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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 PHBS.ASP@allmail.net.

Course Slides and Other Resources

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 Python crash course (Py Demo). More cheatsheets also available in MLF CMS. Numpy crach course (Py Demo).
04 3.01 Fri Black-Scholes implementation (Py Demo). Implied volatility (Slides | Py demo).
05 3.05 Tues Bachelier model (Slides). Black-Scholes-Merton and Bachelier option pricing with MC (Py Demo). Spread/Basket options (Slides). Correlated Normal RNs (Slides | Py Demo)
06 3.08 Fri Spread/Basket options continued, [HW2: Spread/Basket option implementation, Due next Thursday]
07 3.12 Tues SABR model (Slides: Volatility smile), Suggested project topics
08 3.15 Fri SABR model continued (Slides: Local volatility model, Model intro), Introduction to PyFENG package
09 3.19 Tues SABR model continued (Slides: Euler/Milstein method, Conditional MC), Github pull-request (PR), Py Demo (SABR, BsmNdMc), HW3: MC method for SABR
10 3.22 Fri Python Import (Py Demo), SV Model Simulation for Project (Slides)
11 3.26 Tues SV Model Simulation for Project (Slides)
12 3.29 Fri Past Exams Review
13 4.02 Tues Midterm Exam (Solution)
14 4.07 Sun Copula (Slides, Py demo)
15 4.09 Tues Copula (Slides, Py demo)
16 4.12 Fri Research Presentation: NSVh model and Normal SABR (Slides)
17 4.16 Tues Research Presentation: Heston model simulation method (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 (jaehyuk@phbs.pku.edu.cn). 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 9.9 Fri] Generate a function for generating standard normal RN following Problem 2 of 2021.M3 midterm exam. After drawing 1e6 RNs, check if they are truly standard normal RNs.

    • Draw histogram using matplotlib.pyplot
    • Calculate mean/variance/skewness/kurtosis
  • Set 1 [Due by XXX] Simple corporate (default) bond pricing by MC simulation. Starter Code

  • Set 2 [Due by XXX] Pricing basket and spread option using MC. Starter Code

  • Set 3 [Due by XXX] 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

Teaching Assistance: Xin Yang (杨鑫)

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

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%.

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