Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH202
Module Title: Introduction to Financial Mathematics
Module Level: Level 2
Module Credits: 5.00
Semester: SEM1/SEM2
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims This module is designed to provide an introduction to the pricing of financial derivative products. The course will develop the mathematical foundations of the Black-Scholes method.
 Learning outcomes A. Understand the main principles of financial markets and the common terminology B. Understand and analyze the use of financial derivatives and hedging strategies C. Be able to price and analyze forwards, futures, and options D. Understand, implement, and analyze the binomial tree model E. Understand, analyze and use probability distributions in option pricing applications F. Utilize stochastic calculus such as Ito’s Lemma in the Black-Scholes framework G. Understand and use diffusion processes
 Method of teaching and learning This module will be repeated over two semesters. In semester 1, the module will be delivered for
 Syllabus Financial Assets Shares (stocks, equity, assets). Market capitalisation. Dividend. Index (e.g. FTSE 100). Risk-free assets. Derivatives Futures and forward contracts. European call and put options. Gearing, speculation. Risk-management, hedging. Arbitrage Why there is no risk-free profit. Short-selling (shorting). Portfolios. Futures pricing (special case of derivatives pricing). Put-Call parity. Inequalities of options prices. Asset Price Models Market efficiency. Binary tree model for option pricing. Statistics Review: Stochastic variables. Mean (expectation value), variance. Probability density function. Normal distribution, N(x). Use of tables of N(x). Log-normal model of share prices. Discrete random walk Relation to normal distribution. Random walk with drift. Volatility and expected growth. Estimation from historic share data. Stochastic Calculus Stochastic differential equation for share price S. Ito's lemma and stochastic differential equation for f(S). Discrete random walk vs. normally distributed step. Link between random walk and diffusion equation. Black-Scholes Model Option pricing. Black-Scholes analysis via risk-free portfolio. Black-Scholes equation. Boundary conditions for call and put options. Solutions C(S,t) and P(S,t) for call and put options. (Stated, derived next section.) Sample solutions. Delta-hedging and risk-free portfolios. Implied volatility. Diffusion Equations Diffusion equation. Delta-function. Similarity solutions of diffusion equation. General solutions for given boundary conditions. Black-Scholes equation as a diffusion equation. Solutions for call and put options. Risk-neutral approach. Black-Scholes equation for an asset paying dividends. Other options. Introduction to American options
Delivery Hours
 Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total Hours/Semester 39 13 98 150

## Assessment

 Sequence Method % of Final Mark 1 Coursework 1 15.00 2 Coursework 2 15.00 3 Final Exam 70.00
 Module Catalogue generated from SITS CUT-OFF: 6/2/2020 12:34:43 AM