Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH403
Module Title: Introduction to Pricing and Hedging
Module Level: Level 4
Module Credits: 5.00
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A

 Aims To enhance students with a powerful mathematical machinery in order to apply the risk-neutral pricing of various financial instruments via the fundamentals theorems of asset pricing
 Learning outcomes By the end of this module students should be able to understand and analyze the following:A. 1.The binomial option pricing model and arbitrage pricing in discrete, multi-period modelsB. 2. Probability spaces, filtrations, conditional probabilities and expectations.C. 3. The main results and basic applications of continuous time stochastic processes: Brownian motion, martingales.D. 4. Ito’s calculus, in particular, the stochastic Ito integral and Ito's formula.E. 5. Define and apply various concepts related to continuous time dynamic portfolio strategies using the Martingale Representation Theorem, apply the concept of an arbitrage free market and a complete market. State and prove the first Fundamental Theorem of Asset Pricing I and II.F. 6. Be able to use measure transformations to price European options using expectations of martingale measures, and apply the risk-neutral formula in pricing options.G. 7) The mathematical analysis of the American put option.
 Method of teaching and learning Lectures and homework exercises
 Syllabus 1.The Binomial No-Arbitrage Pricing Model 2. Measure Theory and Probability Theory 3. State Prices 4. Brownian Motion, Stochastic Integration, and Ito’s lemma 5. Derivation and Solution of the Black-Scholes equation 6. Risk-neutral Pricing and Girsanov Theorem 7. American Derivative Securities
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 Cw (Assignments) 25.00 2 Class Test 15.00 3 Final Exam 60.00
 Module Catalogue generated from SITS CUT-OFF: 12/10/2019 12:05:24 AM