MATH375: Stochastic modelling in insurance and finance
Introduction
This module is about pricing financial derivatives. These are financial contracts whose value depends on, or derives from, the value of another asset, called an underlying. Two examples of the underlying are stocks and bonds.
An example of a financial derivative is a European call option defined as: a contract that gives its holder the right, but not the obligation, to buy a specified asset for a price K at time T.
Another example of a financial derivative is the forward contract defined as: a contract between two parties where one party has agreed to sell a specified asset for a price K at time T, whereas the other party has agreed to buy that asset for the price K at time T.
Note that a forward contract is not an option, i.e. it is an obligation.
Mathematically, the European call option and the forward contract are random variables, i.e. their values at time T are, respectively:
where S(T) is the value of underlying at time T (and the value of forward contract corresponds to the party that has agreed to buy the underlying).
The main aim of this module is find the price (value) of these contracts for time t ∈ [0,T]. This is given by the risk-neutral pricing formula:
where X is the terminal value of the financial derivative.
In this module, we cover the necessary mathematics to derive this formula and then apply it for pricing various financial derivatives.
Delivery
The module will be delivered by two lecturers. I will cover the first six weeks, whereas the remaining five weeks are delivered by Dr Ronnie Loeffen (email:[email protected]; office: room 307 of the Maths building).
The last week, Week 12, will be revision.
Beginning with Week 2, there will be three hours of lectures and one hour tutorial.
In Week 1 there will be no tutorials, i.e. there will be four hours of lectures during this week.
I will deliver the lectures by writing on my tablet and/or on the board. You are encouraged to take notes during the lectures.
During the tutorials, we will go through some of the questions together.
The typed lecture notes will be uploaded on CANVAS at the beginning of each week, whereas the writing during lectures will be uploaded on CANVAS at the end of each week.
The tutorial questions and solutions will also be uploaded on canvas each week.
All lectures will be recorded, and should appear on CANVAS after the lectures.
The lecture notes and the tutorials are sufficient for this module.
Those of you who would like to read more on this subject can consult the books:
1. S. Shreve, Stochastic calculus for finance II: continuous-time models, Springer, 2008.
2. N. H. Bingham and R. Kiesel, Risk-neutral valuation, Springer, 2004.