MA32068: Probability and finance
[Page last updated: 22 May 2025]
| Academic Year: | 2025/26 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 5 [equivalent to 10 CATS credits] |
| Notional Study Hours: | 100 |
| Level: | Honours (FHEQ level 6) |
| Period: |
- Semester 2
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| Assessment Summary: | EXCB 100% |
| Assessment Detail: |
- Closed-book written examination (EXCB 100%)
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| Supplementary Assessment: |
- Like-for-like reassessment (where allowed by programme regulations)
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| Requisites: |
Before or while taking this module you must take MA32071 OR take MA30125
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| Learning Outcomes: |
On completing the unit, you will be able to:
- Compute the prices of options in the one-period and many-period Binomial model;
- Explain how the principle of arbitrage can be used in determining the prices of derivative contracts;
- Define a Brownian motion, and determine basic properties of Brownian motion;
- Apply the Black-Scholes formula to find the price of a European Call option.
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| Synopsis: | You will advance your mathematical modelling skills in probability and learn how to apply them in finance. You will learn about different ways of modelling the evolution of asset prices. You will perform calculations to compute certain quantities relating to the underlying stochastic processes and explore how these quantities can be important in pricing financial derivatives.
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| Content: | Discrete time: trading portfolio, Binomial model, arbitrage, derivative pricing using arbitrage. Radon-Nikodym derivative, change of measure, Fundamental Theorem of Asset pricing.
Brownian motion: definition, basic properties.
Sketch introduction to Stochastic Integration and stochastic differential equations. Ito's Lemma, Girsanov's Theorem.
Black-Scholes model: Geometric Brownian motion as a model for asset prices, risk-neutral measure, European call price formula, Fundamental Theorem of Asset pricing.
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| Course availability: |
MA32068 is Optional on the following courses:
Department of Computer Science
- USCM-AFB32 : BSc(Hons) Computer Science and Mathematics (Year 3)
- USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
- USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
Department of Economics
- UHES-AFB12 : BSc(Hons) Economics and Mathematics (Year 3)
- UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
- UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
- UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
- USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
- USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
- USMA-AFB30 : BSc(Hons) Mathematics (Year 3)
- USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
- USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
- USMA-AFB32 : BSc(Hons) Mathematics and Statistics (Year 3)
- USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
- USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
- USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 3)
- USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 4)
- USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 4)
- USMA-AFM30 : MMath(Hons) Mathematics (Year 3)
- USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
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Notes: - This unit catalogue is applicable for the 2025/26 academic year only. Students continuing their studies into 2026/27 and beyond should not assume that this unit will be available in future years in the format displayed here for 2025/26.
- 好色tv 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.
- Find out more about these and other important University terms and conditions here.
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