Questions tagged [simulations]
The simulations tag has no usage guidance.
76
questions with no upvoted or accepted answers
7
votes
0
answers
335
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 $...
- 353
4
votes
0
answers
105
views
Pathwise sensitivities of American options - Derivative of the American payoff function
How can I compute the derivative of the payoff function for an American put option?
In the paper "Smoking adjoints: fast Monte Carlo Greeks" by Giles and Glasserman (2006) they compare two ...
- 428
4
votes
0
answers
125
views
Long-term proportion of convex and concave strategies in artificial financial markets
In their classic paper "Dynamic Strategies for Asset Allocation" Perold and Sharpe state:
"That convex and concave strategies are mirror images of one
another tells us that the more demand there ...
- 27.2k
4
votes
0
answers
132
views
How does one simulate intraday strategies which don't end up flat at the close?
I ran into this trying to simulate trading interlisted names between the NYSE and the TSX.
Depending on my strategy parametrization it would sometimes end up with a significant short or long dollar ...
3
votes
0
answers
113
views
Continuation value in Longstaff-Schwartz: Why the expected value?
In the paper by Longstaff and Schwartz on American option pricing, the continuation value at time $t_k$ is given by:
\begin{align}
F(\omega;t_k) = \mathbb{E}_Q\Big[\sum_{j=k+1}^Kexp\Big(-\int_{t_k}^{...
- 521
3
votes
0
answers
60
views
Numerical approximation of SPDE
I've already posted this question on MSE, but I'm not quite sure if it's the right community so I'm posting it here as well.
Background
I want to approximate an SPDE of adensity process $V_t$. The ...
- 141
3
votes
0
answers
2k
views
Simulating correlated Geometric Brownian Motion in Python
I want to simulate two correlated Geometric Brownian Motion processes in Python. I found an implementation from Matlab (https://www.goddardconsulting.ca/matlab-monte-carlo-assetpaths-corr.html) and ...
- 63
3
votes
1
answer
464
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Simulation scheme for SABR beside the standard Euler discretization
QUESTION:
Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics?
Simulation that will withstand even for high volatilities....
- 1,617
3
votes
0
answers
193
views
Simulating volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes
I am trying to simulate the volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes. In fact, giving $\mathbf{X}$ a $n$-dimensional vector ...
- 131
3
votes
0
answers
93
views
Equity Options - "How do I build a forward simulation model with regards to shocks in spot pricing and IV?"
I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security.
Simply put, the objective is for me to test the ...
- 31
3
votes
0
answers
104
views
Electricity Prices: Change of measure in practice
I'm working on a model of electricity prices. I have empirical data $X(t)$ and managed to find a reasonable fit given by a Levy process $\hat{X}(t)$. I understand in theory what a risk-neutral ...
- 151
3
votes
0
answers
50
views
Regularity requirement for convergence of Euler scheme for stochastic integral?
Let $S_t$ be follow Black Scholes, then I am interesting in simulating the process
$\int ^t _0 e^{-rt}1_{\{S_t\leq K\}}dS_t$
which is like a naive hedge of a European put, which does not work in ...
- 987
3
votes
0
answers
203
views
How to simulate stock price with support and resistance level
I couldn't find good resources on how to simulate a stock price data sequence including some basic effects.
The basis might be a Brownian motion model; but in real stock prices, there are additional ...
- 31
3
votes
0
answers
4k
views
Models for simulating FX movements
My goal is to develop a model to simulate long term FX movements. (I am not sure if long term makes any difference, but if it does I am more interested in long term fx movements)
These Monte Carlo ...
- 31
3
votes
0
answers
69
views
Credit spreads vs default events dependence
Reading this note it strikes me that credit spreads and defaults seem not to be commonly modeled jointly (e.g. more or less directly in structural models), but at best with some kind of "ex post" ...
- 1,543
2
votes
0
answers
36
views
Models that can improve FHS (with possible residuals manipulation)
The Filtered Historical Simulation (FHS) is a tough benchmark.
By:
choosing among the most complicated ARMA-GARCH variants with automatic model and lag selection,
manipulating standardized residuals ...
- 2,086
2
votes
0
answers
141
views
Jump Diffusion Model - Volatility and Mean of Jumps
I am trying to understand the concept of jump diffusion model. So far what I've understood is that by adding a Jump parameter to a GBM (Geometric Brownian Motion) we can generate a Jump diffusion ...
- 131
2
votes
0
answers
66
views
Negative theta in Log-linear stochastic volatility model
I was asked to simulate the following geometric Brownian motion to get paths for the SPX stock price. the process follows a Log-Linear stochastic volatility.
$dS_t = \mu S_tdt+e^VS_tdW_1 $
where ...
- 51
2
votes
0
answers
2k
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Longstaff-Schwartz, special american option simulation using Python (numpy package)
I got a put option, which can be exercised 3 times, all at different times, which are each month of a year $$t_1 = \frac{1}{12}, t_2 = \frac{2}{12} ... t_{12} = 1$$.
Respectively, if exercised at $$...
- 273
2
votes
0
answers
262
views
Multivariate Hawkes Process Simulation
I am trying to implement Ogata's thinning algorithm to simulate multivariate Hawkes Processes in Python (the algorithm can be found here: https://www.math.fsu.edu/~ychen/research/Thinning%20algorithm....
- 91
2
votes
0
answers
148
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Generating Correlated Quasi Random Numbers
Hi I am trying to generate correlated quasi random numbers using a sobol sequence in matlab. My Problem is the Following: Using "standard" random numbers it is easy to generate the 6 correlated random ...
- 165
2
votes
0
answers
52
views
Simulating Asset Prices by Independently Simulating Supply and Demand
If I have an asset, whose supply is generally mean-reverting and whose demand is generally cyclical, could I somehow simulate / project the supply and demand levels across multiple discrete time ...
- 327
2
votes
0
answers
174
views
Simulating t-distributed returns by calibrating degrees of freedom $\nu$ from variance or kurtosis
A slight twist (I hope) on the familiar problem of simulating log returns from a t-distribution. My two questions concern calibration to sample data.
First, one can infer the degrees of freedom, $\nu$...
- 21
1
vote
1
answer
119
views
GARCH process simulation in R
I'm trying to learn how to simulate the GARCH(1,1) for option pricing using Monte Carlo. I need to learn how to code the equations for the stock log returns and the variance process. I'm trying to ...
1
vote
0
answers
184
views
CEV model effective simulation
I want to simulate the following CEV process : $$ dM_t = \sigma_t M_t^{\eta} dW_t $$
Using Euler discretization to $M_t$, if at a given time $t$, $M_t$ takes a negative value then $M_{t+1} = M_t + \...
- 11
1
vote
0
answers
84
views
Simulating the same stock price with different methods/distributions
I would like to ask if we could simulate stock price paths with different methods/techniques.
What I mean is : say we have a specific stock price hence we can extract historical mean and standard ...
- 129
1
vote
0
answers
100
views
Backtesting - treatment of holidays for global (i.e. multi-market) portfolios
Assume a daily trading strategy where each day we rebalance our portfolio weights:
Situation A: all constituents of our portfolio are from the same market (e.g. a portfolio of S&P 500 stocks)
...
- 123
1
vote
0
answers
75
views
How to get Risk-Neutral Drift for Trading Volume from Time Series
I am trying to price an option with Monte-Carlo simulation, where the payoff depends on some constants and a time-series (trading volume) which I model to follow a GBM. Now if I understood it ...
- 21
1
vote
0
answers
113
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Valuing American Options using Tilley algorithm
Hey I want to implement Tilley's algorithm (Valuing American Options in a Path Simulation Model by JA Tilley, 1993) to price american options. Where can I find implementation of this method in any ...
- 71
1
vote
0
answers
166
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Milstein scheme for Heston model - rate of convergence
Heston model is described by following SDE
\begin{equation}
\begin{aligned}
dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\
d\nu_t &= \kappa(\theta - \nu_t) dt + \xi \sqrt{\nu_t} dW^{\nu}_t \\
...
- 433
1
vote
0
answers
49
views
Gaussian Copulas: My Marginal Distribution Includes Negatives but My Copula is Non-Negative?
Attempting Copula in R for Stock Returns, Bond Returns, and Inflation Rates. This is my first attempt with Copulas but I have looked many places and cannot determine what I'm doing wrong. My Marginal ...
- 11
1
vote
1
answer
310
views
Simulating correlated Geometric Brownian Motion with lag
I know that it is possible to simulate two correlated GBM in e.g. Matlab (Generating Correlated Asset Paths in MATLAB) based on cholesky decomposition. However, they take as input the correlation ...
- 63
1
vote
0
answers
497
views
Source on multivariate correlated geometric Brownian motion returns, not prices
Can anyone provide a source that formulates how to generate multivariate geometric Brownian motion returns using the Cholesky method with target correlation matrix, instead of correlated GBM prices?
...
- 2,935
1
vote
0
answers
37
views
Combining multiple securities' Net Asset Value time-series into one total NAV series
I have a number of individual securities that each have a Net Asset Value (NAV) time-series. For example:
...
- 193
1
vote
0
answers
76
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Anyone got references where we can find examples of codes for agent-based simulations of financial markets?
I'm looking for references with codes for trying out simple agent-based simulations for modeling financial markets. I mostly worked with MATLAB and R, but I know a bit of python and I am learning C++ ...
- 2,406
1
vote
0
answers
81
views
CVA for a portfolio of long and short options
I am looking to estimate the CVA/DVA for a portfolio of options.
For simplicity sake, let's assume there are two FX options in the portfolio, one long and one short. Both options have the same ...
- 11
1
vote
0
answers
39
views
ES using historic simulation
Why is the data obtained from 91-100 days all eliminated from the calculation of the 1-day 95% ES? My interpretation is because the first day to calculate the 95% ES should be the 90th day? But I can'...
- 171
1
vote
0
answers
35
views
Why do simulation schemes have difficulty in pricing options with low spots?
If you apply a simulation Scheme (log-Euler discretization, Euler discretization and even more advanced ones) on for instance SABR and other models, then they price a call option (where we can easy ...
- 1,617
1
vote
0
answers
111
views
Pricing call option on bond under CIR model by simulating noncentral chi square distribution
In the original paper of CIR model, there is a pricing formula about call option on bond
$$
\begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
- 21
1
vote
0
answers
39
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Why no prepayment fee for the reverse mortgage?
I am currently studying the costs (to lender) of adding certain additional options to the reverse mortgage, including the option of prepayment. Would there be any scenarios of housing price/mortgage ...
- 339
1
vote
0
answers
24
views
Simulating Taxed Equity Return Series (U.S.)
I'm looking to learn how to correctly simulate taxes on dividends and capital gains on simulated return series for U.S. Equities with dividend reinvestment. I understand I will have to keep track of ...
- 1,601
1
vote
0
answers
131
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Monte Carlo Simulation of correlated returns based on different frequencies
I am simulating through Monte Carlo, multivariate correlated returns of different products composing an Oil&Gas portfolio. The historical prices (from which I computed the log-returns) of the ...
- 63
1
vote
0
answers
48
views
Bootstrapping to Judge the Fit of a Sampled Return Distribution
Consider the following: I have sampled yearly stock returns from a specified distribution.
What I want to do is compare how well my sampled distribution fits the empirical distribution of yearly ...
- 137
1
vote
0
answers
262
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Open Source library for calculating exposures?
I would like to know an open source quantitative library/ies that can calculate exposures out of the box (I have investigated a bit on OpenGamma/Strata libraries with no luck and the website of ...
- 23
1
vote
0
answers
154
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Simulating asset returns: (Academia) state of the art
I want to run some simulation studies of (linear) factor models and for that reasons I am wondering about the features such a simulation should contain - every suggestion is welcome, I'll do my best ...
- 1,446
1
vote
0
answers
145
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Smooth ornstein uhlenbeck process
I want to simulate paths for a commodity price. I use the historic data in the following way:
$X_t$ is the price.
$\ln\left(\frac{X_t}{X_{t-1}}\right)$ is the daily return.
I calculate the slope of ...
- 121
1
vote
0
answers
93
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How are Levy driven SDE simulated?
Do you just use an Euler scheme as before?
E.g. take this process, OU process with a Levy driver.
\begin{equation}
\text{d}V_t = -\lambda V_t\text{d}t + dZ_t
\end{equation}
Do you just have
$V_{...
- 987
1
vote
0
answers
683
views
Stochastic Vol simulation - Quant job interview question
this is a question from a quant interview (FO quant for IR Exotics for a big 4). First it might be useful when preparing your interviews, second, any brainstorming will be appreciated. Note that no ...
- 701
1
vote
0
answers
47
views
Optimizing Monte Carl integral calculation with control variate
For an exercise I am asked to calculate an integral with a monte carlo simulation, after that I need to optimize the results with a control variate. This was the given integral:
$\int_0^1 \! \frac{\...
- 189
1
vote
0
answers
124
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Generating financial data
I am trying to generate monthly stock data using a one-factor model:
$$R_{a,t} = \alpha + BR_{b,t}+\epsilon_{t}$$
The description says:
$R_{a,t}$ is the excess asset returns vector, $\alpha$ is the ...
- 43