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35
votes
0answers
958 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 ...
29
votes
0answers
1k 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+ \...
18
votes
0answers
204 views

Is there a relationship between Risk Neutral Pricing framework and Nash Equilibria?

Based on the Fundamental Theorem of Asset Pricing, the risk neutral price of a contingent claim on an asset in a liquid, arbitrage free market can be determined by switching to an equivalent $Q-$ ...
18
votes
0answers
518 views

Questions on Kelly criterion

I am new to asset allocation problems and have some concerns regarding the derivation of the continuous-time Kelly criterion (i.e. not the original version destined to discrete sports betting/Casino). ...
17
votes
0answers
1k 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 ...
16
votes
0answers
649 views

Local Stochastic Volatility - Break even levels

In Chapter 12 of his excellent book Stochastic Volatility Modeling, Lorenzo Bergomi discusses the topic of local-stochastic volatility models (LSV). As most of you are probably aware of, the idea is ...
15
votes
1answer
817 views

Stochastic modelling of derivatives on dividends

I consider pricing and risk analysis of derivatives on dividends of the members of equity indices (such as Dow Jones EuroStoxx). There are options but I focus on futures. What are common stochastic ...
14
votes
3answers
2k views

Estimating Parameters - Vasicek

The Vasicek model for the short rate $r_t$ is given by the SDE $$ dr_t = \alpha(\beta - r_t)dt + \sigma dW_t, $$ where $W_t$ is a Brownian motion under the physical measure. I'd like to compute bond ...
13
votes
1answer
544 views

Consistency of economic scenarios in nested stochastics simulation

I am interested in references on research regarding the consistency of economic scenarios in nested stochastics for risk measurement. Background: Pricing by Monte-Carlo: For pricing complex ...
13
votes
0answers
534 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 ...
12
votes
0answers
288 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 ...
12
votes
0answers
316 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 managers....
12
votes
0answers
510 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 ...
12
votes
1answer
465 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}} \end{...
11
votes
1answer
498 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 :...
11
votes
1answer
490 views

Distribution of hitting time of the integrated CIR process

If an increasing process $X_t$ has a known Laplace transform $\mathbb{E} e^{-s X_t} = m_t(s)$, define its hitting time $\tau$ to some level $B$ to be $$ \tau = \inf\{ u > 0 : X_u \geq B \}. $$ Can ...
10
votes
1answer
555 views

Variance swap volatility - ATMF vol, Skew and Curvature

In a pure diffusion setting, it is a well known result that the volatility $\sigma_T$ of a fresh-start variance swap of maturity $T$ as seen of $t=0$ verifies \begin{align} \sigma_T^2 &= \Bbb{E}_0^...
10
votes
0answers
6k views

How to use statsmodels' Granger causality test to measure the lag between two time series?

I am using the Granger causality test to measure the lag between pairs of time series where it is already apparent that one is following the other. So I am not expecting this test to tell me whether ...
10
votes
0answers
844 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 ...
10
votes
0answers
476 views

Computing Value at Risk for portfolio in R

I know how to compute VaR with long positions using PerformanceAnalytics. What about a portfolio consisting in two equities A and B, 100 USD long positions in each, and 2 stock options for the same ...
10
votes
0answers
211 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 ...
10
votes
0answers
1k 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 $...
10
votes
0answers
1k 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 ...
10
votes
0answers
332 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 ...
10
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 ...
10
votes
0answers
409 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 ...
9
votes
0answers
344 views

Zero Coupon Bond prices in One Factor Hull White model

I implemented the one factor Hull White model for educational purposes and I calibrated the model from a given (made up!) yield curve: The Zero Coupon Bond Prices from this yield curve are: Taking ...
9
votes
0answers
286 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 ...
9
votes
1answer
387 views

Block bootstrap to synthesize asset prices

I have a few basic questions on block bootstrapping on a financial time series ('TS'). Assuming my trade universe consists of 10 stocks, I would like to create a set of synthetic prices for all 10 ...
9
votes
2answers
2k views

What does the cointegration coefficient represent in pairs trading when cointegrating log stock prices?

In Pairs Trading by Vidyamurthy, on page 83 (and throughout the book), the author describes an elementary example of trading with log prices. The long run equilibrium of the basic portfolio is given ...
9
votes
1answer
712 views

Issue with OLS Regression for Nelson Siegel Svensson parameters

I have been working on getting input parameters to the Non-Linear Optimization which gives the Nelson Siegel Svensson model parameters and am carrying out the OLS regression as described in this ...
9
votes
0answers
4k views

Bridgewater's Daily Observations

Bridgewater Associates send out Daily Observations to their clients, but I haven't found many traces of these publications online. The series started some 40 years ago by Ray Dalio, and there're just ...
9
votes
0answers
762 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 ...
8
votes
0answers
303 views

Market Maker portfolio management

I am interested in articles/strategies related to portfolio and inventory management for market makers and to management of order cancellation, updates of order, etc. Most of the strategies from ...
8
votes
0answers
174 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 ...
8
votes
0answers
193 views

No arbitrage conditions for normal implied volatility

usually the term implied volatility refers to Black-Scholes implied volatility (also Log-Normal volatility): it is defined as a quantity which when plugged in the Black-Scholes formula returns the ...
8
votes
1answer
251 views

Heston model reparametrisation

It is well-known that calibrating Heston to the vanilla market is not as easy as it seems: some parameters are "interdependent" and the objective function exhibit plateaus in the parameter space (at ...
8
votes
1answer
523 views

Transforming 3M volatilities into 6M volatilities in EUR forecast curves

I have implemented a stripping algorithm to extract forward volatilities from cap/floor flat volatilities for different currencies. I am however struggling a bit when implementing a method to convert ...
8
votes
0answers
357 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 ...
8
votes
0answers
245 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} Z_t^{T_j})[R(t,...
8
votes
0answers
207 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 $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
8
votes
0answers
627 views

compute time from FX forward, how use DEPO rates?

assume I have following delta-term vol data from broker: ...
8
votes
0answers
3k 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 ...
7
votes
0answers
63 views

Quanto basket payoff

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{\...
7
votes
0answers
127 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}\...
7
votes
0answers
83 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/...
7
votes
1answer
389 views

Risk-Neutral CAPM

In the paper Measuring Equity Risk with Option-implied Correlations, Buss and Vilkov replace the standard CAPM beta: $$ \beta_{iM,t}^P=\frac{\sigma_{i,t}^P\sum_{j=1}^N w_j \sigma_{j,t}^P\rho_{ij,t}^P}...
7
votes
0answers
367 views

Why are my GARCH forecasts biased?

I've run an ARMA(1, 1)-GARCH(1, 1) model with normal density on log returns for twelve stocks. I computed the one-step-ahead out of sample forecast for daily volatility on a rolling windows for 500 ...
7
votes
0answers
760 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 ...
7
votes
0answers
237 views

Libraries for calculating options strategy-based margin

Hopefully, this is an acceptable question in this forum, even if it isn't analytically focused. As part of an effort to analyse the effect of different option trade structures on a portfolio, I need ...

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