Quantitative Finance
Ilya Dergunov
Higher School of Economics
Module 2, 2023
Course Outline
Course: Quantitative Finance
Module 2, 2023
Lectures and Tutorials:
Thursdays 14:40 – 17:40, Nov 2 – Dec 7
Wednesdays 16:20 – 17:40, Dec 13 and Dec 20
Ilya Dergunov, PhD in Finance
Office S1017
Email: idergunov@hse.ru
Consult: drop email for an appointment
Telegram channel:
Quantitative Finance
Ilya Dergunov 1
Course Outline
Course: Quantitative Finance
Course Contents
1Binomial model
2Stochastic Calculus
3Black-Scholes model
4Black-Scholes specific properties of Plain Vanilla Options,
Greeks and Implied Volatility
5Solving the Black-Scholes PDE numerically with finite
differences
6Monte Carlo Simulations
7Pricing American Options via Monte Carlo using
Longstaff-Schwartz algorithm
8Heston stochastic volatility model
Quantitative Finance
Ilya Dergunov 2
Course Outline
Course: Quantitative Finance
Textbooks:
1Hull, J. C: Options, Futures, and other Derivatives,
Prentice-Hall, New York.
2Tomas Bjork (2009) Arbitrage Theory in Continuous Time
(Third Edition)
Additional:
1S. Shreve: Stochastic Calculus for Finance II
2H. T. Huynh, V. S. Lai, and I. Soumare (2008) Stochastic
Simulation and Applications in Finance with MATLAB
Programs
3R. Korn, E. Korn, G. Kroisandt (2010) Monte Carlo Methods
and Models in Finance and Insurance
Quantitative Finance
Ilya Dergunov 3
Course Outline
Course: Quantitative Finance
Grading:
14 Problem sets; 15% each ⇒60% in total
2First test (’mid-term test’) – 20%
3Final test – 20%
Final Grade
=P4
i=1 ×(HAi×0.15) + Mid −term ×0.2 + Final ×0.2.
Each problem set may contain optional exercises denoted by ∗
which are not compulsory to solve. Attempting to provide a
solution/partial solution to such exercises as well as active in-class
participation during tutorials can give an additional benefit to the
student towards the overall grade of about 10%.
Quantitative Finance
Ilya Dergunov 4
Course Outline
Course: Quantitative Finance
Problem sets:
1Theoretical exercises where a student is supposed to derive
and show some results
2Programming part where a student is supposed to do some
programing exercises and work with data (potentially)
3Each home assignment must be submitted within 2-week time
4Software: Python, Matlab, Julia, or R (whichever you feel
comfortable with)
5You can work in groups of 2-3 people
6Clarity and intermediate steps in solutions are essential. For
programming exercises comments are essential.
Quantitative Finance
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Course Outline
Options types that will be covered
Plain vanilla options: call and put options
European options
American options
Exotic options (e.g. Lookback, Digital, Asian Options)
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Ilya Dergunov 6
Course Outline
Option pricing models covered
Binomial option pricing model
Black-Scholes-model
Heston model
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Course Outline
Implementation methods covered
Binomial trees
Solving the Black-Scholes PDE with finite differences
Monte Carlo methods for pricing
including Longstaff-Schwartz algorithm for American options
Implementation of the Heston model (?)
Quantitative Finance
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Binomial model
Binomial Model
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Binomial model
Formal Definition: Call and Put Options
Definition
AEuropean call option on the asset Swith strike price Kand
maturity date Tis a contract written at t= 0 with the following
properties:
The holder of the contract has, exactly at the time t=T, the
right to buy asset Sat the price K.
The holder of the option has no obligation to buy the asset.
AEuropean put option is the right to sell the asset S.
An American option can be exercised at any time prior to the
maturity date T.
Quantitative Finance
Ilya Dergunov 10
Binomial model
Payoff from options
Payoff from buying the call
Π = max[ST−K,0] = (ST−K)+
