# All Questions

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### 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 ...
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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+ ... 0answers 314 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 ... 0answers 174 views ### Portfolios from Sorts Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as r_1 > r_2 >... > r_N instead of explicit expected returns: see portfolios ... 0answers 167 views ### Regression in liquidity risk model of Jarrow/Protter In the paper "Liquidity Risk and Risk Measure Computation" authors describe a linear supply curve model for liquidity risks in presence of market impact, i.e. impact-affected asset price S(t,x) is ... 0answers 369 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 ... 0answers 245 views ### Do intraday volume and volatility share the same properties? volatility clustering and mean reversion are very well known properties that one could use when trading. Traders, especially in options world, do take realized vol into account (e.g. by forecasting it ... 0answers 128 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 ... 0answers 159 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 ... 0answers 379 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 ... 0answers 216 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 ... 0answers 509 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 ... 0answers 206 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 ... 0answers 1k 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 ... 0answers 411 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 ... 0answers 245 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 \sigma'=\sqrt{\frac{ln(1+\frac{\sigma}{\mu})^{2}}{t}} ... 0answers 52 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, ... 0answers 220 views ### On the interface between Quant finance and actuarial-science/insurance-math Actuaries (at least in Europe) are frequently severily lacking in quant finance topics. At best they are familiar with B&S model. People going into quant finane or striving to become a quant on ... 0answers 73 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 ... 0answers 985 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 ... 0answers 271 views ### What good papers of short term (<30 seconds) volatility estimation I am looking for good papers of short term (<30 sec) volatility estimation AND short term volatility forecasting. Do you have something in mind ? 0answers 199 views ### Time series analysis on illiquid price data? Say for example I have the following company in some specialized industry: A - Company that is about to be listed in Exchange 1, i.e., no price history B - Company that produce similar products as ... 0answers 103 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)} ... 0answers 795 views ### Tools/R code for predicting Dragon-Kings The theory of the so called Dragon-Kings, esp. by Didier Sornette (ETH Zürich), basically states that financial crises and crashes are predictable (contrary to the theory of black swans). The ... 0answers 149 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 ... 0answers 497 views ### Risk Budgets with Target Portfolio Volatility I'm working through the implementation of a risk budgeting approach as described in the recent Roncalli paper. The idea is that the portfolio manager sets a contribution of total portfolio volatility ... 0answers 179 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 ... 0answers 981 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 ... 0answers 420 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 ... 0answers 144 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 ... 0answers 314 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 ... 0answers 138 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 ... 0answers 259 views ### Can Hurst exponent be used to characterize nonlinear dependence in time series? It appears to me that the answer is no, because Hurst exponent measures persistence in terms of autocorrelation, which is a linear measure. So even if a time series of asset returns is driven by ... 0answers 256 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 ... 0answers 576 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 ... 0answers 101 views ### Some clarifications on eigenvectors and eigenvalues from PCA Could somebody tell me whether suggestions in bold true or not? Q # 1: http://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf ... 0answers 106 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 ... 0answers 78 views ### Does GARCH derived variance explain the auto-correlation in a time series? Given a time series of u_i returns where i=1 to t. \sigma_i is calculated from GARCH(1,1) as \sigma_i^2=w+\alpha u_{i-1}^2 +\beta \sigma_{i-1}^2 . What is the mathematical basis to say that ... 0answers 299 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 ... 0answers 145 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 ... 0answers 50 views ### FTAP a-la Harrison, Kreps and Pliska I was reading the papers co-authored by Harrison, Kreps and Pliska, that initiated the formal research on the connection between pricing, martingale measures, arbitrage and completeness. I have some ... 0answers 38 views ### What type of interpolation should be used in key rate perturbation models? When perturbing a key rate in order to assess sensitivity of portfolio value, what sort of interpolation is standard? A book I am looking at says linear, but this seems pretty unrealistic to me--and ... 0answers 184 views ### Algorithmic Trading Model Calculation and Stale Data I'd like ask everyone a more concurrency programming but definitely quant-finance related question. How do you deal with staleness of data in market hours as quote ticks are streaming and your model ... 0answers 93 views ### Finding the dynamics of a dividend paying asset under arbitrary numeraire Assuming I have a dividend paying asset S with dividend process D. Now I would like to use the bank account process B as numeraire and determine the dynamics of S under the the corresponding ... 0answers 212 views ### Optimization: Factor model versus asset-by-asset model In portfolio management one often has to solve problems of the quadratic form$$ w^T \Sigma w + w^T c \rightarrow Min $$with portfolio weights w \in \mathbb{R}^N a constant c \in \mathbb{R}^N and ... 0answers 353 views ### Formula for the efficient portfolios (mean-variance optimisation)? Consider the setting of mean-variance portfolio optimisation: n assets with expected returns \overline{r}_1,...,\overline{r}_n and standard deviations \sigma_1,...\sigma_n. For a certain fixed ... 0answers 96 views ### Applications of distance correlation This question mentions distance correlation. Where has this concept been applied to financial data and provided new insight? Do you know any examples or references? 0answers 81 views ### Risk neutral measure in exponential levy model Is there a method of finding a risk-neutral measure for assets driven by the levy process? I understand there is the esscher transform but I think it tends to transform the processes into ... 0answers 293 views ### Shrinkage Estimator for Newey-West Covariance Matrix I like to apply the Newey-West covariance estimator for portfolio optmization which is given by$$ \Sigma = \Sigma(0) + \frac12 \left (\Sigma(1) + \Sigma(1)^T \right), $$where \Sigma(i) is the lag ... 0answers 245 views ### Value-at-Risk formula when using skewed-t distribution I am trying to find a formula for the skewed-t VaR. For example the VaR formula for a t-distribution is$$ \sqrt{\frac{df-2}{df}} \times \Sigma{t} \times \mbox{quantitle}(t-\mbox{dist}, 0.01) + \mu ...

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