Advanced Options Trading

Students of derivatives pricing initially learn Black-Scholes theory in which the volatility of an asset is assumed constant. However, when coming to work in the finance industry, the very first thing that any derivatives trading professional must learn is that this assumption is wrong, and there is an implied volatility smile. In this course we will learn what the Smile is and why it exists and learn how to value vanilla and exotic derivative contracts properly with smile.

The course will appeal to all those wishing to gain a deeper understanding of derivatives pricing including traders, structurers, quantitative analysts, risk managers and product control professionals. Participants benefitting most from the course will have a numerate background including some calculus, and some previous study of Black-Scholes pricing. The course material is applicable to equities, foreign exchange and commodities derivatives trading, and also to some interest rate instruments.

Duration: Two days (9.00am to 5.00pm)
Location: Apex City of London Hotel – London, UK
Trainer: Paul Darbyshire
Course fee: £2195 + VAT – Register online

Course Outline


+ Why derivatives?
+ Principle of no arbitrage
+ Forward contracts
+ Vanilla options

Stochastic Calculus and Brownian Motion

+ Brownian motion
+ Stochastic model for stock price evolution
+ Ito's rule
+ Log-normal stock price evolution

Martingale pricing and Black-Scholes Theory

+ Tradeable assets and numeraires
+ Changing the measure made easy
+ How Martingales help us
+ The beauty of Black-Scholes

Dynamic Hedging and Replication

+ Delta hedging
+ The Greeks
+ Gamma, vega and time decay

Exotic Options in Black-Scholes

+ European options
+ Asian options
+ First generation exotics / continuous barrier options

The Smile

+ Why we have a volatility smile
+ Modelling the smile
+ Valuing European options with volatility smile

Local Volatility

+ Why local volatility?
+ A forward PDE for probabilities…
+ Dupire's formula
+ Local volatility in practice

Stochastic Volatility

+ Why stochastic volatility?
+ Properties of stochastic volatility models
+ Famous stochastic volatility models: pros and cons
+ Practical calibration

Numerical Techniques (PDE and Monte Carlo)

+ Introduction to Monte Carlo
+ Variance reduction
+ Introduction to numerical PDE solving
+ Stable and unstable schemes

Local Stochastic Volatility

+ Gyongy's jewel of smile pricing theory
+ Sticky strike and sticky delta dynamics
+ Local stochastic volatility and forward induction
+ How to choose a good LSV model

Risk Managing
+ How to risk manage derivatives
+ What makes a good model
+ Good contracts and bad contracts
+ What we have learned about trading, risk management and derivative valuation

Advanced Topics
+ Volatility Swaps, Variance Swaps and Forward Volatility Agreements
+ Multi-asset

Summaries and Key Points