2021/2022 KANCMECV1250U Mathematical Finance 2: Continuous Time Finance
English Title  
Mathematical Finance 2: Continuous Time Finance 
Course information 

Language  English 
Course ECTS  7.5 ECTS 
Type  Elective 
Level  Full Degree Master 
Duration  One Quarter 
Start time of the course  Second Quarter 
Timetable  Course schedule will be posted at calendar.cbs.dk 
Max. participants  80 
Study board 
Study Board for HA/cand.merc. i erhvervsøkonomi og matematik,
MSc

Course coordinator  


Main academic disciplines  


Teaching methods  


Last updated on 21/12/2021 
Relevant links 
Learning objectives  
By the end of the course, students will be
confident with the probabilistic techniques required to understand
the most widely used models in finance, from the BlackScholes
model to stochastic volatility models and affine term structure
models.
To achieve the grade 12, students should meet the following learning objectives with no or only minor mistakes or errors:


Course prerequisites  
Prerequisites at the level of HA(mat.). It is an
advantage to have followed Matematisk Finansiering 1, but it is not
a prerequisite.
The course includes a voluntary Introductory Python Workshop with prerecorded video lectures and exercises. 

Examination  


Course content, structure and pedagogical approach  
Over the last few years, financial analysts have used more and more sophisticated mathematical concepts to describe the behaviour of markets or to derive computing methods. This course provides an intro duction to stochastic calculus and shows how it can be applied to the pricing and hedging of financial contracts, such as equity options and interest rate derivatives. The goal is to make students confident with the probabilistic techniques required to understand the most widely used financial models. The course is mainly suitable for students who would like to become quantitative analysts, asset managers, traders, risk managers, structurers, or who are simply generally interested in financial markets and want to gain the technical skills needed to understand and model their behaviour.
The course is split into the following sections:
Discrete Time Finance Revision  Binomial model  Derivative pricing and hedging  Riskneutral measure  Selffinancing strategies  Absence of arbitrage
Introduction to Stochastic Processes and Stochastic Calculus  Continuous time limits  Brownian motion  Ito’s lemma  Change of probability  Simulation  FeynmanKac Theorem
Pricing and Hedging in Continuous Time  Arbitrage pricing and hedging theory  BlackScholesMerton (BSM) equation  Relatives of BSM  Hedging in the BSM model  Affine term structure models
Beyond BSM (TIME PERMITTING)  The implied volatility surface  Stochastic volatility models  The rise of volatility products and the VIX  Option trading strategies


Description of the teaching methods  
The pedagogical approach of the course is applied
in nature. That means will we will abstract from much of the (deep)
technical rigour underlying continuous time theory and instead
concentrate on applications and problem solving. In other words, we
will be ‘learningbydoing’, which will require investing time in
problem sets and getting our hands dirty with data and coding
exercises:
 Real life trading resource: At the beginning of the course you will all receive an invitation for a realtime trading account within the student lab at Interactive Brokers: www.interactivebrokers.co.uk Your accounts will be charged with USD 1,000,000 in paper trading equity. Account equity will fluctuate as if trades were executed in the real market and you can trade stocks, options, futures, bonds and currencies, and credit default swaps. We will use this as a resource for real world pricing, calibration exercises, risk management and speculative (trading) exercises  Coding: The financial industry is increasingly adopting Python and recent recruitment trends suggest that Python will soon become the defacto programming language for quantitative analysis in finance. The benefits of Python with respect to its competitors is are that it is (a) easy to learn, read and write; (b) is a highlevel programming language; (c) fast and easily scalable; (d) has vast library support; (e) is free and open source. This course includes an introductory set of lectures in Python for financial analysis. We will begin with the basics such as installation, an overview of the programming environment and tips on how to code ‘Pythonically’. You will learn the fundamentals of Python variables, loops, functions, data structures and learn powerful methods to efficiently practice data science and visualise data. The course will be prerecorded online allowing students to progress at their own pace and will be accompanied by a series of exercises designed to implement techniques learned in the lectures. 

Feedback during the teaching period  
Each lecture will consist of a set of slides
Exercise sets will be regularly distributed and selected problems solved in class Solutions will be provided Dropin office hours will be held weekly There will be a voluntary midterm assignment that will test students on course material. Feedback will be given. 

Student workload  


Further Information  
The course can be taken by any interested student


Expected literature  
Main course textbooks are:
``Options, Futures and Other Derivatives'' (8th edition or later), John Hull ``Analytical Finance: Volume I: The Mathematics of Equity Derivatives, Markets, Risk Valuation'' Jan Röman (2017) (The books are available online through CBS library)
Hand outs from selected chapters of:
``Fixed Income Securities: Valuation, Risk, and Risk Management'', Pietro Veronesi (2010) ``A Course in Derivative Securities'', Kerry Back (2005) ``Arbitrage Theory in Continuous Time'', Björk (2004) ``Stochastic Calculus for Finance: Continuoustime Models'' , Shreve
