Quantitative Finance

2023/2024

Academic Year

ENG

Instruction in English

5

ECTS credits

Delivered at:

Big Data and Information Retrieval School

Course type:

Elective course

When:

4 year, 1, 2 module

Instructor

Zhitlukhin, Mikhail

Course Syllabus

Abstract

This course gives an introduction to quantitative finance – the mathematical theory of pricing of financial securities like futures, options, swaps, etc. This is a deep and interesting subject and the corresponding theory is actively used in modern financial markets.

Learning Objectives

• The purpose of the course is to explain the theory behind securities pricing based on the probability theory and random processes, and to discuss practical implementations of pricing algorithms and models.

Expected Learning Outcomes

• Know the basic discrete-time models of stock markets, e.g., the binomial model and its derivatives.
• Know the foundations of stochastic calculus, including the concept of Brownian motion and Ito’s integral.
• Know how to derive the Black-Scholes formula for option pricing
• Understand the limitations of the Black-Scholes formula and how it should (and should not) be used in practice.
• Understand the concept of implied volatility and how it is used in derivatives trading
• Know how to price the exotic securities using the Monte-Carlo method

Course Contents

• Basic concepts of financial markets.
• The one-period binomial model.
• The Cox-Ross-Rubinstein model.
• Auxiliary results from the theory of random processes in discrete time.
• Martingale methods for discrete time markets.
• The fundamental theorem of asset pricing.
• The limit of the binomial model.
• Ito’s integral and Ito’s processes.
• The Black-Scholes model.
• Implied volatility, Greeks.
• The Black model.
• The Heston model.

Assessment Elements

• Homework module 1 (HW1)
• Mid-term test
• Exam
  Written examination conducted in the classroom. Duration 120 minutes. The examination paper contains 4 or 5 theoretical questions and problems. The use of printed materials is allowed. The use of electronic devices in not allowed. If plagiarism is detected, the assessment element will be assigned a score of "0". If the student is suspected of preparing the task not on his own, the teacher has the right to initiate additional verification or defense of this particular assessment element. Then such an assessment element will be graded based on the additional verification or the defense.
• Homework module 2 (HW2)

Interim Assessment

• 2023/2024 2nd module
  Final = RoundUp(0.16*HW1 + 0.16*HW2 + 0.28*T + 0.4*E), where HW1 is the average grade for homework in module 1, HW2 is the average grade for homework in module 2, T is the grade for the mid-term test, E is the grade for the exam.

Bibliography

Recommended Core Bibliography

• Introduction to mathematical finance : discrete time models, Pliska, S.R., 2005
• Options, futures, and other derivatives, Hull, J. C., 2018
• Paul Wilmott introduces quantitative finance, Wilmott, P., 2009
• The volatility surface : a practitioner's guide, Gatheral, J., 2006

Recommended Additional Bibliography

• Föllmer, H., & Schied, A. (2011). Stochastic Finance : An Introduction in Discrete Time (Vol. 3rd, and extended ed). Berlin: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=388088
• Martingale methods in financial modelling, Musiela, M., 2005