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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Stochastic Finance (Intermediate)
Module Code MS426
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Paolo Guasoni
Semester 2: Paolo Guasoni
Autumn: Paolo Guasoni
Module TeachersPaolo Guasoni
NFQ level 8 Credit Rating 7.5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

This undergraduate course covers asset pricing, with emphasis on continuous-time models. Arbitrage, trading strategies, market completeness. Portfolio choice in complete and incomplete markets. Myopic and hedging demand. Derivatives pricing: risk-neutral pricing and risk premia.

Learning Outcomes

1. Use basic models to price assets
2. Apply common hedging techniques
3. Derive heuristic solutions to portfolio choice problems
4. Understand the payoffs of different trading strategies
5. Use risk-neutral methods to price derivative contracts
6. Relate discrete-time models with their continuous-time counterparts

Workload Full-time hours per semester
Type Hours Description
Directed learning2Final Exam
Seminars5Attendance to Research Seminars
Independent Study150Independent work on textbooks and related papers
Total Workload: 193

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Assets, Payoffs, Simple and Gross Returns, Strategies, Self-financing portfolios, Arbitrage, Stochastic Discount Factors, First and Second Fundamental Theorems of Asset Pricing, Law of one price.

Arbitrage bounds, Replication Bounds, Superhedging, Superreplication Theorem, Market Completeness, Perfect Replication, Redundancy of Assets

Utility Functions, Absolute and Relative Risk Aversion, Allais and Ellsberg paradoxes, Savage Representation, Arbitrage and Utility, First-order condition, Investment and Consumption. Logarithmic, Power, and Exponential Utilities.

Mean-Variance Analysis
Expected Return and Risk, State Price-Beta Representation, Hansen-Jagannathan Bound, Mean-Variance Frontier, Two-fund Separation

Legendre Transforms and their properties, Duality Method for Verification, Pricing by Marginal Utility. Duality Bounds.

Continuous Time
Bachelier and Samuelson models. Continuous trading. Doubling strategies. Admissible Strategies. Local Martingales and Supermartingales. No arbitrage and Admissibility. Stochastic Discount Factors and Martingale Measures. Bayes' formula.

Diffusion models
Instantaneous returns and covariances. Stochastic exponential. Discount factors in diffusion models and risk premia. Representation of payoffs.

Portfolio Choice
Utility maximization from terminal wealth and consumption. Solution by Duality in Bachelier and Samuelson models with exponential and power utility. Merton and Markowitz formulas. General solution in complete markets. Duality with consumption.

Stochastic Control
Dynamic programming. Value Function. Hamilton-Jacobi-Bellman equations. Verification. Homogeneity.

Stochastic Investment Opportunities.
Asset Prices and State Variables. Incompleteness. Intertemporal Hedging. Logarithmic and Power Transformations. Long-run limits. Martingale Measures and Risk-Neutral Dynamics. Long-run optimality. Finite-horizon Bounds.

Assessment Breakdown
Continuous Assessment0% Examination Weight100%
Course Work Breakdown
TypeDescription% of totalAssessment Date
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 1
Indicative Reading List

  • Hans Follmer, Alexander Schied: 0, Stochastic finance, 3110183463
  • Darrell Duffie: 2001, Dynamic asset pricing theory, Princeton University Press, Princeton, N.J., 978-0691090221
Other Resources

Programme or List of Programmes
ACMBSc in Actuarial Mathematics
BSSAStudy Abroad (DCU Business School)
BSSAOStudy Abroad (DCU Business School)
FIMB.Sc. Financial Mathematics
HMSAStudy Abroad (Humanities & Soc Science)
HMSAOStudy Abroad (Humanities & Soc Science)
IESAStudy Abroad (Institute of Education)
IESAOStudy Abroad (Institute of Education)
SHSAStudy Abroad (Science & Health)
SHSAOStudy Abroad (Science & Health)

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