2023/2024

Quantitative Finance

Category 'Best Course for Career Development'

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'

Category 'Best Course for New Knowledge and Skills'

Type: Mago-Lego

Delivered by: School of Finance

When: 2 module

Open to: students of one campus

Instructors: Ilya Dergunov

Language: English

ECTS credits: 3

Contact hours: 28

Course Syllabus

Abstract

The theoretical part of the course will refresh our knowledge of the basics of binomial model, stochastic calculus, Black-Scholes model and Heston stochastic volatility model. Then course will proceed to introduce the basics of the Monte Carlo simulation technique as well as main methods for efficient numerical valuation of derivative contracts in a Black-Scholes world and implementation of various pricing methods, for instance, in Julia or Python programming languages (e.g simulation of the stochastic differential equations; finite-difference-based methods for the solution of the partial differential equations; calculation of greeks, implied volatility and etc.).

Learning Objectives

• Understand tree-based approach to pricing derivatives
• Understand PDE-based approaches to pricing financial products
• Understand Monte Carlo approach
• Coding appropriate algorithms for pricing derivatives
• Understand basics of Stochastic Calculus and Black-Scholes Model

Expected Learning Outcomes

• Implement basic Monte Carlo technique for different financial problems
• Implement variance reduction techniques
• Calculate sensitivities (delta, gamma, vega and others)
• Price American Options via Monte Carlo using Longstaff-Schwartz algorithm
• Implement numerical schemes to solve Black-Scholes-Merton PDE
• Price derivatives via solving Black-Scholes-Merton PDE
• Price derivatives via Binomial tree approach
• Apply Ito formula. Solve basic stochastic calculus problems. Simulate Brownian motion paths

Course Contents

• Binomial Model
• Stochastic Calculus
• Monte Carlo Simulations
• Black-Scholes model
• Black-Scholes specific properties of Plain Vanilla Options and Implied Volatility
• Solving the Black-Scholes PDE numerically with finite differences
• Pricing American Options
• Heston stochastic volatility model

Assessment Elements

• Home Assignment 1
  Binomial model.
• Home Assignment 2
  Stochastic Calculus
• Home Assignment 3
  Black-Scholes, Greeks, Implied Vola
• Home Assignment 4
  Monte Carlo methods
• Mid term test
  Mid-term test
• Final test
  Final test
• Home assignment 5
  Volutarily home assignment. Longstaff-Schwartz algorithm.

Interim Assessment

• 2023/2024 2nd module
  0.2 * Final test + 0.15 * Home Assignment 1 + 0.15 * Home Assignment 2 + 0.15 * Home Assignment 3 + 0.15 * Home Assignment 4 + 0 * Home assignment 5 + 0.2 * Mid term test

Bibliography

Recommended Core Bibliography

• Arbitrage theory in continuous time, Bjork, T., 2004
• Bjork, T. (2009). Arbitrage Theory in Continuous Time. Oxford University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.oxp.obooks.9780199574742
• Hull, J. C. (2017). Options, Futures, and Other Derivatives, Global Edition. [Place of publication not identified]: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1538007
• Monte Carlo methods in financial engineering, Glasserman, P., 2004
• Options, futures, and other derivatives, Hull, J. C., 2009

Recommended Additional Bibliography

• Stochastic calculus for finance. Vol.2: Continuous-time models, Shreve, S. E., 2004