Module Specifications..
Current Academic Year 2023 - 2024
Please note that this information is subject to change.
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Description This postgraduate course covers asset pricing, with emphasis on a rigorous analysis of 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. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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Learning Outcomes 1. Prove the main results in Mathematical Finance 2. Solve portfolio choice problems rigorously 3. Price assets and derivatives with advanced models 4. Design hedging strategies for new financial products 5. Develop customized pricing methods 6. Critically evaluate the assumptions underlying different asset pricing models | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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 |
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Indicative Content and Learning Activities
ArbitrageAssets, 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.HedgingHedging Arbitrage bounds, Replication Bounds, Superhedging, Superreplication Theorem, Market Completeness, Perfect Replication, Redundancy of Assets.OptimalityUtility 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 AnalysisExpected Return and Risk, State Price-Beta Representation, Hansen-Jagannathan Bound, Mean-Variance Frontier, Two-fund SeparationDualityLegendre Transforms and their properties, Duality Method for Verification, Pricing by Marginal Utility. Duality Bounds.Continuous TimeBachelier 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 ModelsInstantaneous returns and covariances. Stochastic exponential. Discount factors in diffusion models and risk premia. Representation of payoffs.Portfolio ChoiceUtility 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 ControlDynamic 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. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||||||||||||||||
Programme or List of Programmes
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