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Магистратура 2023/2024

Количественные финансы

Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Направление: 38.04.08. Финансы и кредит
Кто читает: Школа финансов
Когда читается: 2-й курс, 2 модуль
Формат изучения: без онлайн-курса
Охват аудитории: для своего кампуса
Прогр. обучения: Стратегическое управление финансами фирмы
Язык: английский
Кредиты: 3
Контактные часы: 28

Course Syllabus

Abstract

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

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

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

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

Assessment Elements

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

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

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

Authors

  • DERGUNOV ILYA EVGENEVICH