Derivatives

Programme

Basic concepts of the future value of money and mathematical statistics

• Present and future value, discounting
• Approximating the price change of fixed-coupon bonds with a Taylor series
• Probability density functions.

Workshop: consolidating the basics of mathematical statistics

VaR — value at risk, calculation methods

• The delta-normal method
• The historical simulation method
• The Monte Carlo method
• Practical application of VaR for risk management

Workshop: practising the VaR methodology

Derivative financial instruments

• Main trends in the market for derivative financial instruments and structured products
• General concepts and definitions of the derivatives market
• Valuing forward and futures contracts
• Practical examples of using forward and futures contracts
• Swaps. Definition, valuation. Using swaps for risk management
• Put/call options, intrinsic and extrinsic value of options
• Black-Scholes valuation

Workshop: consolidating the skills of calculating derivative financial instruments

Credit derivatives

• Classification. Asset swaps and total return swaps (TRS). Practical application as credit risk management tools
• Credit default swaps and options
• Credit spread products (forwards, options)
• Structured products
• Collateralised debt obligations (CDO)
• Credit-linked notes (CLN)
• Practical examples of using credit derivatives and structured products

Workshop: consolidating the skills of calculating credit derivatives

The arbitrage problem and hedging strategies

• The hedge ratio
• The perfect hedge
• The minimum variance hedge ratio
• Deriving the minimum variance hedge ratio
• Estimating the minimum variance hedge ratio
• OLS regression
• The optimal number of contracts
• Hedge effectiveness
• Hedging with normally distributed returns (adjusting the beta coefficient)
• Hedging with several futures contracts
• Simple answers to questions about hedging with futures

Workshop: consolidating hedging techniques

Option pricing models

• The Black-Scholes formula for option valuation
• European options on shares paying a known dividend
• European options on shares whose dividend is unknown
• American options on shares paying a known dividend
• Options on stock indices
• Options on futures
• Currency options
• Warrants

Option pricing models (continued)

• The binomial pricing model
• European call options one period before expiry
• European call options more than one period before expiry
• The European put option
• American put and call options
• Limitations of the binomial model's results
• Possible extensions of the binomial model

Workshop: option pricing

Sensitivity analysis of option premiums

• The price of the underlying asset, the delta and gamma coefficients
• Example of delta hedging and delta-gamma hedging strategies
• Time to maturity and θ
• The interest rate and ρ
• Volatility of share returns and vega

Volatility, exotics and option strategies

• Determining volatility from historical data
• Implied volatility and the «volatility smile»
• The path-independent option
• The compound option
• The chooser option
• The digital option
• The exchange option
• Path-dependent options
• Barrier options
• Asian options
• The lookback option
• Pricing exotic options by numerical methods
• Option strategies: spreads, strangles, straddles

Workshop: developing an option strategy