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MA50297: Discrete time finance

[Page last updated: 09 August 2024]

Academic Year: 2024/25
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 1
Assessment Summary: EXCB 100%
Assessment Detail:
  • Examination (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Learning Outcomes: Compute the prices of options in the one-period Binomial model.
Explain how the principle of arbitrage can be used in determining the prices of derivative contracts.
Identify simple statistical time-series models such as Autoregressive or Moving Average models, and explain how they can be used to model certain financial quantities.
Interpret and analyse discrete time models which arise for a range of financial settings, for example optimal investment, market making or credit risk
Interpret and calculate in simple models of financial investment. Identify different criteria that can be used to motivate investment choices.


Synopsis: This unit will provide you with tools to model important financial topics using discrete time methods. A subsequent unit will pick up many concepts in a continuous-time framework. You will be introduced to key tools from probability and statistics, and apply them to various financial problems. The problems to be covered will include: optimal investment in discrete time models. Pricing and hedging of financial derivatives in discrete time. Modelling of Credit Risk.

Aims: This unit will develop tools to model important financial topics using discrete time methods. A subsequent unit will pick up many concepts in a continuous-time framework. The unit will introduce key tools from probability and statistics, and apply them to various financial problems. The problems to be covered will include: optimal investment in discrete time models. Pricing and hedging of financial derivatives in discrete time. Modelling of Credit Risk.

Skills: Mathematical modelling (T,F,A) Basic financial concepts (T,F,A) Problem Solving (T,F,A)

Content: Introduction to Financial concepts: financial assets, derivatives, hedging, risk. Probability: Stochastic Processes, Martingales. Principles of arbitrage for pricing simple derivatives (e.g. Forward contracts, interest rate swaps). Models of investment in discrete time. Criteria for optimal investment (utility maximisation, Kelly's criterion, mean-variance). Calculation of optimal strategies. Principles of Dynamic Programming. Pricing of derivatives in discrete time binomial model. Arbitrage, hedging, Fundamental Theorem of Asset pricing. Greeks. Simple statistical models for time series data: Autoregressive and Moving Average models. Further examples such as: Using Markov chains for modelling of credit risk in insurance. Discrete time models for market-making, or limit-order book modelling. Hidden Markov models. Insurance loss modelling.

Course availability:

MA50297 is Compulsory on the following courses:

Department of Mathematical Sciences

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
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