Kurum-İçi Eğitim Programları
B06. Volatility Modelling and Application
Course Syllabus
Data Analysis: The starting point for a scientific approach to financial modelling
o Equity price data, Returns
o Distributions and moments
o Timescales, Drift and volatility
o Basic parameter estimation and sampling error
Binomial Trees: Towards pricing concepts
o The role of drift and volatility
o Delta hedging and no arbitrage, Real and risk neutral
o Relationship to expectations and simulations
o The continuous-time limit
Black-Scholes: A framework for all that follows
o Simple stochastic calculus: Ito versus Taylor
o Partial differential equations, Intuition behind numerical
methods
Volatility Estimation: Simple statistical methods
o Moving windows
o Mean reverting, Exponentially weighted moving average,
RiskMetrics
o GARCH
o Parameter estimation by maximum likelihood
o Expected future path of volatility, Expected future variance
Discrete Hedging: One of the main pitfalls of the model
o Hedging at finite time intervals, Hedging error
o Demonstration
o Hedging with a view, Volatility adjustment
o Non-normal returns
Transaction Costs: An introduction to nonlinearity
o Leland volatility adjustment
o Demonstration
o Hoggard-Whalley-Wilmott, Non-linear pricing
o Introducing static hedging
How to Hedge
o Which formula to use
o Which delta to use
o Implied versus actual
o Who uses which
Volatility Surfaces and Calibration: Love them or loathe them, they are here to stay
o Time-dependent volatility
o Implied versus local volatility
o Risk-neutral density
o Calculating the local volatility surface
o Dangers associated with the technique
o Scientific evidence
o Examples
o The nature of vega
o Why vega is often misleading
Stochastic Volatility: The obvious step towards a better representation of reality
o Dynamic vega hedging
o Market price of risk
o Named models, Examples, Heston
o Programming
o Why parameters are so unstable, the market's perception of risk
Uncertain Volatility: A better idea
o Volatility ranges, Best and worst cases
o Nonlinearity and static hedging
o Optimization
o Why calibration is unnecessary
Advanced Volatility Analysis: Which model to use
o Model estimation from data
o Volatility of volatility
o Drift of volatility and distributions
o Simulations
o Volatility term structure and error bounds
o Alternative uses of stochastic volatility models
Stochastic Volatility and Mean-variance Pricing: Portfolio theory and option pricing come together
o Dynamic delta hedging for minimizing risk
o Residual risk
o Mean and variance
o Global variance minimization and optimal static hedging
SPREADSHEET AND VBA WORKSHOP 4:
o Monte Carlo simulation for path-dependent contracts
o Finite-difference methods for contracts with embedded decisions
SPREADSHEET WORKSHOP 3:
o Implementation of model estimations methods
o Simulating future scenarios
o Constructing a volatility term structure and associated
error bounds
SPREADSHEET WORKSHOP 2:
o Implementation of the popular models using real data
SPREADSHEET WORKSHOP 1:
o Asset simulations, backing out parameters
o Artificial data and real data
o Uses in pricing and risk management
