Introduction to Derivatives and Financial Engineering

2025/2026

Academic Year

ENG

Instruction in English

3

ECTS credits

Delivered at:

Department of Finance

Course type:

Compulsory course

When:

4 year, 2 module

Instructor

Хованский Сергей Константинович

Course Syllabus

Abstract

This course explores the world of financial derivatives, delving into their pricing and hedging. We’ll discuss in details the risk-neutral asset valuations techniques, pricing of derivatives in Binomial and Black-Scholes settings, the concept of derivative hedging, the concept of no-arbitrage pricing. In this course, the students will have an opportunity to learn about the applications of Monte Carlo simulations methods for derivative pricing.

Learning Objectives

• Gain a comprehensive understanding of the major financial markets and exchanges where derivatives and structured products trade
• Identify the different types of derivatives, including options, futures, forwards, swaps
• Analyze the role of derivatives in risk management, particularly hedging and speculation
• Understand how derivatives are valued and influenced by the Greeks mathematical measures
• Understand the concept of abitrage and no-arbitrage pricing of financial derivatives
• Become familiar with Fundamental Theorem of Asset Pricing
• Become familiar with risk-neutral pricing
• Understand Binomial framework for derivative pricing
• Understand the Greeks in the context of Black-Scholes framework
• Understand the Monte-Carlo approach for derivative pricing

Expected Learning Outcomes

• Compute valuation model
• Reflect on Call and Put options, their payoffs for long and short positions.
• Refelct about arbitrage. Be able to compute no-arbitrage bounds for option prices.
• Learn about Put-Call parity, i.e. relation among call, put and forwards values.
• Refelct on what is a forwards contract, its valuation and hedging
• Learn about an arbitrage.
• Reflect on futures and swap contracts
• Reflect about a Binomial model.
• Learn how to price and hedge a derivative in a Binomial model framework.
• Learn about the risk-neutral approach for derivative pricing
• Reflect about the foundation of risk-neutral derivative pricing.
• Learn the relation between an opportunity for an arbitrage and the possibility of risk-neutral pricing of a derivative.
• Learn about the convexity of Call option prices with respect to strikes.
• Learn about possible arbitrage when the convexity is violated.
• Learn about wiener process
• Learn about geometric Brownian motion and its modeling
• Learn how to compute Black-Scholes price for a Call and Put options
• Learn about hedging of an option in Black-Scholes framework
• Learn about implied volatility
• Learn about financial Greeks used for option hedging
• Learn about Monte Carlo approach for derivative pricing
• Learn about introduction to real options
• Learn about value-at-risk as tool for risk management

Course Contents

• Introduction to derivatives: forwards, futures, forwards, swaps
• Options (Call and Put) arbitrage bounds for option prices
• Binomial model, pricing and hedging of a call option, path-dependent exotic options
• Fundamental Theorem of Asset Pricing. Introduction and examples of application
• Wiener process, geometric Brownian motion, Ito's lemma, Black-Scholes price
• Examples of applications of Black-Scholes pricing, hedging, Greeks, implied volatility, Monte Carlo approach for option pricing
• Introduction to the concept of real options and risk management tool of Value-at-Risk

Assessment Elements

• Homework
• Midterm
• Exam

Interim Assessment

• 2025/2026 2nd module
  0.29 * Exam + 0.42 * Homework + 0.29 * Midterm

Bibliography

Recommended Core Bibliography

• Options, futures, and other derivatives, Hull, J. C., 2000
• Options, futures, and other derivatives, Hull, J. C., 2003
• Options, futures, and other derivatives, Hull, J. C., 2006
• Options, futures, and other derivatives, Hull, J. C., 2009
• Options, futures, and other derivatives, Hull, J. C., 2018
• Quantitative finance : its development, mathematical foundations, and current scope, Epps, T. W., 2009
• Stochastic calculus for finance. Vol.1: The binomial asset pricing model, Shreve, S. E., 2004

Authors

• SOLOVEVA EKATERINA EVGENEVNA