All Questions
4,446
questions with no upvoted or accepted answers
35
votes
0answers
1k 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 ...
23
votes
0answers
377 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
683 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).
...
18
votes
1answer
1k 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 ...
17
votes
0answers
990 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 ...
14
votes
0answers
354 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....
13
votes
0answers
619 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
1k 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^...
12
votes
0answers
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 ...
12
votes
0answers
320 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
1answer
599 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
0answers
557 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 ...
11
votes
1answer
770 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
0answers
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 $\...
11
votes
1answer
545 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
0answers
343 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 ...
10
votes
1answer
9k 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
1answer
597 views
Risk-Neutral CAPM
In the paper Measuring Equity Risk with Option-implied Correlations, Buss and Vilkov replace the standard CAPM beta:
$$
\beta_{iM,t}^P=\frac{\sigma_{i,t}^P\sum_{j=1}^N w_j \sigma_{j,t}^P\rho_{ij,t}^P}...
10
votes
0answers
565 views
Block bootstrap to synthesize asset prices
I have a few basic questions on block bootstrapping on a financial time series ('TS').
Assuming my trade universe consists of 10 stocks, I would like to create a set of synthetic prices for all 10 ...
10
votes
0answers
223 views
2-state HMM / ARMA process?
I have issues with this problem:
Let $\{X_t, t\in \Bbb N\}$ be a 2-state stationary Markov chain, with transition $M$ (and $M(1,2)\neq 0 \neq M(2,1)$), let $\{W_t, t\in \Bbb N\}$ be a strong Gaussian ...
10
votes
0answers
1k views
option chain data visualization, sunburst
I think option chains are not represented in the best way. With more and more options products coming out and trading on the various exchanges, I see vendors struggling to keep up with a good way to ...
10
votes
0answers
372 views
Basel CVA VaR with R/WWR
In Basel III the CVA VaR “is restricted to changes in the counterparties’ credit spreads and does not model the sensitivity of CVA to changes in other market factors, such as changes in the value of ...
10
votes
0answers
2k views
Volatility-Based Envelopes
I am following an article by Mohamed Elsaiid (MFTA) about Volatility-Based Envelopes - a quite new technical indicator he has introduced, that is being used by Bloomberg. My goal is to get a simple ...
9
votes
0answers
207 views
Change of numéraire for two risky assets without bank account (Margrabe’s formula?)
I am considering two risky assets following the usual correlated GBM given by
$$\frac{\mathrm{d}S^{(i)}_t}{S^{(i)}_t}=\mu_i\mathrm{d}t+\sigma_i\mathrm{d}W^{(i)}_t,\quad i\in\{1,2\}$$
with
$$\mathrm{d}...
9
votes
0answers
131 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 ${\mathbf M}$.
...
9
votes
0answers
462 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 ...
9
votes
0answers
5k 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
324 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 ...
9
votes
0answers
794 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
1k views
Feller Condition (Cox-Ingersoll-Ross) source
For the Cox-Ingersoll-Ross model $$\text{d}r_t = a(b-r_t)\text{d}t+\sigma\sqrt{r_t}\text{d}W_t$$ the condition (referred to as "Feller condition") $$2ab\geq\sigma^2$$ ensures that the solution is ...
8
votes
0answers
382 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
219 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
1answer
648 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 ...
8
votes
0answers
393 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
275 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.
$$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
8
votes
0answers
2k views
Explanation or implementation of Ledoit-Wolf estimator (without math packages)
I have calculated weights of selected assets in a market-neutral portfolio (presumably with min variance) using PCA and simple data covariance matrix.
The question is :
It is obvious that Cov Matrix ...
8
votes
0answers
221 views
Basket option density in BS model
Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
8
votes
0answers
659 views
compute time from FX forward, how use DEPO rates?
assume I have following delta-term vol data from broker:
...
8
votes
0answers
3k views
VaR model Unconditional Coverage Tests: Is this extension of Kupiec POF test correct?
Background: Kupiec P. in 1995, published paper "Techniques for Verifying the Accuracy of Risk Management Models" on Journal of Derivatives, v3, P73-84, it's a Unconditional Coverage Tests designe for ...
7
votes
0answers
104 views
Has a closed-form formula for the collateral choice option been found?
The collateral choice option problem has been formulated in e.g. Fujii and Takahashi (2011), Piterbarg (2012) or Antonov and Piterbarg (2013), as the computation of an expectation of the following ...
7
votes
0answers
142 views
Random variable minus Integral of Ito Generator is a Martingale under what conditions?
I am reading about american option pricing and the variational inequality, and the book I am reading states, in the derivation of the variational inequality, the following is a martingale: $$M_s = U(s,...
7
votes
0answers
2k views
Understanding and simulating the jumps in Merton's Jump-Diffusion SDE?
I found this great post deriving the solution to the Merton Jump-Diffusion SDE
$$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{2}\right)t + \sigma W_t\right)\prod_{j=0}^{N_t}V_j$$
The first part of ...
7
votes
0answers
824 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 ...
7
votes
1answer
863 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 ...
7
votes
0answers
95 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
565 views
Exposure calculation of a re-coupon swap
How to calculate the exposure of a recoupon swap (when the MTM of an i.r. swap is settled and the fixed rate is reset to the prevailing swap rate for the residual maturity).
It's used to reduce the ...
7
votes
0answers
67 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 ...
7
votes
0answers
809 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
306 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 ...
7
votes
0answers
307 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 $...