Case study: building option pricing models; valuation of European, American option styles

Volatility

• Understanding volatility; the role of volatility in option pricing; volatility as an 'asset class'
• Historic, implied and realised volatility measures
• Volatility estimation: analysis of data samples; sample sizes; weighting sample data
• Volatility surfaces
• Volatility smiles, skews
• Volatility term structure effects
• Volatility properties
• Stochastic volatility
• Mean reversion
• Stochastic volatility models
• Heston stochastic volatility model
• Volatility analysis
• Volatility relative value analysis (implied vs. realised)
• Skew interpretation and analysis
• Volatility trading strategies

Option risks; hedging and risk management of option positions

• First order price risks: delta, vega, theta, rho, phi
• Delta hedging and risk analysis
• Dynamic risk management using delta
• Delta hedging an option portfolio
• Limitations and risks inherent in delta hedging
• PIN risk
• 'Sticky strike' effects
• Expiration effects
• Liquidity effects
• Execution risk (risk vs. agency execution)
• Gamma; 2nd order option price sensitivity
• Interpreting gamma
• Gamma characteristics of in-, at- and out-of-the-money options
• Long and short gamma – risks and opportunity
• Impact of gamma on delta hedge management
• Implied vs. realised volatility exposure
• Maximising profitability from gamma management
• Theta; option price time decay
• Theta as cost of carry
• Inter-relationship between Theta, Gamma
• Vega; implied volatility risk sensitivity
• Rho; Interest rate sensitivity
• Understanding and actively managing inter-relationships between option price sensitivities
• Active management of portfolio delta, gamma and vega risks
• Higher order risks
• Delta time decay (Charm)
• Gamma sensitivity (Speed, Colour)
• Vega (Vanna, Vomma)
• Skew risk
• Risk reversals
• Limitations of option 'Greeks'
• Discontinuities in market price behaviour
• Expiration trading
• Strategies for managing risk when 'Greeks' experience large, discrete changes
• Stress testing and portfolio scenario analysis; identifying potential future risks

Case study: dynamic management of option risks in a single option position/portfolio context; Delta hedging and the analysis of trading p/l over a trading horizon. Exercise will involve managing position gamma in order to attempt to maximise profitability

DAY TWO

Option strategies

• Directional (Delta) and non-directional (volatility/time decay) strategies
• Bullish, bearish directional strategies
• High/low volatility
• Risk/reward (limited vs. unlimited risk strategies)
• Bullish, bearish volatility strategies
• Risk/reward (limited vs. unlimited risk strategies)
• Directional trading and arbitrage strategies
• Put-Call parity
• Conversions and reversals
• Synthetic forwards and options
• Combinations
• Synthetic lending/borrowing
• American options; assignment risk
• Vertical Spreads
• Call and put (Bull and Bear) spreads
• Trading Rationale
• Pricing; impact of skew effects
• Risk characteristics
• Delta hedging
• Gamma; risk reversal
• Skew risk 
• Non-directional (volatility/time decay) trading strategies
• Calendar Spreads
• Rationale
• Volatility term structure (calendar skew) impact
• Sensitivities; volatility/time decay exposure
• Straddles, strangles and butterfly spreads
• Structure and rationale
• Risk characteristics
• Skew effects
• Volatility trading; dynamic management
• Client trading and hedging strategies
• Risk reduction strategies
• Puts, collars
• Put spreads
• Yield enhancement strategies
• Over and under-writing strategies
• Volatility and correlation trading strategies
• Straddles
• Dispersion trading strategies

Case study: structuring option strategies (spreads, collars, butterflies); examination of risk characteristics and position risk management through time

Interest rate options

• Interest rate caps and floors
• Swap options
• Hybrids: collars; corridors
• Pricing and hedging caps and floors
• Interest rate option pricing models
• Risk management
• Delta hedging caps and floors
• Gamma and Vega management; risk bucketing
• Practical applications of interest rate options
• Asset and liability risk management
• Embedded caps and floors; capped FRNs, Minimax FRNs, Reverse FRNs
• European, Bermudan callable and puttable swaps

Case study: corporate interest rate exposure management with options FX options

• Fundamental properties of currency options
• Market conventions, terminology, price quotation basis (base vs. quoted)
• Pricing Vanilla FX options - Garman-Kohlhagen model
• Volatility surfaces for FX options

Equity options

• European and American styles
• Single stock and index options
• Basket (index) options
• Correlation impact on valuation
• Implied vs. realised correlation

Commodity options

• Pricing models for commodities
• Backwardation effects and hedging considerations
• Mean reversion effects

DAY THREE

New generation products

• Volatility and variance swaps
• Mechanics of variance swaps
• Pricing and hedging
• Uses and applications of variance swaps
• Volatility trading
• Dispersion trading

Exotic options

• Exotic option classification
• Pay-off structure
• Motivations and applications of exotic options
• Pricing and valuation issues
• Black-Scholes, analytical models; advantages and shortcomings
• Numerical methods (Binomial, Trinomial lattice models, Monte Carlo simulation)
• Modelling considerations for exotic option payoffs
• Skew effects

Barrier options

• Pricing and valuation issues
• Risk management of barrier option risks; risk reversals
• Application of barrier options in trading and hedging strategies
• Embedded barrier options in equity structured products (e.g. bonus certificates, reverse CBs)

Case study: barrier option hedging strategies: forward plus, knock-in collars, knock-out forwards Average rate (Asian) options

• Mechanics of average rate options
• Pricing and risk management characteristics
• Currency hedging with Asian options Digital (binary) options
• Pricing of digital options
• Risk management of digital options; replication and hedging
• Applications: range accrual notes, contingent premium options

Rainbow (multi-asset) options

• Basket, rainbow, quanto options
• Impact of basket parameters (volatility, correlation) on pricing
• Risk management
• Delta matrices; correlation risks
• Applications - trading strategies; structured products