All Questions
5,601
questions with no upvoted or accepted answers
37
votes
0
answers
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 ...
- 4,553
28
votes
0
answers
630
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 $Q-$ ...
- 411
22
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 ...
- 14.5k
21
votes
0
answers
905
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).
...
- 211
16
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 ...
- 303
16
votes
0
answers
394
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....
- 325
14
votes
1
answer
656
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 ...
14
votes
0
answers
378
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 ...
- 290
14
votes
0
answers
765
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 ...
- 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 ...
- 2,111
12
votes
0
answers
476
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 ...
- 2,746
12
votes
1
answer
915
views
Risk-Neutral CAPM
In the paper Measuring Equity Risk with Option-implied Correlations, Buss and Vilkov replace the standard CAPM beta:
$$
\beta_{iM,t}^P=\frac{\sigma_{i,t}^P\sum_{j=1}^N w_j \sigma_{j,t}^P\rho_{ij,t}^P}...
- 8,052
12
votes
0
answers
3k
views
Volatility-Based Envelopes
I am following an article by Mohamed Elsaiid (MFTA) about Volatility-Based Envelopes - a quite new technical indicator he has introduced, that is being used by Bloomberg. My goal is to get a simple ...
- 449
11
votes
0
answers
727
views
Block bootstrap to synthesize asset prices
I have a few basic questions on block bootstrapping on a financial time series ('TS').
Assuming my trade universe consists of 10 stocks, I would like to create a set of synthetic prices for all 10 ...
- 211
11
votes
0
answers
5k
views
Bridgewater's Daily Observations
Bridgewater Associates send out Daily Observations to their clients, but I haven't found many traces of these publications online. The series started some 40 years ago by Ray Dalio, and there're just ...
- 713
11
votes
0
answers
2k
views
Formula for the efficient portfolios in mean-variance optimisation?
Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$.
For a certain fixed $\...
- 1,192
11
votes
1
answer
657
views
Distribution of hitting time of the integrated CIR process
If an increasing process $X_t$ has a known Laplace transform $\mathbb{E} e^{-s X_t} = m_t(s)$, define its hitting time $\tau$ to some level $B$ to be
$$
\tau = \inf\{ u > 0 : X_u \geq B \}.
$$
Can ...
- 111
10
votes
0
answers
278
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}$.
...
- 2,996
10
votes
0
answers
599
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 ...
- 201
10
votes
0
answers
434
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 ...
- 101
10
votes
0
answers
443
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 ...
- 405
10
votes
0
answers
250
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 ...
- 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 ...
- 1,862
10
votes
0
answers
424
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 ...
- 1,543
10
votes
0
answers
829
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
...
- 487
9
votes
0
answers
340
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]},\...
- 91
9
votes
0
answers
767
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 ...
- 111
9
votes
0
answers
281
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 ...
- 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 ...
- 415
9
votes
0
answers
246
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)}$ ...
- 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 ...
- 2,211
8
votes
0
answers
270
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 ...
- 4,359
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 ...
- 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 ...
- 2,980
8
votes
0
answers
170
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,...
- 656
8
votes
0
answers
379
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 ...
- 133
8
votes
0
answers
294
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.
$$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
- 1,217
8
votes
1
answer
698
views
Up and Down days in GBPUSD and a Filter
I want to study if the odds of an up or down day in a forex pairs is 50-50. I just count the total number of up and down days in X years and compare it with the total days. The results are very ...
- 121
8
votes
4
answers
589
views
American put option. Exercise time is a random variable, calculation of expected payoff
I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
- 273
7
votes
1
answer
520
views
Time series strategy versus cross section strategy?
Suppose we have a universe of $n$ stocks, and for each time period $t$ we have $n$ predictions for their future returns. Now we can calculate the information coefficient for our predictions in two ...
- 438
7
votes
0
answers
135
views
Implied vol bounded if and only if instantaneous vol bounded
I'd like to show that in diffusion models IV is bounded iff instantaneous vol is bounded if there is to be no arbitrage. So, assume a model under the pricing measure of the form
$$
dS_u = \sigma_u S_u ...
user34971
7
votes
0
answers
344
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 ...
- 98
7
votes
0
answers
183
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- $\sigma$-...
- 383
7
votes
2
answers
277
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 ...
- 609
7
votes
0
answers
137
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 ($B = (B^1, B^2, B^3)$...
- 81
7
votes
0
answers
204
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 ...
- 7,999
7
votes
0
answers
235
views
Produce volatility smile/skew with G2++ model
Suppose I have a G2++ short rate model:
$$r(t)=x(t)+y(t)+\phi(t), \quad r(0)=r_0$$
with
$$dx(t)=-ax(t)dt+\sigma dW_1(t), \quad x(0)=0$$
$$dy(t)=-bx(t)dt+\eta dW_2(t), \quad y(0)=0$$
$$d\langle W_1,W_2\...
- 1,012
7
votes
0
answers
2k
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 ...
- 81
7
votes
0
answers
124
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/...
- 71
7
votes
0
answers
86
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 ...
- 13.6k