Futures and Options - Pricing Workshop

• Pricing Futures Using Cost-of-Carry
• Cheapest-to-Deliver (CTD) Analysis
• Black-Scholes Analysis
• Binomial Models
• Pricing American Options
• Monte Carlo Simulation
• Pricing "Path Dependent" Options

The objective of this workshop is to give the participants a thorough understanding of and hands-on, practical experience with the valuation of futures and options. First, we explain how futures are priced, using the "basic" Cost-of-Carry model as well as more advanced versions of this model that take into account the role of the delivery option, margin payments and other special features. We also demonstrate in detail how the "Cheapest-to-Deliver" (CTD) bond for delivery against bond futures can be properly identified, and, using arbitrage arguments, we explain the links between the delivery option, volatility and the "basis". We then look at a number of models and techniques for pricing options. We start with the basic Black-Scholes model, but participants will also work with derivations of this model, including the Black 76 model for options on forwards, the Garman-Kohlhagen model for currency options, and the Margrabe model for exchange options. In each case, we show how the fair option value, the "Greeks", and the implied volatility are calculated. Further, we present, explain and demonstrate some numerical option pricing models, including the Cox-Ross-Rubinstein model for valuing American options and the BDT model for valuing interest rate options. Finally, we explain and demonstrate a Monte Carlo simulation approach to valuing more complex options structures, including path-dependent structures such as Barrier, Asian and Lookbacks.

 

Day One

09.00 - 09.15 Welcome and Introduction

09.15 - 10.15 Pricing Futures

• Brief Review of the Cost-of-Carry Model
• Cheapest-to-Deliver (CTD) Analysis
• Workshop: Identifying the CTD Bond
• Sensitivity Analysis

10.30 - 12.00 Analytical Option Pricing

• The Principle of Risk Neutral Valuation
• Derivation of the Black-Scholes Model
• Other Analytical Models
  • Black 76
  • Garman-Kohlhagen
  • Margrabe
• Option Sensitivities
• Workshop: Pricing and sensitivity analysis of selected stock, bond and currency options

12.00 - 13.00 Lunch

13.00 - 16.00 Numerical Option Pricing

• Binomial Models for Stock Options
  • The Cox-Ross-Rubinstein Model
  • Pricing American Stock Options
  • Handling Dividend Payments
  • Workshop: Setting up a CRR tree and valuing American Stock Options
• Models for Interest Rate Options
  • Equilibrium and No-arbitrage models
  • Valuing selected interest rate options
  • Workshop: Pricing bond options using the BDT model
• Monte Carlo Simulation
  • Random number generation
  • Setting up and simulating stochastic differential equations
  • Pricing "Path Dependent" Options
  • Workshop: Using simplified MC approach to valuing path-dependent options

16.00 - 16.15 Evaluation and Termination of the Seminar