Бакалавриат
2026/2027
Введение в деривативы и финансовая инженерия
Статус:
Курс обязательный (Международная программа по бизнесу и экономике)
Кто читает:
Департамент финансов
Где читается:
Санкт-Петербургская школа экономики и менеджмента
Когда читается:
4-й курс, 2 модуль
Охват аудитории:
для своего кампуса
Преподаватели:
Хованский Сергей Константинович
Язык:
английский
Кредиты:
3
Контактные часы:
28
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
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