Mathematical Finance in Continuous Time - MAT00097H
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 |
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A | Semester 2 2023-24 |
Module aims
Module gives an introduction to classical methods of asset pricing in continuous time.
Module learning outcomes
At the end of this module, students will be able to:
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Use the main notions of Stochastic Calculus in continuous time.
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Apply the Black-Scholes formula for option pricing.
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Use basic models of interest rates.
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Use basic credit risk models.
Module content
Syllabus
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Stochastic Processes in continuous time. Ito Lemma.
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Stochastic differential equations and martingales.
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Equivalent measures and Girsanov Theorem.
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Black-Scholes model of a stock market.
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Self-financing trading strategies. No-arbitrage principle.
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European derivative securities. Pricing by replication.
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Black-Scholes partial differential equation.
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Black-Scholes pricing formula for European call options.
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Equivalent martingale measure and pricing in the Black-Scholes model.
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The Greek parameters.
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Merton model as an example of a structural model of credit risk
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Further examples of stochastic differential equations and the Ornstein Uhlenbeck process
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Modelling credit risk: reduced form models and intensity based models.
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The two-state model for credit ratings and the Jarrow-Lando-Turnbull model
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Models of the term structure of interest rates, including one-factor general diffusion model, and the Vasicek, Cox-Ingersoll-Ross and Hull-White models
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Pricing some standard interest rate derivatives in the above models
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