MF1: Information and Finance—from market filtration to derivatives pricing

Lecturer: Dr Dorje Brody (Imperial College)
Term: Autumn 2009
Course home page: TBA
Place: Room 139, Huxley Building, Imperial College, 180 Queen's Gate SW7                  Times: Monday 18:00-21:00                                                                                                                  First class meeting: Monday 12 October 2009.

1. Introduction and overview

1.1 Introduction 1.2 The modelling framework 1.3 Modelling the cash flows 1.4 Modelling the information flow 1.5 Overview of the course

2. Application to credit risk modelling

2.1 Why information-based approach for credit-risk modelling? 2.2 Simple model for defaultable discount bonds 2.3 Defaultable discount bond price processes 2.4 Defaultable discount bond dynamics 2.5 Bond volatility—information and variance swap 2.6 Perspective from the filtering theory 2.7 Digital bonds and binary bonds with partial recovery 2.8 Dynamic consistency and model calibration 2.9 Simulation of bond price processes

3. Pricing and hedging credit derivatives

3.1 Options on credit-risky bonds 3.2 Measure change technique 3.3 Option Greeks 3.4 Bond option price processes 3.5 Arrow-Debreu method and information derivatives

4. Time-change method and barrier options

4.1 Time-change and Brownian bridge 4.2 Time-changed market information 4.3 Discount function under time change 4.4 Pricing credit-risky bond in time-changed setup 4.5 Asset price dynamics 4.6 Bond option valuation in time-changed setup 4.7 Reflection of Brownian paths 4.8 Barrier option pricing

5. Complex credit-linked structures

5.1 Coupon bonds: the X-factor approach 5.2 Credit default swaps 5.3 Baskets of credit-risky bonds 5.4 Homogeneous baskets

6. Single cash flow to market factors: origin of stochastic volatility

6.1 Asset price dynamics in the case of a single cash flow 6.2 European-style call options 6.3 Examples of specific dividend structures 6.4 Market factors and multiple cash flows 6.5 Geometric Brownian motion model 6.6 Dividend growth 6.7 Assets with common factors 6.8 Origin of unhedgeable stochastic volatility

7. Non-Markovian information flow

7.1 Time-dependent information flow 7.2 Changes of measure for Brownian bridges 7.3 Derivation of the conditional density 7.4 Consistency relations 7.5 Expected dividend 7.6 Asset prices and derivative prices 7.7 Existence of the information process 7.8 Multi-factor models with a time-dependent information flow rate

8. Application to reinsurance contracts

8.1 Introduction: reinsurance claims 8.2 Gamma processes and associated martingales 8.3 Gamma bridge processes 8.4 Further properties of gamma bridges 8.5 Valuation of aggregate claims 8.6 Valuation of general reinsurance contracts 8.7 Discrete cash flows 8.8 Option price process 8.9 Example: gamma-distributed cash flow