22
votes
0answers
635 views

How to show that this weak scheme is a cubature scheme?

Weak schemes, such as Ninomiya-Victoir or Ninomiya-Ninomiya, are typically used for discretization of stochastic volatility models such as the Heston Model. Can anyone familiar with Cubature on ...
14
votes
0answers
647 views

Law of an integrated CIR Process as sum of Independent Random Variables

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+ ...
11
votes
0answers
420 views

performance of historical VaR parameters

An historical VaR measure is parameterized in terms of the confidence level and also number of periods. Specifically, the $\alpha$% T-period VaR is defined as the portfolio loss x in market value over ...
10
votes
0answers
506 views

Probability distribution of maximum value of binary option?

A binary option with payout \$0/\$100 is trading at \$30 with 12 hours to expiration. Assuming the underlying follows a geometric Brownian motion (hence volatility remains constant), what ...
8
votes
0answers
220 views

Extreme Value Theory possible for portfolios with options?

Say you have a portfolio with long exposure to a few linear assets (stock indices) and short exposure to a nonlinear asset (say call options on one of the linear assets). I am interested in ...
8
votes
0answers
269 views

Optimization procedure for entropy pooling

I was wondering if those who used the entropy pooling code provided by Attilio Meucci had issues with the optimization procedure (especially regarding the fminunc function in Matlab). When I stress ...
8
votes
0answers
446 views

Alternative ways to understand time-varying comovement between two time-series?

I have been looking into ways to better understand how the dependencies/correlations/etc between two time series can vary over time. I first thought about using a Kalman/particle filter over a ...
8
votes
0answers
408 views

Can we use White's reality check to compare two Sharpe ratios?

I read a paper from Ledoit and Wolf that proposes a method to compare two Sharpe ratios and a paper from White that proposes a method to compare $n$ trading rules. My question is: Can we use White's ...
7
votes
0answers
67 views

Are there references about liquidation, transaction, market impact costs in portfolio optimization

I am looking for some references treating of what I would call liquidation cost market impact cost transaction cost(*) in the usual "portfolio optimization problem under linear constraints". Let ...
7
votes
0answers
168 views

Quantum Mechanics and Economics… What

I was reading this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2002698&download=yes The author has the model presented here: ...
7
votes
0answers
162 views

Here is an approach for measuring Data Snooping; is it new?

I came up with an approach for measuring data snooping, or overfitting. My question is whether this approach was published and expanded-on already, or is it new? My approach relies on the observation ...
7
votes
0answers
176 views

Proving the asymptotic distribution of Manipulation-Proof Performance Measure (MPPM) (Paper by Goetzmann et al.)

In Goetzmann et al.'s (2007) paper, the authors derive a "Manipulation-Proof Performance Measure" (MPPM), which is a performance measure that is impervious to performance manipulation by fund ...
7
votes
0answers
536 views

Examples of Spectral Risk Measures

Let's take the usual definition of a spectral risk measure. If we look at the integral we see that spectral risk measures have the property that the risk measure of a random variable $X$ can be ...
7
votes
0answers
290 views

Implied term structure from risky discount curve: does it make sense?

We know that, taken every discount curve, it's possible to calculate its forward rates according to our tenor preferences. We know also that it's actually possible to extract an implied term ...
7
votes
0answers
783 views

What are modern algorithms for trade classification?

When dealing with trade data, for example from TAQ, a common problem is that of determining whether a trade was a buy or a sell. The most commonly used classifier is the Lee-Ready algorithm (Inferring ...
7
votes
0answers
2k views

Volatility-Based Envelopes

I am following an article by Mohamed Elsaiid (MFTA) about Volatility-Based Envelopes - a quite new technical indicator he has introduced, that is being used by Bloomberg. My goal is to get a simple ...
7
votes
0answers
284 views

Transformation of Volatility - BS

I have recently seen a paper about the Boeing approach that replaces the "normal" Stdev in the BS formula with the Stdev \begin{equation} \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} ...
6
votes
0answers
50 views

Does price of american (put) option exhibit smooth pasting in time direction under B-S model?

Let us consider the BS model and let $f(s,t)$ denote the price of an American put option with $t$ to expiry, then it is known the solution of the optimal stopping (when it is risk neutral) related to ...
6
votes
0answers
127 views

For which instruments performs SABR/LMM better than LMM?

For which class of instruments the SABR/LIBOR Market Model does perform better than the classical LIBOR Market Model? The LIBOR Market Model The LIBOR Market Model — also known as Brace, Gatarek, ...
6
votes
0answers
147 views

American Swaption Heding with Malliavin Calculus

Hedging American Swaption Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t. $$ C_t = (\delta \sum_{j=n+1}^{M+1} ...
6
votes
0answers
168 views

Graduating Quantitative Finance (please don't move it to meta immidiately)

Seeing how very few actually read the Quant Finance meta I intentionally post it here on the main site. To the more powerful admins: could you leave it here for a day or two and move it to meta ...
6
votes
0answers
100 views

2-state HMM / ARMA process?

I have issues with this problem: Let $\{X_t, t\in \Bbb N\}$ be a 2-state stationary Markov chain, with transition $M$ (and $M(1,2)\neq 0 \neq M(2,1)$), let $\{W_t, t\in \Bbb N\}$ be a strong Gaussian ...
6
votes
0answers
555 views

Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed ...
6
votes
0answers
2k views

Algorithm to fit AR(1)/GARCH(1,1) model of log-returns

I am fitting numerically an AR(1)/GARCH(1,1) process to index and stock log-returns, $r_t=\log(P_t/P_{t-1})$, where $P_t$ is the price at time $t$, and thus far am not clear on where the observed log ...
6
votes
0answers
122 views

Applications of distance correlation

This question mentions distance correlation. Where has this concept been applied to financial data and provided new insight? Do you know any examples or references?
6
votes
0answers
571 views

Testing Valuation, Size and Momentum (proprietary factors) from 1988-2013: No evidence of driving cross-sectional returns

I am currently testing whether three proprietary factors - Valuation, Size and Momentum - explain cross-sectional returns. A sample of 3000 securities was tested using Fama-MacBeth two-pass ...
6
votes
0answers
125 views

Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
6
votes
0answers
359 views

Value-at-Risk formula when using skewed-t distribution

I am trying to find a formula for the skewed-t VaR. For example the VaR formula for a t-distribution is $$ \sqrt{\frac{df-2}{df}} \times \Sigma{t} \times \mbox{quantitle}(t-\mbox{dist}, 0.01) + \mu ...
5
votes
0answers
139 views

Pricing an American call under the CGMY model

I am pricing an American call under the CGMY model ($0 < Y < 1$) with strike $K$ at grid point $(x_i,\tau_j)$ where $x_i=x_{min}+i\,\Delta x $ for $i=0,1,...N$ and $\Delta ...
5
votes
0answers
167 views

Covariance estimation

Shrinkage was much en-vogue before RMT took everybody's attention, however the latter also showed its limits. A plethora of other estimators has been presented, but I could not yet spot a golden ...
5
votes
0answers
214 views

Stress testing covariance

Going one level beyond stressed scenarios, to parameters e.g. for a VaR measure: what are the most common approaches for stressing a covariance/correlation matrix, especially taking portfolio exposure ...
5
votes
0answers
2k views

VaR model Unconditional Coverage Tests: Is this extension of Kupiec POF test correct?

Background: Kupiec P. in 1995, published paper "Techniques for Verifying the Accuracy of Risk Management Models" on Journal of Derivatives, v3, P73-84, it's a Unconditional Coverage Tests designe for ...
5
votes
0answers
550 views

option chain data visualization, sunburst

I think option chains are not represented in the best way. With more and more options products coming out and trading on the various exchanges, I see vendors struggling to keep up with a good way to ...
5
votes
0answers
209 views

is there a mapping from Altman Z-score for private companies to bond ratings or probability of default?

On wikipedia, there is a formula to calculate the Altman Z-score for private companies: Z-score estimated for private firms: T1 = (Current Assets − Current Liabilities) / Total Assets T2 = Retained ...
5
votes
0answers
180 views

Basel CVA VaR with R/WWR

In Basel III the CVA VaR “is restricted to changes in the counterparties’ credit spreads and does not model the sensitivity of CVA to changes in other market factors, such as changes in the value of ...
5
votes
0answers
151 views

Testing for stock market herding over short periods

The literature has well established methods for testing stock market herding over a decent time window. Are there any ways that have appeared in the literature to test for stock market herding over ...
5
votes
0answers
301 views

generating (or tracking) the DJUBS commodity index

Dow Jones and UBS publish one of the most popular commodity index families, the Dow Jones-UBS Commodity Index and its subindices. They provide a detailed manual describing the composition of the index ...
5
votes
0answers
613 views

Alternative to Block Bootstrap for Multivariate Time Series

I currently use the following process for bootstrapping a multivariate time series in R: Determine block sizes - run the function b.star in the np package which produces a block size for each series ...
4
votes
0answers
96 views

Momentum - Statistical Argument

In their seminal paper Jegadeesh and Titman (1993) develop a statistical model to infer where moment comes from. In practice they setup the following: $r_{it}=\mu_i + b_i f_t +e_{it}$ ...
4
votes
0answers
126 views

Markov-Switching Multifractal and FX Rates

Is there a better model than Markov-Switching Multifractal (MSM) for detecting regime shifts in FX rates across multiple time horizons? I am especially interested in the different aspects of the ...
4
votes
0answers
81 views

pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
4
votes
0answers
58 views

Transition densities in the Heson model

Knowing the Characteristic function $\Phi_{T,t} = \mathbb{E} [ e^{i u S_T} | S_t, V_t]$ (or equivalently, the Laplace transform) of an affine process, it's possible to know the distribution of the ...
4
votes
0answers
83 views

“Extract” the density of the underlying, given the implied volatility “surface”

Suppose given implied volatility quotations $\widehat{\sigma}(T_i,K_j)$ of call options on an underlying $S$ for various expiries $T_i$'s and strikes $K_j$'s. I am interested in the following problem ...
4
votes
0answers
77 views

Is Least Median Squares (LMS) regression commonly used in Finance?

Least Median Squares is often argued to give more stable results than does OLS. Whereas in OLS one minimises the mean of squared residuals, in LMS, one instead minimises the median of squared ...
4
votes
0answers
82 views

Why is Weighted Least Squares necessary in fundamental factor model?

Why is Weighted Least Squares necessary in fundamental factor model while it is not in a standard Macroeconomic factor model? I understand that $\mathbb{E}[\epsilon^2_{it}]=\sigma_i^2$ varies across ...
4
votes
0answers
164 views

Integral-differential equation for forward rates

I am struggling in this question: Let $P(t,T)$ denote the price of a zero-coupon bond (with marturity at time $T$) at time $t \in [0,T]$. As usual, at time $t$ for maturity $T$, the forward rate is ...
4
votes
0answers
392 views

A model to stochastic hazard rate and CDS spread term structure

I'm interested in the term structure of CDS spread. It's known that the Market CDS rate (fair CDS spread or T-maturity spread) of a CDS contract initiated at $s$, maturity $T$ and recovery function ...
4
votes
0answers
164 views

What is the most convenient data structure for backtesting a model of futures options prices?

I have an empirical model for the dynamics of futures prices in a particular market that I have implemented using a long series of the front five contracts. (I account for the roll in my model.) I ...
4
votes
0answers
159 views

Calculating volatility of inhomogeneous time series

I am reading an article by Zumbach and Müller whose name is Operators on Inhomogeneous Time Series. This is interesting in general, but my main goal is to learn a good and efficient method to ...
4
votes
0answers
1k views

Calculate interest rate swap curve from Eurodollar futures price

So I was reading Robert McDonald's "Derivatives Markets" and it says Eurodollar futures price can be used to obtain a strip of forward interest rates. We can then use this to obtain the implied ...

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