Implement a generic geometric brownian motion for a stock

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Reference no: EM131698705

Applied Mathematics: Introduction to C++ Scientific Computing Project

Geometric Brownian Motion and Stock Prices: Geometric Brownian motion (GBM) can be simulated using a numerical solution to a stochastic differential equation, using schemes such as the Euler-Maruyama Method that are similar to the Euler method we used to solve an ODE in assignment 2 and 3 but have an additional random noise term (note that the std library contains implementations of almost any random number distribution you might wish, for example std::normal_distribution would be helpful for this project). GBM is used to model stock-prices in the Black-Sholes model. In this project you would investigate using simulations of many realizations of a GBM in order to model stock and option pricing. For a mini-project you could implement a generic GBM for a stock and work out the expectation values for the price of the stock at some later time, along with it's standard deviation (related to the risk or volatility). For the main project you would add some option pricing, and potentially some other functions related to the Black-Sholes model. Extensions would include constructing a local volatility model (perhaps based on some historical data such as index prices you could download from somewhere) or a stochastic volatility model.

Textbook - Undergraduate Topics in Computer Science - Guide to Scientific Computing in C++ by Joe Pitt-Francis and Jonathan Whiteley.

Reference no: EM131698705

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Reviews

len1698705

10/31/2017 2:42:22 AM

I want Question 6 (Parts 2 -6) in 5 hours. It is not a difficult program – I have an exam so I a unable to finish it on tie. Please let me know if you guys can help. Note to Expert: Please find the enclosed textbook pdf with the chapters we will cover for this course. Therefore, the material for this assignment should be based on these topics. Please pass this along to the experts. Also, could you please use the Amazon stock as an example to simulate the Geometric Brownian Motion and Option prices and everything else the project.

len1698705

10/31/2017 2:42:14 AM

This document is not the full specification for the project, more details may be given later. However, this should be enough of a specification for you to construct your outline which is due on 30th of October. Your Outline document (one outline per group) should contain: 1. Group members’ names: 1-3 people from this class. 2. ½ to 1 page description of your proposed project 3. ¼ to ½ page description of your proposed mini-project. When deciding on your group, keep in mind that a larger group will be expected to accomplish more. For example, the written description (not including figures, code, or sample I/O) of the project might be expected to be about 4-6 pages (Arial 12 point single-spaced) for a group of 1, but about 9-12 pages for a group of 3. In addition, all members must be involved in the coding, the write-up, and the presentation (you can divide each of these tasks up, but each member must have some significant contribution to each aspect of the project).

len1698705

10/31/2017 2:42:05 AM

Your project description should include something like what is included in the samples below along with some indication that you have thought about how to implement the project (such as some classes you might need to create (you are expected to use object-oriented programming for this project so there must be multiple classes involved), including some functions that might be needed, etc).

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