Course: B8.3 Mathematical Models of Financial Derivatives (2024-25)

Lecturer: Profile: Sam Howison

Course information

General Prerequisites:

B8.1 Probability, Measure and Martingales (previously named Martingales Through Measure Theory) would be good background. Part A Probability is a prerequisite. Part A Integration is also good background, though not a prerequisite.

Course Term: Hilary

Course Lecture Information: 16 lectures

Course Weight: 1

Course Level: H

Assessment Type: Written Examination

Course Overview:

The course aims to introduce students to derivative security valuation in financial markets. At the end of the course the student should be able to formulate a model for an asset price and then determine the prices of a range of derivatives based on the underlying asset using arbitrage free pricing ideas.

Learning Outcomes:

Students will have a familiarity with the mathematics behind the models and analytical tools used in Mathematical Finance. This includes being able to formulate a model for an asset price and then determining the prices of a range of derivatives based on the underlying asset using arbitrage free pricing ideas.

Course Synopsis:

Discrete-time models (binomial trees) and arbitrage in finance
Hedging in continuous times and the Black-Scholes model
European-style options and
Introduction to Brownian motion and Ito's Lemma
American-style options, PDEs and the Feynman-Kac formula
Perpetual and other exotic options
Implied volatility: smiles and smirks
The Merton Jump-Diffusion model and option prices
Consumption-based pricing
Limit order books and optimal execution models

Section outline

Select section General

General

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- Select activity Announcements
  
  Announcements Forum
- Select activity Reading List
  
  Reading List URL
- Select activity Discussion Forum
  
  Discussion Forum
Select section Course Materials

Course Materials
- Select activity B8.3 Problem Sheet 1
  
  B8.3 Problem Sheet 1 Assignment
- Select activity B8.3 Problem Sheet 2
  
  B8.3 Problem Sheet 2 Assignment
- Select activity B8.3 Problem Sheet 3
  
  B8.3 Problem Sheet 3 Assignment
- Select activity B8.3 Problem Sheet 4
  
  B8.3 Problem Sheet 4 Assignment
- Select activity MMSC special topic suggestions
  
  MMSC special topic suggestions File
- Select activity Printable version of the slides
  
  Printable version of the slides Assignment
  
  Printable version of slides, three slides per A4 side. Some images may have dark backgrounds. Slides for later lectures will be added as we go. (The slides used in lectures will have dark backgrounds.)
- Select activity Slides from 23/24
  
  Slides from 23/24 File
  
  Last year's slides (for background but note they take a slightly different approach in places).
- Select activity Notes
  
  Notes File
  
  Lecture notes from 2023/24 by Alvaro Cartea. They are close to the course but may take a different approach in places.
- Select activity B8.3 Slides from lectures
  
  B8.3 Slides from lectures Assignment
  
  The dark-mode slides as used in lectures. NOT SUITABLE FOR PRINTING.
- Select activity Barchart.com S&P 500 options
  
  Barchart.com S&P 500 options URL
  
  The website shows a lot of option prices: have a look around to familiarise yourself with them.
- Select activity Bybit live BTC LOB
  
  Bybit live BTC LOB URL
  
  Live evolution of the Bitcoin price as seen in Lecture 1. Note the order book and trade list feeds.
- Select activity Hyperliquid blockckain-based exchange
  
  Hyperliquid blockckain-based exchange URL
Select section Intercollegiate Classes

Intercollegiate Classes
- Select activity Class Signup
  
  Class Signup Class registration
  
  Registration start: Monday, 13 January 2025, 12:00 PM
  
  Registration end: Friday, 14 February 2025, 12:00 PM
- Select activity Class Tutor's Comments
  
  Class Tutor's Comments Assignment
  
  Class tutors will use this activity to provide overall feedback to students at the end of the course.
  
  Not available unless: You have signed up to a class

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Section outline

General

Course Materials

Intercollegiate Classes