Quantitative Finance 2

2024/2025

Academic Year

ENG

Instruction in English

6

ECTS credits

Delivered at:

School of Finance

Course type:

Elective course

When:

2 year, 1, 2 module

Instructors

Afonina, Maria

Dergunov, Ilya

Course Syllabus

Abstract

The theoretical part of the course will refresh our knowledge of the basics of binomial model,stochastic calculus, various option pricing models as well as stochastic models of the short rate. In the practical (main) part of the course we will discuss basic numerical methods for the valuation of derivative securities, like Monte Carlo simulation, finite difference methods, and regression-based valuation of American options in detail. We will mostly focus on equity derivatives in the geometric Brownian motion framework, but we will also discuss alternative models like the Heston stochastic volatility model or Merton’s jump-diffusion model. The course is not meant to be a course in numerical mathematics with detailed and extensive theorems and proofs, its focus is rather on the basics of a set of very useful numerical techniques, which are widely applied in industry practice and in research. The implementation will be done in Python (also possible in Julia, Matlab, R).

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 the usage of exotic derivatives
• Understand calibration techniques of different stochastic models

Expected Learning Outcomes

• Implement basic Monte Carlo technique for different financial problems
• Implement variance reduction techniques
• Calculate sensitivities (delta, gamma, vega and others)
• 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
• Implement stochastic volatility models
• Calibrate term structure of interest rates
• Calculate Distance-to-Default
• Implement VaR and ES via Monte Carlo
• Implement calibration procedures for option pricing models
• Pricing American style options

Course Contents

• Tree-based pricing methods
• Review of derivative pricing methods
• Monte Carlo Simulations
• Estimating price sensitivities in MC
• Pricing of American Options
• Alternative option pricing models
• Interest rate modeling
• Credit risk modeling. Merton Distance-to-Default Model
• Monte Carlo Methods for VaR & ES

Assessment Elements

• Home Assignment 1
  Tree-base modeling
• Home Assignment 2
  Stochastic Calculus
• Home Assignment 3
  Review of Derivatives Pricing
• Home Assignment 4
  Monte Carlo methods
• Mid term test
• Home Assignment 5
  Pricing American Options
• Home Assignment 6
  Alternative option pricing models
• Home Assignment 7
  Stochastic short rate models
• Home Assignment 8
  Credit risk modeling. Merton Distance-to-Default Model
• Home Assignment 9
  Monte Carlo Methods for VaR
• Final test
  Final test

Interim Assessment

• 2024/2025 2nd module
  0.3 * Final test + 0.05 * Home Assignment 1 + 0.05 * Home Assignment 2 + 0.05 * Home Assignment 3 + 0.05 * Home Assignment 4 + 0.05 * Home Assignment 5 + 0.05 * Home Assignment 6 + 0.05 * Home Assignment 7 + 0.05 * Home Assignment 8 + 0.05 * Home Assignment 9 + 0.25 * 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., 2018

Recommended Additional Bibliography

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

Authors

• DERGUNOV ILYA EVGENEVICH