Applied Stochastic Processes 2023-24 Module 3 (Spring 2024)

Announcements

• The WeChat group will be created by TA. (No 1-to-1 chat please.)
• Email is the preferred method of communication. The class mailing list will be created as [email protected].

Course Slides and Other Resources

• Prelims: Probability Statistics Review
• Past Midterm Exams: All Exams (2017-18, 2018-19, 2019-20, 2020-21, 2021-22, 2022-23)
• Term Projects: Current, 2022-23, 2021-22, 2020-21, 2019-20, 2018-19, 2017-18
• PyFeng package (PyPI | Github | Documentation)
• Scientific computing, MC method, RN generation (Slides | Py demo)
• Black-Scholes model (Py demo, MC demo): Also see Ch. 10 of StoFin Course Notes
• Bachelier (Normal) model (Slides) from Stochastic Finance class
• Implied volatility (Slides | Py demo)
• Spread/Basket options (Slides)
• SABR model (Slides) | NSVh model (Slides)
• SV model (Slides): Advanced methods for Heston Model and OUSV Model
• Variance Derivatives (Slides)
• Numerical Integral (Slides)
• Copula (Slides, Py demo)

Lectures

No	Date	Contents
01	2.20 Tues	Course overview, Scientific computing, MC method, RN generation (Slides | Py demo)
02	2.23 Fri	Continued (Slides | Py demo)
03	2.27 Tues	Numpy crach course (Py Demo). Python crash course (Py Demo). More cheatsheets also available in MLF CMS.
04	3.01 Fri	Black-Scholes implementation (Py Demo). Implied volatility (Slides | Py demo). Bachelier model (Slides). Black-Scholes-Merton and Bachelier option pricing with MC (Py Demo).
05	3.05 Tues	Spread/Basket options (Slides). Correlated Normal RNs (Slides | Py Demo), [HW2: Spread/Basket option implementation, Due next Thursday]
06	3.08 Fri	SABR model (Slides: Volatility smile)
07	3.12 Tues	SABR model continued (Slides: Local volatility model, Model intro), Introduction to PyFENG package
08	3.15 Fri	SABR model continued (Slides: Euler/Milstein method, Conditional MC), Py Demo (SABR, BsmNdMc), Python Import (Py Demo), HW3: MC method for SABR
09	3.19 Tues	SV Model Simulation for Project (Slides)
10	3.22 Fri	Research Presentation: Heston model simulation method (Slides)
11	3.26 Tues	SV Model Simulation for Project (Slides), Github pull-request (PR). Suggested project topics
12	3.29 Fri
13	4.02 Tues	Past Exams Review
14	4.07 Sun	Midterm Exam (Solution)
15	4.09 Tues	Copula (Slides, Py demo)
16	4.12 Fri	Copula (Slides, Py demo)
17	4.16 Tues	Research Presentation: NSVh model and Normal SABR (Slides)
18	4.19 Fri	Course project presentation

Homeworks:

• Set 0: (Due by XXX)

  • Register on Github.com and send your ID and student number to Prof. Choi via email ([email protected]). Use your full name in your profile. Accept invitation to the PHBS organization from TA. Install Github Desktop.
  • Install Anaconda Python distribution (3.X version, not 2.X version). Anaconda distribution is core Python + useful scientific computation libraries (e.g., numpy, scipy, pandas) + package management system (pip or conda)
  • Send the screenshot of Github desktop and Anaconda installed to TA. (Example: Github Desktop, Anaconda Spyder)

• Set 1 [Due by 3.16] Pricing basket and spread option using MC. Starter Code

  • Create a designated repository YOUR_GITHUB_ID/PHBS_ASP_2023 for your HW and project. Tick Initialize this repository with a README and select python under .gitignore
  • Copy HW2 folder from ASP repository to YOUR_GITHUB_ID/PHBS_ASP_2023 repository.
  • Upload your HW to the folder HW2 and update the repository. (Commit to master and Fetch Origin).

• Set 2 [Due by 3.30] Simulating SABR model. Starter Code

Course Project: Project Description (Previous year: 2017 | 2018 | 2019 | 2019 | 2020 | 2021)

Classes:

• Lectures: Tues & Fri 10:30 AM – 12:20 PM
• Venue: PHBS Building, Room 313

Instructor: Jaehyuk Choi

• Office: PHBS Building, Room 755
• Phone: 86-755-2603-0568
• Email: [email protected]
• Office Hours: Mon 7-9 PM

Teaching Assistance: Xin Yang (杨鑫)

• Email: [email protected]
• TA Office Hour: TBA (Room 213/214)

Course overview:

Applied Stochastic Processes (ASP) is intended for students who are seeking advanced knowledge in stochastic calculus and are eventually interested in jobs in financial engineering. As the name indicates, the course will emphasize on applications such as numerical calculation and programming. On completion of this course, the students will learn how financial observations (e.g. stock prices and FX rate) are modeled with stochastic processes and how they can be computed using analytics or computer simulations.

Prerequisites:

Stochastic Finance (FIN 519), a year 1 required course for a quantitative finance program, is a prerequisite for the ASP since it provides theoretical background. Undergraduate-level knowledge in probability, statistics, linear algebra, and programming skills (Python) are also highly recommended.

Extra Reading Materials

• Monte Carlo Methods in Finance by Peter Jaeckel
• Option Valuation Under Stochastic Volatility by Alan Lewis
• Stochastic Calculus and Financial Applications by J. Michael Steele (Stochastic finance course notes)

Assessment/Grading Details

Attendance 20%, Mid-term Exam 30%, Assignments 20%, Course Project 30%

• Midterm exam: 4.06 Wed. Open-book exam without computer/phone/calculator use. No final exam.
• Course project: Presentation (Last week). Group up to X people.
• Attendance: Randomly checked. The score is calculated as 20 – 2x(#of absence). Leave requests should be made 24 hours before with supporting documents, except for emergencies. Job interview/internship cannot be a valid reason for leave
• Grade in letters (e.g., A+, A-, ... ,D+, D, F). A- or above < 30% and B- or below > 10%.