EQUITY DERIVATIVES:
Advanced Models
Course Outline
This course introduces and applies advanced models for the pricing of equity derivatives. The objective of the workshop is to develop a solid understanding of the current frameworks for pricing equity derivatives and to give participants the mathematical and practical background necessary to apply the various pricing methodologies to the market.
All delegates will receive a copy of Schoutens's book, Lévy Processes in Finance: Pricing Financial Derivatives
Who The Course is For
- Quantitative analysts
- Risk managers
- Fund managers
- Financial engineers
- Researchers
- Credit managers
- Accountants
- Corporate and financial consultants
- Treasury managers
- Portfolio managers
- Venture Capital executives
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Prior Knowledge
Probability theory, basics of stochastic processes, basic concepts of financial products, bionomial tree modelling and the Black-Scholes setting, a good maths background and knowledge of basic maths models, knowledge of basic programming.
This
program is eligible for 24 Continuing Education credit hours from the
CFA Institute. If you are a CFA Institute member, CE credit for your participation
in this program will be automatically recorded in your CE Diary.
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Day One
Equity Models
- Description, construction and analysis of some of the popular advanced mathematical models for the pricing of financial derivatives in an equity setting.
Shortfalls of the Black-Scholes Model
- Problems with the Normal Distribution
- The need for stochastic volatility
- Implied volatility
- Stylised features of financial returns
An Introduction to Lévy Processes
- Definitions
- Lévy-Kinthchin representation
- Properties
- Examples
Jump Models
- Lévy models
- Variance Gamma model
- Risk-neutral modelling - equivalent martingale measures
- Extensions of the VG model
Workshop: PC-based implementation of the VG model (Matlab)
Day Two
Stochastic Volatility
- Stylised features of volatility
- Heston model
- Heston with jumps
- Lévy models with stochastic volatility
Pricing European Options using Characteristic Functions
- Characteristic functions
- Carr-Madan formula for European options
- FFT techniques
- Characteristic function technique for other payoffs
Calibration
- Basic concepts of calibration
- Search algorithm
- Choosing starting values
- Examples
Workshop: PC-based implementation of FFT pricing and calibration algorithm (Matlab)
Day Three
Monte Carlo Simulations: Theory
- Standard sampling of Heston paths
- Standard sampling VG paths
- Advanced sampling methods: Milstein's scheme
- Sampling Lévy processes with stochastic volatility paths
Exotic Option Pricing
- Pricing European options using Monte Carlo simulation
Workshop: PC-based implementation of Monte Carlo Simulations and Exotic Option pricing (Matlab): Pricing of Barriers, Cliquets, reverse Cliquets, Asians
At the end of the course delegates should have running on their machines (Matlab):
- FFT pricer for vanillas for VG and/or Heston
- Calibration algorithm for VG and/or Heston
- Monte Carlo Pricers for VG and/or Heston for a range of exotic options
