DERIVATIVES
This course provides an introduction to derivatives, with particular attention given to exchange-traded futures and options on stocks, stock indexes, currencies and underlying futures. Both the standard binomial and Black-Scholes option pricing models are developed. Attention is paid to the estimation of volatility from past price changes as well as the inference of volatility from option prices. Many of these concepts are illustrated by an extended real life portfolio insurance replication example. Time permitting, the course continues by showing how to modify binomial and Black-Scholes models to handle over-the-counter exotic options and ends with a discussion of new research on implied binomial trees.
1. Introduction
1.1 An Example
1.2 Underlying Assets
1.3 Types of Derivatives
1.4 Derivative Markets
2. Forwards, Futures and Swaps
2.1 Asset and Cash
2.2 Forwards and Futures
2.3 Specific Forwards and Futures
2.4 Swaps
3. Introduction to Options
3.1 Basic Option Positions
3.2 Combined Option Positions
3.3 Option Valuation
3.4 Option Dynamic Replication
4. Binomial Option Pricing Model
4.1 Introduction
4.2 Single-Period Model
4.3 Multi-Period Model
4.4 Hedging Parameters, Options on Futures and Currency Options
5. Black-Scholes Formula
5.1 Derivations and Interpretation
5.2 Hedging Parameters for Single Options and Portfolios
5.3 Options on Futures and Currency Options
5.4 Generalizations and Assumptions
6. Volatility
6.1 Historical Volatility
6.2 Implied Volatility
7. Dynamic Strategies
7.1 Dynamic Asset Allocation
7.2 Portfolio Insurance
7.3 Portfolio Insurance Simulation
8. Exotic Options
2.1 Survey
2.2 Packages
2.3 Forward Starts
2.4 Compounds
2.5 Lock-Ins
2.6 Barriers
2.7 Binaries
2.8 Lookbacks
2.9 Asians
2.10 Exchange Options
2.11 Currency-Translated Options
2.12 Rainbow Options
9. Implied Binomial Trees
5.1 Recovering Implied Risk-Neutral Probabilities
5.2 Recovering Implied Risk-Neutral Stochastic Processes
5.3 Applications to Option Pricing and Hedging
Texts:
Mark Rubinstein: Derivatives: A PowerPoint Picture Book, Volume I
Reading:
Mark Rubinstein and Eric Reiner: Exotic Options
Mark Rubinstein: "Implied Binomial Trees" (Journal of Finance, July 1994)
Computer Programs:
Mark Rubinstein and Gerard Gennotte: Futures and Options Trading Simulator
Suggested Additional Readings:
John Cox and Mark Rubinstein: Option Markets (Prentice Hall 1985)
John Hull, Options, Futures, and Other Derivative Securities, 3rd Edition (Prentice-Hall 1997)
The course will be relatively quantitative. Students will be expected not only to reproduce mathematical proofs of important formulas during the final examination, but also to apply or generalize these formulas creatively in unfamiliar situations. The course features an extensive computer exercise which simulates intra-day trading in S&P500 index futures and options as it actually occurred during a six month period on the floors of the Chicago Mercantile Exchange and the Chicago Board Options Exchange.
Course Requirements
(1) written exercises (50%)
(2) final examination (50%)
The written exercises are to be done in groups of two students each. The final examination will be closed book, but a calculator is allowed.