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9
votes
1answer
390 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) = ...
1
vote
1answer
85 views

CDS spread scenarios from historical market data

I'm searching for information on the best way to generate scenarios to be used in VaR or ES calculations, for CDS spreads. Given that we need significant historical data in order to achieve a decent ...
0
votes
1answer
35 views

Quantum Computing for Quantitative Finance

It's been a while that quantum computing is looked as the next step in computational science. I somewhat always tought we were decade aways from it's happening but it appears I was wrong: ...
0
votes
1answer
43 views

Deduce expected exposure profile from option/structure delta?

I am thinking about whether there exists a relationship between the delta of an option (or any structured derivative) and it's expected positive/negative exposure? An intuitive question would be ...
5
votes
0answers
55 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 ...
4
votes
0answers
40 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 ...
3
votes
0answers
71 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 ...
3
votes
0answers
92 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
0answers
58 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" ...
2
votes
0answers
72 views

Simulate correlated Geometric Brownian Motion in the R programming language

In response to this question: How to simulate correlated Geometric brownian motion for n assets? One of the responses provides an implementation in MATLAB: ...
2
votes
0answers
65 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
0answers
97 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
269 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 ...
2
votes
0answers
2k 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
17 views

Calibrating and simulating returns from a t-distribution

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 in the ...
1
vote
0answers
17 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 \! ...
1
vote
0answers
90 views

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 ...
1
vote
0answers
64 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 ...
1
vote
0answers
139 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 ...
1
vote
0answers
93 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 ...
1
vote
0answers
69 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 ...
1
vote
0answers
100 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 ...
0
votes
0answers
43 views

measuring portfolio performance using monte carlo simulation

I have a financial portfolio comprising standard asset classes such as equities, bonds, and commodities. I developped a strategy (optimized) and I include it in the financial portfolio. I want to ...
0
votes
0answers
27 views

Approximating the conditional expectation in simulations

I am simulating stock returns, which are governed by the following equations $r_t = \mu + \delta r_{t-1} + \sigma_t z_t$ $\sigma^2_t = \omega + \alpha \varepsilon_{t-1}^2 + \beta \sigma^2_{t-1}$ ...
0
votes
0answers
26 views

Generating random numbers from the skew-t distribution

in another question I was trying to replicate density plots using random numbers coming from the skew-t distribution of Hansen (1994). Now I need to obtain a series of random numbers coming from this ...
0
votes
0answers
41 views

Correlate the G2++ with a GBM model

In Matlab one can use the LinearGaussian2F function together with the simTermStructs function to create a simulated zero curve based on the G2++ model. Next to simulating the interest rates I need to ...
0
votes
0answers
36 views

SAS code for Brownian Motion

I want to simulate call options using monte carlo algorithm. I am a noob SAS user but i know that i need to: -simulate random stock prices with no dividend in respect to different ...
0
votes
0answers
24 views

CIR model, realistic parameters and usage

I'm currently working on SDE's, in particular with mean-reversion processes like CIR and Vasicek. The definition of the CIR model is \begin{equation} dX_t = \kappa(\theta-X_t)dt + \sigma ...
0
votes
0answers
52 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 ...