All Questions
9
votes
2answers
1k views
Fundamental Theorem of Asset Pricing (FTAP)
In the spirit of canonical questions please state here versions of the FTAP in the following form (please only one theorem by answer) :
Necessary definitions (or a direct link to definitions)
...
9
votes
3answers
444 views
Maximization of CARA utility function: unique solution with an unbounded parameter?
An investor at time $t_0$ can invest his wealth $w_0$ in a risky asset $x$ for an amount $a$ and the remain part in the riskless asset $w_0-a$.
At the end of the period $t_1$, the investor will ...
9
votes
2answers
1k views
Why a self-financing replicating portfolio should always exist?
According to my understanding the derivation of the Black-Scholes PDE is based on the assumption that the price of the option should change in time in such a way that it should be possible to ...
9
votes
2answers
1k views
How can I learn about the quantitative aspects of market making in illiquid single stock options?
I would like to learn more about the possible ways of doing quantitative research regarding option market making. In particular, while the mainstream index option market may be very liquid, the ...
9
votes
3answers
775 views
How to solve for the implied stock lending rate given equity options prices?
When market makers price options on hard-to-borrow equities, they include the cost to borrow the underlying equity that their broker is going to charge them to sell the security short to hedge. I'm ...
9
votes
2answers
451 views
What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?
Is there any relationship between the risk aversion coefficient in an individual's utility function (commonly used in portfolio optimization) and the preference for higher moments such as skewness and ...
9
votes
2answers
203 views
Effective Euro-USD (EURUSD) Exchange Rate Prior to Euro's Existence
Motivation: I am running a quantitative analysis that requires long-term, exchange rate data.
Problem: Does anyone have methods for dealing with the EURUSD exchange rate prior to the Euro's ...
9
votes
3answers
2k views
Total Return measurement paradox w/ Adjusted Close Prices
Using total return calculations is critical in developing security selection models.
The standard way to measure total return is to develop a series of price-adjusted data. Investopedia describes the ...
9
votes
1answer
309 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 ...
9
votes
1answer
207 views
Is a linear combination of GARCH processes also a GARCH process?
If two time series follow a GARCH process, and a third is a linear combination of them, is the third also GARCH process?
9
votes
4answers
100 views
Are there any valuation models of securities that use hyperbolic discounting?
To quote Wikipedia:
In hyperbolic discounting, valuations fall very rapidly for small delay periods, but then fall slowly for longer delay periods. This contrasts with exponential discounting, in ...
9
votes
2answers
1k views
How do I calculate the skewness of a portfolio of assets?
I need to calculate the skewness of a portfolio consisting of 6 assets. I know that for that I would need the co-skewness matrix between the assets. Does anybody know the formula for co-skewness or ...
9
votes
2answers
596 views
How to simulate slippage
I'm backtesting a trading strategy, using free OHLC data from yahoo or google. I'm simulating friction by lopping a flat percentage (say 0.5%) off my returns for each day that I make a trade. Whats ...
9
votes
3answers
429 views
How would you test the hypothesis “There are no idiosyncratic returns available in the market”?
A commentary attributed to Matt Rothman had recently (in the past six months) been making the rounds of the internet echo chamber claimed "There are no idiosyncratic returns available in the market". ...
9
votes
2answers
452 views
How to compute performance attribution between daily rebalanced strategies?
I have a daily rebalanced portfolio of several strategies.
After one month, I now want to attribute the performance to the different strategies. There are several ways to do it.
For instance one ...
9
votes
1answer
305 views
How do you estimate the volatility of a sample when points are irregularly spaced?
I was looking again at this question which basically haunts every quant I believe, and I was thinking about the effect of these gaps when computing volatility of the series.
Let's define the problem ...
9
votes
3answers
399 views
Literature on generating synthetic time series for testing
I have some market data (daily time series) for bond prices and CDS indices and I would like to generate synthetic versions of these which are statistically "similar" for testing trading strategies. ...
9
votes
2answers
405 views
When is the LIBOR market model Markovian?
The question is inspired by a short passage on the LMM in Mark Joshi's book.
The LMM cannot be truly Markovian in the underlying Brownian motions due to the presence of state-dependent drifts. ...
9
votes
1answer
665 views
Is there a popular curve fitting formula of options skew vs strike price or vs Delta?
I was trying to build a options trading/optimization system. But it often gets more inaccurate as it scans through the far from ATM options because, you know, options skews.
That is because I did ...
9
votes
2answers
498 views
Are e-mini markets manipulated?
Are the prices of e-minis such as S&P 500, Russell 2000, EUROSTOXX, etc. manipulated? That is, are there traders who trade large enough positions to make the price go in the direction they want, ...
9
votes
1answer
431 views
One dimensional analog of cleansing a correlation matrix via random matrix theory
The general idea of cleansing a correlation matrix via random matrix theory is to compare its eigenvalues to that of a random one to see which parts of it are beyond normal randomness. These are then ...
9
votes
2answers
227 views
When is it rational to exercise a bond option early?
Consider american options on interest rate futures such as the 10-year treasury note. When is early exercise optimal?
9
votes
1answer
1k views
How do I compare implied and historic volatility?
what would you suggest are the starting points for comparing, in an easy, visual way, implied and delivered volatility surfaces? I'd like to see what the differences are between the historic surfaces, ...
9
votes
2answers
1k views
Drawbacks & Caveats of using (N)Esper for ESP/CEP in trading systems?
Esper and its .NET port NEsper are components that enable Complex Event Processing (CEP) and Event Stream Processing (ESP) engines. They are especially suitable for trading applications. They can, ...
9
votes
1answer
378 views
What to ask for in a good prototyping framework?
Reading up on quantitative methods, model development, and back-testing, one obvious question springs to mind:
What should one ask of a prototyping (model testing) framework?
I know a lot of people ...
9
votes
2answers
2k 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:
...
9
votes
3answers
2k views
How to calculate future distribution of price using volatility?
I want to create a lognormal distribution of future stock prices. Using a monte carlo simulation I came up with the standard deviation as being $\sqrt{(days/252)}$ $*volatility*mean*$ $\log(mean)$. ...
9
votes
3answers
192 views
Does entropy pooling apply to distributions with time-varying drift?
I have a returns process that is drawn from a normal distribution with a nonlinear time-varying drift, so I was wondering if the entropy pooling method still applies or if I need an invariant ?
9
votes
1answer
305 views
copula-marginal algorithm
has there been any interesting work or advances on the copula-marginal algorithm (CMA) as proposed by
Attilio Meucci. I am unable to find anything on the web other then the original article, here is ...
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 ...
9
votes
3answers
797 views
What is the ideal ratio of in-sample length to out-of-sample length?
Suppose you are running a portfolio of quantitative strategies and that you develop a new potential strategy to be added to the mix. Assume for simplicity that the new strategy is independent of the ...
9
votes
2answers
308 views
local price return and volume relationship
I wanted to see how the stock price and volume relationship is locally.
So I tried ranking both the daily return (at day t) and volume (at day t) base on a 30 day rolling window with historical daily ...
9
votes
4answers
710 views
Is the risk-free rate really limited by inflation?
In all the classic texts on equities derivatives, there is an assumption of the risk-free rate r. We can immediately dismiss the concept of a fixed rate; all interest rates are variable (and ...
9
votes
2answers
511 views
Quantitative Derivatives Trading vs. Time
Most quantitative investment strategies focus on the changing prices of a commodity or equity over time. Derivatives, however, make this more complicated. How can I apply quantitative strategies to ...
9
votes
1answer
156 views
Breaking Transactions Down into Derivatives
We were talking about merger arb in a class I had last night, and when we got do deal construction it was mentioned that the different ways can be viewed as different options. For instance a fixed ...
9
votes
1answer
383 views
How are Expected Shortfall and Variance related?
I would like to know how Expected Shortfall $SF_\alpha$ and variance $\sigma^2$ are related.
If I follow what Aaron Brown answered in this post, when the underlying distribution is Normal with ...
9
votes
1answer
310 views
Models for measuring insurance risk exposure
I've recently begun working as a quant for a large bank, and one of my first tasks will be to improve the model determining the risk exposure of their insurance portfolio. The portfolio is fairly ...
9
votes
1answer
383 views
Can VIX be interpreted as a proxy for instantaneous volatility?
BJO06 (Table 2) estimate the following Cox-Ingersoll-Ross model for market variance, $\sigma^2_t$:
$\mathrm{d}\sigma^2_t = (\alpha_0 + \alpha_1\sigma^2_t)\mathrm{d}t + ...
9
votes
1answer
234 views
Could banks move to continuous (rather than overnight) funding?
The dominant frequencies for Money Market and FX instruments were 6m and 3m for a long time, and banks slowly moved to commercial trades at those frequencies but funding overnight. If this is a step ...
9
votes
2answers
1k views
How to get list of all CUSIPS/ISIN?
I want a list of all CUSIPs/ISINs. It would be nice if they were also categorized (e.g. Bonds/Funds etc). Where can I get such a data?
9
votes
1answer
232 views
Is there a standard / methodology to determine and grade the quality of OHLC data?
Inputs are most important to any decision making.
For strategy backtesting, the OHLC data is one of the most inputs.
So to ensure the correctness and integrity of OHLC data, we have checks on the ...
9
votes
1answer
713 views
What are the advantages / disadvantages of the ANTICOR algorithm?
The algorithm is introduced in the paper, Can We Learn to Beat the Best Stock.
The obvious advantage is superior risk-adjusted returns (if you can actually achieve them). Transaction costs and ...
9
votes
1answer
241 views
Cost function for hedging portfolio
Let's say I am hedging an exotic instrument $E$ with $N$ liquid instruments $L_i$, each of which has an associated hedging ratio $R_i$ and a bid-ask spread $\delta_i$ (per dollar of notional). What ...
9
votes
1answer
248 views
Appropriate measure of Volatility for economic returns from an asset?
I am doing research on uncertainty analysis and risk assessment for oil field development. For doing economic forecast and valuation I use Real Options theory, which is almost similar to theory used ...
9
votes
1answer
522 views
How to use macroeconomic indicators for long/short trading strategies?
I am trying to understand how to use macroeconomic data in my trading. I understand that using such data could be used to gauge an overall view of the market and how it's doing as a whole. I have been ...
9
votes
1answer
358 views
Comparing backtesting returns with real trading returns
I have 10 years of backtested simulated performance of some trading strategy (using historical prices), and N months of actual trading performance. What statistical test can I do find out if I'm on ...
9
votes
1answer
339 views
How to estimate the covariance of an index with a basket of stocks?
What would be an ideal way to estimate the covariance of an index with a basket of stocks? For example, should I use one-tail ANOVA test or an individual stock & index F-test?
9
votes
1answer
346 views
Fixed income modeling
I am currently working on my research paper and trying to explain a two-dimensional variable: volume and instrument of corporate debt financing.
Independent variables that I believe must be included ...
9
votes
1answer
273 views
penalizing negative skewness by linking $U(\mu)$ and $U(\Sigma)$
Consider $U_1(\mu,\Sigma)$ and $U_2(\mu,\Sigma)$, where $U_1(\mu, \cdot) = U_2(\mu, \cdot)$, $U_1(\cdot, \Sigma) = U_2(\cdot, \Sigma)$ such that
\begin{equation*}
arg\inf\limits_{\mu \in U_1(\mu, ...
9
votes
1answer
248 views
Currency Hedged ETFs
At work we were talking about currency hedging our equity index exposures but I am struggling to understand how this happens in a typical iShares ETF.
If we take the Japan ETF IJPN then we see this ...
