Mathematical Finance in Continuous Time - MAT00097H

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Module summary

Module gives an introduction to classical methods of asset pricing in continuous time.

Professional requirements

Counts towards IFoA exemption.

Related modules

Module will run

Occurrence	Teaching period
A	Semester 2 2025-26

Module aims

The module introduces and applies the main mathematical continuous-time tools that are used to value assets that are traded in financial markets, such as bonds, futures and options.

Module learning outcomes

After successful completion of this module, students are able to apply and explain:
• some basic concepts and results of stochastic calculus in continuous time;
• the Black-Scholes formula for option pricing;
• basic models of interest rates;
• basic credit risk models.

Module content

• Stochastic Processes in continuous time.
• Stochastic calculus.
• Black-Scholes model of a stock market.
• Black-Scholes pricing formula for European call options.
• Pricing of credit risk instruments.
• Pricing of fixed-income securities.

Indicative assessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	80
Essay/coursework	20

Special assessment rules

None

Indicative reassessment

Task	% of module mark
Closed/in-person Exam (Centrally scheduled)	80
Essay/coursework	20

Module feedback

Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

Z. Brzezniak, T. Zastawniak, Basic stochastic processes : a course through exercises. Springer

M. Capinski and T. Zastawniak, Mathematics for Finance. An Introduction to Financial Engineering, Springer

M. Capinski and T. Zastawniak, Credit Risk (elect. resource)

D. McInerney and T. Zastawniak, Stochastic Interest rates (elect. resource)

M. Musiela, M. Rutkowski, Martingale Methods in Financial Modelling, Springer.

M. Steele, Stochastic calculus and financial applications, Springer