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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 ...
1k views

198 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 $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
603 views

compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
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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 ...
748 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 ...
I have a payoff that is the worst of the returns two indices: S&P500 (SPX) and Euro Stoxx 50 (SX5E). $\pi = \min \left\{\left(\frac{\text{SPX}_\tau-\text{SPX}_0}{\text{SPX}_0}\right),\left(\frac{\... 0answers 87 views Does your Parkinson volatility ratio work as Taleb explained? According to Dynamic Hedging: Managing Vanilla and Exotic Options (Taleb, 1997), the Parkison volatility estimator has several meaningful properties. It is defined $$P=\sqrt{\frac{1}{n}\sum_{i=1}^{n}\... 0answers 80 views Predicting bond auction result. Should I train separate models for different maturity in face of Data deficiency? Problem Statement Trying to predict how bond auction result ( in terms of yield ) is different from its forecast (the when-issued yield ). More info:http://www.mortgagenewsdaily.com/mortgage_rates/... 0answers 169 views Jim Gatheral's ansatz In the Ansatz section of Jim Gatheral's book Volatility Surface (page 32), he assumes$$\mathbb E[x_s|x_T]=x_T\frac{\hat w_s}{\hat w_T}$$where \hat w_t:=\int_0^t \hat v_s ds is the expected total ... 0answers 731 views Python Backtesting Framework Similar to Quantstrat I use Quantstrat heavily for strategy research and optimisation. I have two Python developers about to join my team and would like to use it as an opportunity to diversify our research tools so we are ... 0answers 271 views simulating from the CIR++ I am looking at the CIR++ model which is described in interest rate models by Brigo et al, and was wondering on how to actually simulate from this model. The model reads$$r_t=x_t+\phi(t),$$where ... 0answers 577 views Up and Down days in GBPUSD and a Filter I want to study if the odds of an up or down day in a forex pairs is 50-50. I just count the total number of up and down days in X years and compare it with the total days. The results are very ... 0answers 306 views Pricing an American call under the CGMY model I am pricing an American call under the CGMY model (0 < Y < 1) with strike K at grid point (x_i,\tau_j) where x_i=x_{min}+i\,\Delta x for i=0,1,...N and \Delta x=\frac{x_{max}-x_{min}... 0answers 247 views Transition densities in the Heston model Knowing the Characteristic function \Phi_{T,t} = \mathbb{E} [ e^{i u S_T} | S_t, V_t] (or equivalently, the Laplace transform) of an affine process, it's possible to know the distribution of the ... 0answers 780 views Constructing Volatility Smile from American Options My question is about best practices for reconstructing volatility smiles for a fixed tenor from American option data. For simplicity/liquidity, I am currently considering options on SPY. I am ... 0answers 245 views Applications of distance correlation This question mentions distance correlation. Where has this concept been applied to financial data and provided new insight? Do you know any examples or references? 0answers 92 views Random variable minus Integral of Ito Generator is a Martingale under what conditions? I am reading about american option pricing and the variational inequality, and the book I am reading states, in the derivation of the variational inequality, the following is a martingale:$$M_s = U(s,... 0answers 56 views Formal proof market incompleteness under jump diffusion Does anyone have formal proof of markets incompleteness under jump diffusion ? I am familiar with the intuitive approach as mentioned in Tankov (delta), yet I am looking for a formal approach and ... 0answers 145 views Arbitrage free smoothing of volatility smile - cubic spline - implementation procedure I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf). The problem I want to solve is much simpler ... 0answers 155 views Determining Hurst exponent of a Brownian motion I am trying to determine the Hurst exponent of a simple Brownian motion, however, I seem to get a result that differs from 0.5. I am following the instructions given on the Wikipedia-page, and here is ... 0answers 49 views Quantitative and regulatory aspects of portfolio integration in IRB credit portfolios Say bank A buys a credit portfolio "B" (e.g. corporate loans or retail mortgage, ...) from bank B. Bank A fulfills the the requirements of CRR (capital requirement regulation) for its existing ... 0answers 108 views Measure how different forecasted volatility is from realized volatility Hi Quantitative Finance Stack Exchange, I'm looking for an opinion on a simple question. Suppose I use a Garch(1,1) model to make a volatility forecast. At time$t$, I have realized volatility$\...
I have following problem: Imagine I generate large number of homogenous poisson process sample paths (by sample path I mean a sequence of arrival times $\tau_i$ all with the same intensity. However ...