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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 ...
TheBridge's user avatar
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30 votes
0 answers
683 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 $Q-$ ...
Ali Fathi's user avatar
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23 votes
0 answers
2k 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 ...
Quantuple's user avatar
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22 votes
0 answers
944 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). ...
user22568's user avatar
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17 votes
0 answers
1k 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 ...
ismael's user avatar
  • 313
17 votes
0 answers
404 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....
SwiftMo's user avatar
  • 335
16 votes
1 answer
750 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 ...
Catherine Janssen's user avatar
15 votes
0 answers
390 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 ...
greg's user avatar
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14 votes
0 answers
798 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 ...
Bytesize's user avatar
  • 421
13 votes
1 answer
2k views

Risk management tools for long term Gamma/Vega sellers subject to margin calls

TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you ...
Lisa Ann's user avatar
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13 votes
0 answers
511 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 ...
Hans's user avatar
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13 votes
1 answer
986 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}...
phdstudent's user avatar
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12 votes
0 answers
3k 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 ...
Bach's user avatar
  • 449
11 votes
0 answers
771 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 ...
NoviceProg's user avatar
11 votes
0 answers
6k 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 ...
Anton Tarasenko's user avatar
11 votes
0 answers
482 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 ...
lush90's user avatar
  • 111
11 votes
0 answers
2k views

Formula for the efficient portfolios in 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 $\...
Phil-ZXX's user avatar
  • 1,042
11 votes
1 answer
677 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 ...
Kakashi Hatake's user avatar
10 votes
0 answers
305 views

Unwinding a Portfolio

I have a portfolio ${\mathbf P}$ made up of positions $n_i$ in each of $N$ securities, which I'm assuming are jointly normally distributed with means $x_i$, and covariance matrix ${\mathbf M}$. ...
StackG's user avatar
  • 3,046
10 votes
0 answers
617 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 ...
mugen's user avatar
  • 201
10 votes
0 answers
448 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 ...
Drew's user avatar
  • 405
10 votes
0 answers
256 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 ...
mookid's user avatar
  • 201
10 votes
0 answers
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 ...
CQM's user avatar
  • 1,862
10 votes
0 answers
431 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 ...
Quartz's user avatar
  • 1,553
10 votes
0 answers
845 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 ...
ProbablePattern's user avatar
9 votes
1 answer
754 views

Time series strategy versus cross section strategy?

Suppose we have a universe of $n$ stocks, and for each time period $t$ we have $n$ predictions for their future returns. Now we can calculate the information coefficient for our predictions in two ...
autoencoder's user avatar
9 votes
0 answers
389 views

On a time integral of Brownian motion up to the hitting time

Just come up with a 'simple' and interesting problem that I've been struggling to deal with for some time. Consider a filtered probability space $(\Omega, \mathcal{F}, \{\mathcal{F}_t\}_{t\in[0,T]},\...
FoolAlex's user avatar
  • 101
9 votes
0 answers
928 views

Autocallable option Delta

There have been numerous exotic trading desk blow ups lately, related to various reasons. However, in particular, one bank had some issues where they were pricing autocallable notes with Local ...
ellie_cat's user avatar
  • 111
9 votes
0 answers
3k 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 ...
AnUser's user avatar
  • 101
9 votes
0 answers
288 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 ...
BillyJean's user avatar
  • 191
9 votes
0 answers
4k views

Explanation or implementation of Ledoit-Wolf estimator (without math packages)

I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix. The question is : It is obvious that Cov Matrix ...
Anonymous's user avatar
  • 415
9 votes
0 answers
248 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 $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
KAT's user avatar
  • 326
9 votes
0 answers
4k 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 ...
athos's user avatar
  • 2,231
8 votes
0 answers
3k views

Replicating Bloomberg Swap Prices with QuantLib

I'm trying to learn more about the QuantLib python package and as an exercise I'm trying to replicate some swaps on Bloomberg. However, when I do so, it seems like my swaps are consistently ...
K. Mao's user avatar
  • 181
8 votes
0 answers
2k views

How good is the inverse-volatility portfolio?

Heuristic portfolio construction techniques include the equally-weighted portfolio (1/N) and the inverse volatility portfolio (IVP), which is based on the low-volatility effect. They can be assembled ...
develarist's user avatar
  • 3,040
8 votes
0 answers
177 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,...
Slade's user avatar
  • 656
8 votes
0 answers
413 views

Merton's portfolio problem with constraints

Suppose the investor can invest in a Black-Scholes market with one risky asset $S$ with drift $\alpha$ and volatility $\sigma$ and a riskless asset $B$ with a riskless rate of return $r$, and the ...
user128836's user avatar
8 votes
0 answers
159 views

recent developments in American options?

I have read the paper written by Egloff (2005) using machine learning techniques to solve the optimal stopping problem. Is there any development in pricing American options during 2005-2016? (based ...
Lookout's user avatar
  • 257
8 votes
0 answers
306 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,...
Lucas Morin's user avatar
8 votes
1 answer
2k views

Measuring implied move priced into an event

It's well known that options price in an expected move in the underlying going into events, such as earnings announcements. I currently measure this implied move by computing the forward variance ...
user3294195's user avatar
8 votes
1 answer
705 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 ...
tn240's user avatar
  • 121
8 votes
4 answers
648 views

American put option. Exercise time is a random variable, calculation of expected payoff

I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
Makina's user avatar
  • 273
7 votes
0 answers
157 views

Recent developments in interest rate modelling

Brigo and Mercurio published the 2nd edition of their (classic? definitive?) book on interest rate models in 2006. Have there been any major theoretical developments since then? Has anyone published a ...
Jamie Ballingall's user avatar
7 votes
0 answers
141 views

Implied vol bounded if and only if instantaneous vol bounded

I'd like to show that in diffusion models IV is bounded iff instantaneous vol is bounded if there is to be no arbitrage. So, assume a model under the pricing measure of the form $$ dS_u = \sigma_u S_u ...
user avatar
7 votes
0 answers
375 views

Solving option market making problem

I am currently working on a paper for quoting option as a market maker from Bastien Baldacci , Philippe Bergault & Olivier Guéant Without dwelling on details on how to obtain the HJB equation for ...
Kupoc's user avatar
  • 98
7 votes
0 answers
293 views

Seeking criticism of model assumptions

I have been trying to publish a new calculus and options model for seven years. I have been consistently desk rejected, so what I am trying to do is get criticism of my assumptions because they ...
Dave Harris's user avatar
  • 4,309
7 votes
0 answers
188 views

Let $\mathbb{P} \sim \mathbb{Q} \sim \mathbb{R}$ be equivalent probability measures on some measurable space

Let $\mathbb{P} \sim \mathbb{Q} \sim \mathbb{R}$ be equivalent probability measures on some measurable space $(\Omega, \mathcal{F})$, and let $\mathcal{G} \subset \mathcal{F}$ be a sub- $\sigma$-...
codelearner's user avatar
7 votes
2 answers
332 views

Likelihood ratio and pathwise sensitivity method for coupled SDEs

I have two coupled SDEs \begin{align*} dS_t=rS_tdt+V_tdW_t^{(1)},\\ dV_t=aV_tdt+b(V_t)dW_t^{(2)},\\ \end{align*} where $W_t^{(1)}$ and $W_t^{(2)}$ are independent Brownian motions, initial input data ...
user107224's user avatar
7 votes
0 answers
148 views

Non attainable claim - Incomplete market

I am wondering whether there is a standard procedure to find a non attainable (i.e. non replicable) asset in an incomplete market. As an example, let us have the following market ($B = (B^1, B^2, B^3)$...
notSoSure's user avatar
7 votes
0 answers
213 views

Has a closed-form formula for the collateral choice option been found?

The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
Daneel Olivaw's user avatar

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