium via “hedging” argument? (or why even in the real world $\mu$ should equal $r$)

Since I began thinking about portfolio optimization and option pricing, I've struggled to get an intuition for the risk premium, i.e. that investors are only willing to buy risky instruments when they ...
2k views

Does anyone know of a utility that can download historical Implied Volatility (IV) data from Interactive Brokers' Trader Workstation?
551 views

### How to fit ARMA+GARCH Model In R?

I am currently working on ARMA+GARCH model using R. I am looking out for example which explain step by step explanation for fitting this model in R. I have time series which is stationary and I am ...
161 views

### How is historical data for forex collected or computed?

I'm looking at four sources of forex data, as compiled in the question, What data sources are available online? And I think I must be misunderstanding something, perhaps something fundamental, but I'm ...
685 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( ...
312 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

### Is Visual Basic a fast enough for millisecond orders

I have an API that for an order routing platform that is in visual basic. The maximum frequency or orders to exchanges will be milliseconds, where the underlying systems are expected to be able to ...
412 views

### What is a reasonable upper bound on the performance of a daily trading strategy?

I am backtesting an equity trading strategy which trades only once per day. Is there a general rule of thumb for the reasonable upper bound on the rate of return of such a strategy? For example, a ...
300 views

### What distribution should I apply to estimate the likelihood of extreme returns?

Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns. Because the estimate will require extrapolation, I ...
6k 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 ...
605 views

### Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
864 views

### Analyzing tick data

What are some of the commonly used techniques to analyze tick data? I am looking at tick data to see how the quotes/ mid-price evolves due to certain events in the market. Since tick data is ...
594 views

### Library of basic indicators

I am looking to start developing a trend following strategy and have been looking to do something in either C# or Java and wondered if there was a library or framework out there that would make ...
757 views

### What is an efficient data structure to model order book?

What is an efficient data structure to model order book of prices and quantities to ensure: constant look up iteration in order of prices retrieving best bid and ask in constant time fast quantity ...
386 views

### Proof for non-positive semi-definite covariance matrix estimator

It is well known that the standard estimator of the covariance matrix can lose the property of being positive-semidefinite if the number of variables (e.g. number of stocks) exceeds the number of ...
338 views

### How to apply quasi-Monte Carlo to path-dependent options?

Following up on my recent question on variance reduction in a Cox-Ingersoll-Ross Monte Carlo simulation, I would like to learn more about using a quasi-random sequence, such as Sobol or Niederreiter, ...
The Black-scholes formula typically has time as $\sqrt{T-t}$ or some such. My questions: What is the granularity of this? If we treat $t$ as the number of days, then logically on the day of expiry, ...