Module: Stochastic Finance (Intermediate)

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-ordinator	Semester 1: Paolo Guasoni Semester 2: Paolo Guasoni Autumn: Paolo Guasoni
Module Teachers	Paolo Guasoni
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

None

Description

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

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Classes
Directed learning	2	Final Exam
Seminars	5	Attendance to Research Seminars
Independent Study	150	Independent 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

Arbitrage
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.

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

Optimality
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

Duality
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 Assessment	0%	Examination Weight	100%

Type	Description	% of total	Assessment Date
Course Work Breakdown

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

None

Programme or List of Programmes

ACM	BSc in Actuarial Mathematics
BSSA	Study Abroad (DCU Business School)
BSSAO	Study Abroad (DCU Business School)
FIM	B.Sc. Financial Mathematics
HMSA	Study Abroad (Humanities & Soc Science)
HMSAO	Study Abroad (Humanities & Soc Science)
IESA	Study Abroad (Institute of Education)
IESAO	Study Abroad (Institute of Education)
SHSA	Study Abroad (Science & Health)
SHSAO	Study Abroad (Science & Health)

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