All Questions
10
votes
2answers
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 ...
10
votes
1answer
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 ...
10
votes
4answers
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 ...
9
votes
3answers
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
...
9
votes
4answers
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?
7
votes
2answers
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 ...
6
votes
3answers
4k views
Trading C++ Libraries
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.
...
5
votes
2answers
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 ...
5
votes
1answer
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. ...
5
votes
2answers
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 ...
5
votes
2answers
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 ...
5
votes
2answers
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 ...
4
votes
2answers
457 views
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 ...
3
votes
5answers
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 ...
1
vote
2answers
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 ...
10
votes
7answers
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 ...
8
votes
1answer
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 ...
8
votes
2answers
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 ...
7
votes
2answers
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?
7
votes
4answers
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 ...
7
votes
4answers
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 ...
7
votes
3answers
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 ...
6
votes
4answers
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 ...
6
votes
1answer
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 ...
6
votes
1answer
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 ...
6
votes
2answers
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 ...
6
votes
2answers
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 ...
5
votes
2answers
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 ...
5
votes
1answer
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 ...
4
votes
2answers
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.
...
4
votes
1answer
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:
...
3
votes
2answers
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 ...
3
votes
2answers
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 ...
3
votes
4answers
2k views
Utility to download historical Implied Volatility data from Interactive Brokers?
Does anyone know of a utility that can download historical Implied Volatility (IV) data from Interactive Brokers' Trader Workstation?
2
votes
1answer
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 ...
1
vote
2answers
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 ...
10
votes
5answers
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( ...
9
votes
2answers
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 ...
7
votes
5answers
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 ...
7
votes
2answers
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 ...
6
votes
1answer
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 ...
6
votes
3answers
6k views
What is the difference between Option Adjusted Spread (OAS) and Z-spread?
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 ...
6
votes
2answers
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?
5
votes
4answers
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 ...
5
votes
4answers
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 ...
5
votes
1answer
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 ...
5
votes
1answer
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 ...
4
votes
1answer
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, ...
4
votes
1answer
387 views
What research is available on the performance of convertible bond arbitrage models?
The basic principles of convertible bond arbitrage have been clear at least since Thorp and Kassouf (1967). For those who are not familiar, the arbitrage entails purchasing a convertible bond and ...
3
votes
4answers
548 views
Ways of treating time in the BS formula
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, ...
