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2
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0answers
34 views

Effective simulation of multi factor Heston model

Im looking for a quick way (as in runs quick, not necessarily is quick to implement) of simulating multiple square root processes for a stochastic volatility model, flexible enough to allow for ...
2
votes
0answers
25 views

Does GARCH derived variance explain the auto-correlation in a time series?

Given a time series of $u_i$ returns where i=1 to t. $\sigma_i$ is calculated from GARCH(1,1) as $\sigma_i^2=w+\alpha u_{i-1}^2 +\beta \sigma_{i-1}^2$ . What is the mathematical basis to say that ...
3
votes
1answer
942 views

Valuing Total Return Swaps

In my quest for simulated data, I am trying to generate prices for Total Return Swaps by calculating the NPVs of the fixed and floating leg. My problem: Given the fixed leg, how do I set the spread on ...
2
votes
1answer
135 views

Distribution of Geometric Brownian Motion

Please let me know where I have been mistaken! Let the SDE satisfied by the GBM $S(t)$ be $$ \frac{dS(t)}{S(t)} = \mu dt + \sigma dW(t). $$ Then, the underlying BM $X(t)$ will satisfy $$ dX(t) = ...
0
votes
1answer
72 views

How do I simulate stock prices for a 10 asset portfolio, over a period of 10 years in MATLAB? [closed]

If I have given vectors for return and volatility (i.e. I have two 1x10 vectors), and I assume at first that their correlation is 0 (meaning my covariance-variance matrix is just diagonal), how do I ...
5
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2answers
7k views

How to simulate stock prices with a Geometric Brownian Motion?

I want to simulate stock price paths with different stochastic processes. I started with the famous geometric brownian motion. I simulated the values with the following formula: ...
2
votes
2answers
154 views

Random Brownian Simulation Startling Results

I was playing around in Excel the other day, simulating possible equity curve/P&L paths for a simple game I designed. The game is really trying to find an optimal risk managment strategy. I start ...
2
votes
1answer
124 views

SDE simulation: P or Q?

Let's take a GBM under $P$: $dS=\mu dt+\sigma dW_{t}^{P}$ and then under $Q$ $dS=r dt+\sigma dW_{t}^{Q}$, where $dW_{t}^{Q} = dW_{t}^{P} + (\mu - r)/\sigma dt $ Now, let's say that I have ...
1
vote
1answer
93 views

What's wrong with this asset growth simulation?

Sorry if this is too basic, but I have this spreadsheet that simulates asset growth of a portfolio under a given return and risk using MPT. Here is a plot of probability distribution of asset ...
3
votes
1answer
218 views

How does the 2-factor Hull White model propagate the forward rates curve?

I've been trying to get a grasp on some of the basics of interest rate modeling, and am looking to simulate rates using the 2 factor Hull White model, which I am aware offers a more realistic model of ...
2
votes
0answers
114 views

Credit Valuation Adjustment Implementation

I am trying to help a friend with her thesis on Counterparty Credit Risk where she intends to have a somewhat lengthy treatment on Credit Valuation Adjustment (CVA). Specifically I am looking to help ...
1
vote
0answers
425 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 ...
3
votes
1answer
372 views

Monte Carlo simulating Cox-Ingersoll-Ross process

The CIR process is given by the SDE $$ \mathrm dr_t = \theta(\mu-r_t)\mathrm dt + \sigma\sqrt{r_t}\mathrm dW_t $$ where $W_t$ is a Brownian motion. I am interested in finite-difference schemes of ...
1
vote
0answers
68 views

Problems with exact Heston simulations

I am just wondering if there is any problem with the so-called "exact" Heston simulations? So far what I have seen are the good things about it, what are the disadvantages? Because if it is so ...
3
votes
0answers
54 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" ...
5
votes
2answers
457 views

Simulation of GBM

I have a question regarding the simulation of a GBM. I have found similar questions here but nothing which takes reference to my specific problem: Given a GBM of the form $dS(t) = \mu S(t) dt + ...
3
votes
1answer
1k views

How to simulate a Merton Jump Diffusion process?

I am talking about the Merton Jump Diffusion model, on this page, where they give the following formula: $$ dS_t = \mu S_t dt + \sigma S_t dW_t + (\eta-1) dq$$ where $W_t$ is a standard brownian ...
12
votes
3answers
757 views

How to account for transaction costs in a simulated market environment?

I am simulating a market for my trading system. I have no ask-bid prices in my dataset and use adjusted close for both buy and sell price. To account for this I plan to use a relative transaction ...
3
votes
1answer
688 views

Michaud's Resampled Efficient Frontier - Out of Sample Simulation Testing

I will be putting ALL my account points on bounty to whoever answers this question [if your answer is crap but it's the only answer, you're getting the 165 points]. You will have to wait 2 days or so ...
8
votes
2answers
2k views

When to use Monte Carlo simulation over analytical methods for options pricing?

I've been using Monte Carlo simulation (MC) for pricing vanilla options with non-lognormal underlyings returns. I'm tempted to start using MC as my primary option-valuating technique as I can get ...
1
vote
1answer
145 views

transaction size and liquidity in simulation of US stocks

i am developing a simulation trading in US stocks. i have 1 transaction a day per stock, assumed for simplicity to be executed at the daily closing price. in order to determine a reasonable maximal ...
6
votes
2answers
710 views

How to simulate cointegrated prices

Is there any simple way to simulate cointegrated prices?
8
votes
3answers
228 views

Are there any standard techniques for adding realistic synthetic microstructure noise to a price series?

This may seem like a strange question, but for my particular application we need to actually add synthetic microstructure noise to real time charts. The signal should still be representative of the ...
10
votes
3answers
548 views

Literature on generating synthetic time series for testing

I have some market data (daily time series) for bond prices and CDS indices and I would like to generate synthetic versions of these which are statistically "similar" for testing trading strategies. ...
5
votes
1answer
713 views

How to simulate correlated assets for illustrating portfolio diversification?

I have seen multiple instances where people try to explain the diversification effects of having assets with a certain level of correlation, especially in the "most diversified portfolio" literature. ...
10
votes
6answers
1k views

How to generate a random price series with a specified range and correlation with an actual price?

I want to generate a mock price series. I want it to be within a certain range and have a defined correlation with the original price series. If I choose, say, oil, I want as many time series which ...
8
votes
3answers
448 views

How to test for and how to simulate price rise/fall asymmetry in the stock market

One of the stylized facts of financial time series seems to be a fundamental asymmetry between smooth upward movements over longer periods of time followed by abrupt declines over relatively shorter ...
7
votes
1answer
413 views

Simulating conditional expectations

There is a multidimensional process X defined via its SDE (we can assume that its a diffusion type process), and lets define another process by $g_t = E[G(X_T)|X_t]$ for $t\leq T$. I would like to ...
6
votes
1answer
309 views

How to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?

I am working out a numerical integral for option pricing in which I'm simulating an interest rate process using a Cox-Ingersoll-Ross process. Each step in my Monte Carlo generated path is a ...
7
votes
1answer
496 views

Monte carlo portfolio risk simulation

My objective is to show the distribution of a portfolio's expected utilities via random sampling. The utility function has two random components. The first component is an expected return vector ...
10
votes
1answer
307 views

Enhancing Monte-Carlo convergence (crude method)

I am currently doing a project involving Monte-Carlo method. I wonder if there is papers dealing with a "learning" refinement method to enhance the MC-convergence, example : Objective : estimate of ...
8
votes
2answers
557 views

Is Walk Forward Analysis a good method to estimate the edge of a trading system?

Do you think Walk Forward Analysis is a good method to estimate the predictability or edge of a trading system? Are there similar methods to know (estimate) how much alpha can capture an algo (in the ...
6
votes
1answer
161 views

What tradeoff is there to using an accurate estimate with a large confidence interval?

I am working on calibrating a Heston model from simulated historical stock data. After obtaining an accurate estimate of the model parameters I found very large 95% confidence intervals for these ...
10
votes
2answers
913 views

Simulating Returns

I'll start this off with a rather broad question: I am trying to simulate returns of a large number of assets within a portfolio of different classes - equity and fixed income in a first step, say 100 ...