Project

Because we manage securities in an uncertain environment, we need to understand the nature of the stochastic processes that underlie our securities pricing, risk management efforts and portfolio selection. Uncertainty has major effects on all of the inputs needed for derivatives analysis, including underlying security price evolution(s) over time, volatility estimates, interest rate shifts, etc. Stochastic processes used to model this uncertainty can take on discrete or continuous forms over time and state space or even some combination of the two. The purpose of this assignment is to enable students to develop some level of comfort and expertise modeling derivative securities in stochastic environment and to apply their skills to pricing, analyzing volatility parameters, hedging and managing risk in such environments.

Students may, either individually or in groups of 2 or 3, work on any one of the (mostly) spreadsheet-based projects described below. Students should sign up by email to the course instructor (either as individuals or in groups) for one of the projects listed below on or before the end of the second week of the semester. Groups made up of one, two or three students will list each of their names together in this email to the instructor. 

The project for this course can be described as involving two stages. The first stage concerns your simulation of a stochastic process moving forward in time. You have some choices here, as indicated in the list below this description. After completing the first stage of your project, generally referred to as your first draft, you can begin the second stage. Details of your second stage are not given here but will be assigned by the course instructor after you submit the output of the first stage of your project. This second stage will likely apply your first draft (stochastic process simulation) to an instrument, series of instruments or market that the course instructor will designate such as currencies and/or their derivatives, fixed income instruments and/or related derivatives, CDOs, derivative and underlying equity price series, etc. The stochastic process that you modeled will be applied to some input of interest such as exchange rates, interest rates, underlying security price volatility levels, underlying security prices, etc. You will ultimately assemble these to prepare a finished product or deliverable that constitutes a useful tool applying derivatives analysis.

This assignment is to count for 25% of the overall course grade your assignment is accepted by the instructor. This 25% includes 5% for the first draft, due at the end of Week 8, 5% for the second draft, due at the end of Week 12 and 15% for the final project, due at the end of the 15^th week. Projects and project drafts can be submitted before deadline dates; in fact, I encourage this so that students can get earlier starts on the second drafts and final versions of their projects earlier. So, for example, I have no objection to a student submitting the first draft of their project well before its Week 8 deadline; students will have much more time for the second and third stages of their projects by submitting the first stages early.

Students must inform the instructor by the end of the second week of the semester of their intent to complete given projects, whether they intend to do so in a group or individually, and if in a group, identifying their project selection along with that group member or members, if any, and subject to the limitations discussed above. Please inform the instructor as soon as possible if you change your mind about doing a given project or withdraw from a given group. Students should not submit projects that have been or will be submitted in other courses. The final version of the project will be due on the last day of the semester as noted in the Course Syllabus.

If applicable, students are expected to develop "user-friendly" and entirely original spreadsheet files of professional quality capable of performing one of the tasks listed below (or a satisfactory alternative as discussed with the instructor). The first draft will complete this task. The submitted file should be original and not have been used before in any other class, and not a file adapted from one found on the Internet or from another project. The spreadsheet files should include appropriate documentation (often instructions within the spreadsheet will suffice), User-Defined-Functions, VBA code and/or macros as is necessary to run the file in a very user-friendly setting.

Students should feel free to discuss their projects with the course instructor to obtain direction as needed. Students are encouraged to assist each other, to test each other’s programs and to "work out bugs" in each other’s programs. The spreadsheet files should be usable in Excel from MS Office 2007 or MS Office/365 2022 to 24, etc. I emphasize that the package should be user-friendly with detailed on-screen instructions, macros and/or visual basic routines as necessary to ensure this. The project should include adequate documentation for its use by anyone familiar with the relevant analytical techniques and the financial problem. It should be assumed that the user has no familiarity working with the group's original spreadsheet and will not remember any verbal instructions given by students.

After reviewing the first draft of student submissions, the course instructor will propose direction for the project’s second stage. It is likely that the instructor will suggest continuing development of the submitted first draft to modeling the behavior of some financial price, rate or other model input over time, then applying this model to a given security type or market. The third stage of the project will, I hope, to be for simply addressing instructor comments on the second stage of the project.

As always, do be aware of and follow all AAP and JHU rules, policies and guidelines concerning all assignments. In all cases, students should carefully cite any work, paper, book, article, Internet site, electronic communication or software, whether published or unpublished, that was consulted or otherwise used as a reference for their own work. Any material that was copied or paraphrased into a student’s work must be appropriately footnoted (end-noted or otherwise cited) along with appropriate publication or other details. Sufficient information should be provided in the citation for the instructor or other readers to access the referenced material as easily as possible. Any non-written materials (e.g., oral communication, television, etc.) must be cited as well. Appropriate style manuals can be consulted for citation style. All projects are to be considered to be independent projects, completed without assistance of others except for the course instructor, and members of the student's project group, though outsiders including other students may be used to test the project. Authors of any written material should take great care in ensuring that their papers are well-written and conform to appropriate style and Institute academic honesty guidelines. Students should not copy code or other material into their files from outside sources. Groups and their members should not collaborate or share work or information with other students and groups in the preparation of this project, though, of course, students working together in a group should collaborate with other members of their group. And again, students may use outsiders to test and comment on the usability of their projects.

The first three projects listed below are multi-stage projects. For their first drafts, students and/or student groups will complete the first stage of their projects as defined below.

Specific Projects

           1.      Simulating a Binomial Stochastic Environment

The user of this Stage 1 package should be able to analyze a generic standard binomial process through time. Going into Stage 2, this binomial process might be used to simulate stochastic interest rates, non-constant variances, underlying security price movements, etc. However, for Stage 1, students should concern themselves only with the process of simulating a generic binomial process for a random variable through time. The user of this spreadsheet should be able to input various parameters for the generic random process. Among the allowable user-inputs should be an initial or starting value for the generic random variable along with:

·         At least one of or better yet some combination of a variance for the process, relevant potential proportional upjump/downjump increments for the binomial process.

·         A number of nodes and/or time periods in the generic process. The modeled number of time periods would be  user-input, but the model must be able to accommodate any integer value of time periods between 1 and 150, which implies that the model must be able to accommodate between 2 and 2^150 nodes or potential final outcomes.

It is useful to appreciate that many financial models make certain assumptions that allow for a specific relationship between process variance and proportional upjump/downjump increments, e.g., σ = f(u,d). For example, most binomial option pricing models that you will see online will specify relationships among underlying security variances, multiplicative upward and downward price jumps. You may assume that this draft will be developed in the second stage to work with calendar time inputs and "number of days" (e.g., T and t_d). However, for the first stage, you do not know what random variables will be modeled in the second stage or what securities you will use for your model. The first stage is intended to be generic and flexible enough to apply to many potential securities and markets.

2.         2.    Simulating a Continuous Time-Space Brownian Motion Environment

The user of this Stage 1 package should be able to analyze a generic generalized (drift or mean-variance) Brownian motion process through time. Going into Stage 2, this generalized Brownian motion process might be used to simulate stochastic interest rates, non-constant variances, underlying security price movements, etc. However, for Stage 1, students should concern themselves only with the process of simulating a generic generalized Brownian motion process for a random variable through time. The user of this spreadsheet should be able to input various parameters for the generic random process. Among the allowable user-inputs should be an initial or starting value for the generic random variable along with a drift and a variance for the process, and the number of time periods for the process.

However, for the first stage, you do not know what random variables will be modeled in the second stage or what securities you will use for your model. So, your job here is just to simulate a generic Brownian motion process with a known drift and variance. The first stage is intended to be generic and flexible enough to apply to many potential securities and markets.

3.         3.    Simulating a Mixed Jump-Diffusion Process Environment

One of the big problems with the most basic popular options pricing models is that underlying security variances tend not to be constant over time. For example, many U.S. corporations are expected to make earnings announcements quarterly, on well-anticipated dates. It is clear that stock prices are more volatile about these earnings announcement dates than at other periods throughout the year. In addition, election cycles, hurricanes, earthquakes, etc. can impact variances.

The user of this Stage 1 package should be able to analyze a generic mixed jump-diffusion process through time. This means that students might wish that the process will generally be of a Brownian motion type with drift, but include a prospect for drifts, either at designated times or at random intervals. There are many possibilities for how this jump process might be modeled. Going into Stage 2, this generalized Brownian motion process might be used to simulate stochastic interest rates, non-constant variances, underlying security price movements, etc. However, for Stage 1, students should concern themselves only with the process of simulating a mixed jump-diffusion process for a random variable through time. The user of this spreadsheet should be able to input various parameters for the generic random process. Among the allowable user-inputs should be an initial or starting value for the generic random variable along with a drift and a variance for the continuous part of the process, the number of time periods for the process, and parameters for the jumps.

However, for the first stage, you do not know what random variables will be modeled in the second stage or what securities you will use for your model. So, your job here is just to simulate a mixed jump-diffusion process with a known drift and variance for the diffusion part of the process. The first stage is intended to be generic and flexible enough to apply to many potential securities and markets.

General Notes

Make certain that you and your groupmates are at least marginally competent to use spreadsheets, and User Defined Functions and/or VBA can be helpful as well. These latter parts can be remarkably simple to accomplish. If you are clueless now, have a look at the Introduction to VBA on the course web site or one of the many such introductions online. You might be able to create your own fundamental VBA programs to do something useful within a half hour. There are plenty of web sites that will answer your questions when you have them. If you are clueless now, have a look at the Introduction to VBA page on the course web site. There are plenty of web sites that will answer your questions when you have them.

You will probably notice that I already have made available to you on my personal website for the course and on Canvas spreadsheets that accomplish pretty much what I am asking of you here. The spreadsheets don’t necessarily accomplish everything that I have asked of you here, they are not of professional quality, and they are not easily adapted to the valuation of many types of derivative securities. They are intended to be pedagogical demonstrations of illustrative value, something suitable to prepare you to create much better works on your own.

4. Derivatives Trading Project
Here’s an introduction to a very different type of project for this course. Students who wish to engage in paper or virtual trading of derivatives can make a project of it for this course. The first step is to find a suitable trading simulator or paper trading platform for this purpose, as JHU AAP does not subscribe to academic trading simulators such as FTS, Rotman or Trader-X. But there are a number of online alternatives. The details for this project are a bit more lengthy, so link here to a detailed description of this trading project.

Students must inform the instructor by the end of the second week of the semester of their intent to complete the project and whether they intend to do so in a group along with that group member or members, if any, and subject to the limitations discussed above. Please inform the instructor as soon as possible if you change your mind about doing a given project. Students should not submit projects that have been or will be submitted in other courses. Students who wish to discuss customizing their own projects may negotiate terms of this other project type with the course instructor, who should approve it before work commences. The final version of the project will be due on the last day of the semester as noted in the Course Syllabus.