The tag has no wiki summary.

learn more… | top users | synonyms

4
votes
2answers
870 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
45 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 ...
2
votes
2answers
64 views

How to discretize a GBM under P- and Q-measures?

Under the P-measure, a geometric Brownian motion can be specified using the following SDE: $$dS_t=\mu S_tdt+\sigma S_tdW_t^P$$ and its Euler discretization is $$S_{t+\Delta t}=S_t + \mu S_t \Delta ...
3
votes
1answer
89 views

Simulate (imaginary) asset prices using random numbers that follow a Frank Copula

I didn't understand how to simulate asset prices by using non normal random numbers. I am assuming that it would be incorrect to use the standard Geometric Brownian Motion, since it is based solely ...
2
votes
0answers
53 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 ...
0
votes
0answers
9 views

What are commercial impact models and transaction cost analysis models out there for simulation?

I have heard that ITG, LiquidMetrix, MarkIT and TradingScreen has good Transaction Cost Analysis (TCA) research. I wonder which firm one would choose to have an impact model formula inside his ...
2
votes
1answer
76 views

Evaluation of the semi-closed Heston pricing formula for call options

I'd like to know, how the integral part of the semi-closed Heston pricing formula for call options can be simulated for a given set of model parameters. Monte Carlo simulations shoud work for this ...
0
votes
0answers
59 views

Monte Carlo, convexity and Risk-Neutral ZCB Pricing

I've built a simplistic Excel monte carlo model to price a zero-coupon bond, but it came up with a slightly unepxected result so I wanted to confirm whether my maths is just a little rusty or my model ...
0
votes
1answer
32 views

Should earnings be modelled normally or lognormally?

I am having difficulty deciding whether a company's earnings should be modelled normally or lognormally. If we consider two arguments: (i) The earnings of a company are the returns on the assets of ...
3
votes
1answer
81 views

Extended CIR and discretization

Did someone know how to discretize this process efficiently : $dX(t) = \kappa [\theta(t)-X(t)]dt + \sigma \sqrt{X(t)}dW(t)$ I am looking for something more sophisticated than the trivial Euler ...
2
votes
1answer
145 views

UST Yield Curve Forecasting - Bond Structure Testing

I have a project in mind that I am working on, but have little idea where to start. I am a relative newcomer to python (about 1 years exp.) and limited knowledge of quant finance. What I would like ...
3
votes
1answer
102 views

Simulating Brownian motion with jumps

I am trying to improve my understanding of jump processes. As a first step, I want to simulate sample paths for the process $$dX(t) = dw(t) + dJ(t)$$ where $dw(t)$ is a Brownian motion and $dJ(t)$ ...
11
votes
3answers
15k 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: ...
5
votes
1answer
468 views

Kelly Capital Growth Investment Strategy (Example in R)

In the paper Response to Paul A Samuelson letters and papers onthe Kelly Capital Growth Investment Strategy pages 5 and 6 Dr William T Ziemba, gives a praticle example on Kelly Growth. I’m trying to ...
0
votes
1answer
39 views

Simulating a GBM with martingale condition - Ito process moving downwards

I want to correctly simulate a $\mathcal{Q}$ - martingale $S$, which is a geometric Brownian motion and an exponential of a process $X$, \begin{equation} X_t = X_0 + \mu t + \sigma B_t = X_{t-\Delta ...
7
votes
1answer
298 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
73 views

Getting Parameter of Translated Gamma Distribution from Monte Carlo

Spin-off from here. (Edit) Main question: What do I do about a parameter whose suggested values range quite vastly? (Edit) Backstory: I am given data of loss values and the dates that correspond to ...
1
vote
1answer
97 views

Simulating Stock's close, high and low prices

I am testing a model in which I need to simulate closing, high and low prices (i.e. 3 dimensions of prices) of any given stock. Using the simple Geometric Brownion Motion equation I can easily ...
0
votes
1answer
34 views

Compute moments of aggregate loss using Monte Carlo

Spin-off from here. Richard referred to me an article that tells me how to get parameters of a translated gamma distribution to which I should consider fitting simulated aggregated loss values. The ...
0
votes
1answer
136 views

Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
10
votes
3answers
718 views

Strictly local martingales: what is the intuition behind them?

A process $X_t$ is a local martingale if for each increasing sequence of stopping times $\{\tau_k,k=1,2,...\}$ the stopped process is a martingale. All true martingales are local martingales, but the ...
1
vote
0answers
81 views

Review of Excel Stock Simulator

I am currently a senior in high school and I built a stock simulator using knowledge gained from a semester of AP Statistics. I was wondering if someone could tell me if my simulation is ...
0
votes
0answers
45 views

How to generate jump times in in Multilevel path simulation for jump-diffusion SDEs?

I am trying to generate jump times in in Multilevel path simulation for jump-diffusion SDEs using the following MATLAB code: I used following Algorithm in Yuan Xia paper: But I have not reached ...
0
votes
0answers
46 views

What interest rate dynamics would you suggest to simulate a single swap?

I need to calculate the Potential Future Exposure (PFE) for a single swap (not a portfolio). As far as I know, a stochastic model is needed to simulate the interest rate curves (from here). Could ...
2
votes
3answers
265 views

Calibration of a GBM - what should dt be?

I have a time series of daily data that I want to calibrate GBM parameters $\mu$ and $\sigma$ to. Using the discretized solution $$ S_{t_{i+1}} = S_{t_i}\exp\left(\left(\mu - ...
3
votes
1answer
70 views

Copula- AR simulation

I am estimating different copulas for bond factors that i also fit AR(1) models on. Now i would like to test and compare durations and VaRs with my model vs empiric. But how can i simulate AR(1) ...
1
vote
1answer
193 views

Simulate non-stationary time series with cointegration

how can I simulate/generate two non-stationary time series (with unit root) so that they can be also cointegrated (using R or Matlab). Thanks in advance.
1
vote
2answers
202 views

Historic Value at Risk - Ratios vs. Differences

Quick Summary on Historic VaR Let $S_0,...,S_n$ be the daily values of some stock (where $S_0$ is the current value). Then for $i=1,\ldots,n$ we let $$\hat r_i:=S_{i-1}/S_i \quad \text{and}\quad \hat ...
0
votes
2answers
196 views

Getting the next price of a GBM with reversion

Here is the "twin" question of Getting the next price of a GBM (Geometric Brownian Motion) but for GBM with reversion As in that case, I'd like to write a formula for the next price, as function of: ...
0
votes
1answer
194 views

Getting the next price of a GBM (Geometric Brownian Motion)

I am writing a program that creates realizations of a GBM. Starting from an initial price, I get the following price with this formula: ...
3
votes
1answer
266 views

Monte Carlo for MultiFactor Ornstein Uhlenbeck

I'm following loosely the exposition given in "Monte Carlo Methods in Financial Engineering by Glasserman. For a multifactor OU process: $dX(t)=C(b-X(t))dt+DdW(t)$ Where C and D are d*d matrices ...
3
votes
2answers
470 views

When to use the real world drift and when the risk neutral one for a Monte-Carlo simulation?

Under what conditions should the drift be real world and when risk neutral when simulating Delta Hedging option pricing trading strategy any other? For 2. it should be risk neutral. For 1., it ...
1
vote
0answers
55 views

Order 1.5 strong SDE integration methods for systems with diagonal additive noise

I'm looking into simple-to-implement and efficient order 1.5 strong SDE integration schemes for my system. My noise is diagonal and additive (possibly time-varying). Thus methods designed for either ...
2
votes
0answers
86 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 ...
4
votes
0answers
118 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
1k 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 ...
0
votes
1answer
324 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 ...
3
votes
2answers
188 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
196 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
126 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
429 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
207 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
1k 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 ...
1
vote
0answers
86 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
56 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" ...
7
votes
2answers
1k 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 + ...
4
votes
1answer
2k 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 ...
13
votes
3answers
905 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 ...
4
votes
1answer
1k 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 ...
9
votes
2answers
3k 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 ...