CISI Diploma: Financial Derivatives - Session 2 Outline

Principles of Valuing Forwards & Swaps

• Nature of cash flow analysis
• Representing an FRA in notional cash flows
• Marking-to-market an FRA
• De-compounding the swap into a bond and a FRN
• Equating the value of the fixed and floating legs

Deriving the Discount Curve

• Where do the discount factors come from?
• Recent market developments in the choice of instruments
  • Role of the Credit Support Annex (CSA) and other credit mitigation developments
• Calculating the zero-coupon discount function
  • Deriving discount factors from money market instruments
  • Deriving discount factors from market swap rates: bootstrapping explained
• Problems in deriving the discount function
  • Instrument choice
  • Interpolation methodologies

Marking-to-Market Interest Rate & Currency Swaps

• Identifying the cash flows
• Representing the floating cash flows as notional cash flows
• Extending the principle: pricing a deferred start swap
• Marking-to-market a currency swap
• Pricing an asset swap

Pricing Equity Swaps

• Determining the fair price of an equity swap
• What if market hedge instruments are mis-priced?

General Principles of Valuing Futures

• Valuation principles for futures contracts
  • Cost of carry and carry return
• Forward/forwards versus futures
• Arbitrage bounds on futures
• Applying the principle to equity forwards and futures
• Can arbitrage happen in practice?

Pricing Short-Term Interest Rate Contracts

• Understanding the role of the cash rates on the forward rate
• Deriving the forward/forward bid and offer rates
• Calculating the arbitrage-free futures price channel

Forward FX

• Applying cost of carry/carry return to determining the forward FX rate
• Quoting forward FX rates: the concept of forward points
• Marking-to-market forward FX:
  • Using the cash flow approach
  • Using the hedge approach
• FX swaps explained

Pricing Bond Futures Contracts & the Bond Futures Basis

• Calculating the arbitrage free bond futures price
• Implied repo rate versus the actual repo rate
• Understanding the "basis"
• Determining the CTD and the factors that cause it to change
• What is the "net basis"?
• Calculating the Swapnote© futures EDSP
• Factors affecting the Swapnote© price
  • Determining the "fair" value prior to expiry

Theoretical Option Pricing: Numerical Models Approach

• The importance of correct valuation
• The model inputs
• Approaches to valuation explained:
  • Self-financing, replication approach
  • Probabilistic approach and "risk-neutral" valuation
• The Binomial model explained
  • The first building block: A one-step model for valuing European style options
  • Adding realism: A multi-step model
  • Demonstrating the equivalence between the hedge and probabilistic approaches
  • Deriving the model parameters:
    • Cox, Ross, Rubinstein (CRR) model v the equal probability [Jarrow, Rudd (JR)] model
    • Alternative models: the Leisen-Reimer model
  • Applying the approach to valuing American style put and call options
  • What happens when there is a term structure of interest rates
  • Introducing dividends
  • Interest rate option valuation

Theoretical Option Pricing: Continuous Time Approach

• The Black Scholes option pricing model for European style call options explained
  • Understanding the terms: N(d1) and N(d2)
  • The model written in hedge form and probabilistic form
  • Using the model: deriving an option price
  • Extensions to the standard Black-Scholes model:
    • The put option formula and put-call parity
    • Writing the formula in forward form
    • Incorporating a continuous time dividend yield

Special Cases: Valuing Currency & Interest Rate Options

• Adapting Black-Scholes to valuing currency options: the Garman – Kohlhagen model
  • Understanding the model inputs
  • Identifying the domestic and foreign interest rate
  • Interpreting the output
• Adapting the CRR binomial model to price currency options
• The problem with pricing options on interest rates
• Pricing interest rate options using Black 76
  • Bond options
  • Swaptions, caps & floors
• Using term structure models
  • The Black-Derman-Toy (BDT) model v Hull and White model

Models, the Real World & Volatility

• Identifying the theoretical model assumptions
• Implications for option prices
• Measuring volatility
  • Implied v historic
  • Understanding the volatility smile
  • Understanding the term structure of volatility

Understanding the Risk Sensitivities

• Defining "delta"
  • Using delta
  • Understanding the influence of time and volatility changes on delta
• Curvature risk: understanding gamma
  • How time and volatility affect gamma
• Understanding Vega
• The impact of time on option prices

A Prima on Exotic Options

• Categorising exotic options
• Special profile options
  • Pricing digitals (binary; all-or-nothing) options using a Black-Scholes approach
  • Understanding the digital's Greeks
  • Digitals as call or put spreads
  • Risk management of digitals
• Path dependent options
  • Barrier options explained
  • Understanding the delta and gamma of a down-and-out call and up-and-in call
  • Asian style options
• Correlation based instruments
  • Basket options
    • Determining the volatility input
    • Calculating the correlation sensitivity
  • Exchange one asset for another
    • Determining the volatility input
    • Adapting the Black-Scholes formula
    • Relationship to "Best Of" option