Professor Ser-Huang Poon

Continuous Time Finance

This module covers a number of key finance theories that are important building blocks for theoretical and empirical studies in finance. It covers principally Merton’s collection of continuous-time work and studies how the continuous-time method can be applied in consumption-portfolio decisions, two-fund separation theorem, option pricing and capital structure.

Main text:
Merton, Robert C. (1990) Continuous-Time Finance, Book, Basil Blackwell. (M)

Other reference texts:
Cochrane John H. (2005) Asset Pricing, (eBook) Princeton University Press. (C)
Duffie Darrell (2001) Dynamic Asset Pricing Theory, 3rd. Ed., Book, Princeton University Press. (D)
Ingersoll J.E. (1987) Theory of Financial Decision Making, Rowman & Littlefield. (I)

Lecture topics:

1. Continuous Method in Finance

   Continuous trading and discontinuity, instantaneous variance, asymptotic order, instantaneous returns, rare events.
   
   Readings: M Ch3, I "Mathematical Introduction"
   Lecture notes: MCh3
   Exercises: MCh3_Ex
   

2. Single Period Portfolio Selection

   Risk aversion, feasible portfolio, efficient portfolio, Rothchild-Stiglitz risk measure, Merton increasing risk, optimal portfolio.
   
   Readings: M Ch2 (pp.16-32), I Ch12 16, D Ch1-2
   Lecture notes: MCh2a
   Exercises: MCh2a_Ex
   

3. Capital Market Theory

   Spanning, separation, mutual fund theories, CAPM, Capital Structure and MM theories.
   
   Readings: M Ch2 (pp.33-55), I Ch12 16, D Ch1-2
   Lecture notes: MCh2b
   Exercises: MCh2b_Ex
   

4. Intertemporal portfolio selection

   The budget equation, two-asset case, bequest, Bellman equation, infinite time horizon, constant relative risk aversion, optimal decision rule, constant absolute risk aversion.
   
   Readings: M Ch4, I Ch13 15
   Lecture notes: MCh4
   Exercises: MCh4_Ex (Nov26)

5. Optimum consumption and portfolio rules - continuous time analogue to Tobin-Markowitz mean-variance analysis

   Asset dynamics and the budget equations, the equation of optimality, lognormal prices, separation (or mutual fund) theorem, HARA utility and optimal rules.
   
   Readings: M Ch5, I Ch13 15
   Lecture notes: MCh5
   Exercises: MCh5_Ex
   
   
   

6. Option pricing with discontinuity

   Jump, Poisson equivalent, option price process, hedging strategies, option pricing formula.
   
   Readings: M Ch7-9, I Ch14-16
   Lecture notes: MCh9
   Exercises: MCh9_Ex
   
   

7. Contingent claim analysis and the theory of capital structure

   Partial equilibrium one-period model, pricing kernel, debt vs. equity, general equilibrium, pricing defaultable bond.
   
   Readings: M Ch11-12, I Ch19
   Lecture notes: MCh11
   Exercises: MCh11_Ex