arontian2018/asp

PHBS Applied Stochastic Processes Course Website

Applied Stochastic Processes 2022-23 Module 1 (Fall 2022)

Announcements

• Email is the preferred method of communication. 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)
• 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
• Normal (Bachelier) model (Slides) from Stochastic Finance class
• Implied volatility (Slides | Py demo)
• Spread/Basket options (Slides)
• SABR model (Slides) | NSVh model (Slides)
• Copula (Slides, Py demo)

Lectures

No	Date	Contents
01	8.29 Mon	Course overview, Scientific computing, MC method, RN generation (Slides | Py demo)
02	9.01 Thurs	Continued (Slides | Py demo)
03	9.05 Mon	Python crash course (Py Demo). More cheatsheets also available in MLF CMS. Numpy crach course (Py Demo).
04	9.08 Thurs	Black-Scholes implementation (Py Demo). Implied volatility (Slides | Py demo).
05	9.14 Wed	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	9.15 Thurs	Spread/Basket options continued, [HW2: Spread/Basket option implementation, Due next Thursday]
07	9.19 Mon	SABR model (Slides: Volatility smile), Suggested project topics
08	9.22 Thurs	SABR model continued (Slides: Local volatility model, Model intro), Introduction to PyFENG package
09	9.26 Mon	SABR model continued (Slides: Euler/Milstein method, Conditional MC), Github pull-request (PR), Py Demo (SABR, BsmNdMc), HW3: MC method for SABR
10	9.29 Thurs	Python Import (Py Demo), SV Model Simulation for Project (Slides)
11	10.06 Thurs	SV Model Simulation for Project (Slides)
12	10.10 Mon	Past Exams Review
13	10.13 Thurs	Midterm Exam (Solution)
14	10.17 Mon	Copula (Slides, Py demo)
15	10.20 Thurs	Copula (Slides, Py demo)
16	10.24 Mon	Research Presentation: NSVh model and Normal SABR (Slides)
17	10.26 Wed	Research Presentation: Heston model simulation method (Slides)
18	10.27 Thurs	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 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: Mon & Thurs 3:30 – 5:20 PM
• Venue: PHBS Building, Room 211

Instructor: Jaehyuk Choi

• Office: PHBS Building, Room 755
• Phone: [phone]
• Email: [email protected]
• Office Hour: Wed 1-3 PM

Teaching Assistance: Su Nan (苏南)

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

Course overview:

Applied Stochastic Processes (ASP) is intended for the students who are seeking advanced knowledge in stochastic calculus and are eventually interested in the jobs in financial engineering. As the name indicates, the course will emphasis 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 modelled 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 quantitative finance program, is a prerequisite for the ASP since it provides theoretical background. Undergraduate-level knowledge in probability, statistics, linear algebra and programming skill (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 request should be made 24 hours before with supporting documents, except for emergency. 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%.