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# Quantitative Finance

2023/2024
ENG
Instruction in English
3
ECTS credits
Delivered at:
School of Finance
Course type:
Elective course
When:
2 year, 2 module

### 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

#### Recommended Core Bibliography

• Arbitrage theory in continuous time, Bjork, T., 2004