Lecture 13

Course Overview and Revision

Lecture 1

• Basic definitions of:
  • Futures and forwards.
  • Options.
  • Swaps, including interest rate, currency and credit default.
• Differences between futures and forwards.
• Basic payoff diagrams of futures/forwards and options.
• Central, foundational, fundamental building block concepts on which all of financial theory and practice are built:
  • Law of finance and present value (later became risk-neutral pricing).
  • No arbitrage and the law of one price.

• forwards are OTC
• futures have a precise mechanism
• Need to know basic definitions and characteristics
• profit/payoff diagrams, particularly in options
  • include/adjust for the premium
• Assume a risk neutral probability distribution
  • No arbitrage argument
  • LOOP - two portfolios (if one in the future) should maintain the same price

Lec 2-3 Futures & forwards

• Definitions, differences and payoff diagrams of futures and forwards.
• Margin mechanism and leverage eff ect for futures.
• How to calculate the value of a futures/forward contract.
• The following for the main classes of futures and forwards in terms of the underlying asset, namely commodities, equities, currencies and interest rates (FRA and BAB futures):
  • Main contracts and their specifications.
  • Perfect hedging examples.
  • Basic examples of speculating on the price of the underlying asset.
• Contract pricing via the cost of carry approach.
• Basis risk and optimal hedging.

• Leverage effect
• Calculate the value of a futures contract at a particular time
  • always have 0 value upfront, as the price change, your position may move in/out of your favour
• Contract specifications - remember to look for the multiplier
  • Contract multiplier will be given
• futures and forward pricing, definitions
  • optimal hedging examples
  • Little quantitative calculations

Lec 4-8 Options

• Definitions and concepts, including parties (taker, writer), vanilla types (puts & calls, European & American), asymmetric payoffs.
• Moneyness (ITM, ATM, OTM).
• Payoff s vs profits (including the premium).
• Main contracts and markets, contract specifications.
• Pricing bounds and put-call-parity.
• American call premium = European call premium when no dividends.
• Time value and intrinsic value.

• Quite a decent proportion of the final exam on options
• Taker, writer, buyer, seller
  • Basic types, American puts and calls
• Have a lot of quick little conceptual questions
• Specifications of the contracts will be given
• Pricing bounds - little calculation questions
  • most are logical/common sense
• Put/call parity formula (derive through an arbitrage argument, REMEMBER IT)
  • Pricing bounds - premiums should be the same

• European option premiums/prices via the Black-Scholes model:
  • On non-dividend paying assets.
  • For dividend/income paying assets.
  • For currencies (simply viewed as dividend paying assets).
• Black-Scholes assumption of geometric Brownian motion and consequent log-normal distribution of the underlying asset’s price, or normal distribution of the asset’s returns.
• Simulating geometric Brownian motion in preparation for the Monte Carlo approach to derivative security pricing.
• Heuristic (non-rigorous) discussion of risk-neutral pricing.
• Heuristic (hand-waving) interpretation of the factors affecting option prices, and quantification of this via the Black-Scholes model Greeks.

• know what each of the parameters mean
• Work out the Z value from the table
• distributions of the underlying assets returns
  • prices are log-normally distributed
  • Assumptions of the distributions of the returns in the black scholes model
    • Are they normally distribution?
    • Left skewness, fat tails etc.
• Geometric Brownian motion
  • Might simulate some paths
  • might give us data of asset price paths, calculate price paths in an exam
  • What is the price of an ATM call/put option e.g.
  • European arithmetic average/final price
• Haven't been given call/put options for lookback,
  • Maybe one or two of the list in the example tutorial

The greeks

• If market volatility goes up e.g., simple questions like that
• Not the complicated ones, might ask to be calculated.

• Using delta ∆ and gamma Γ to predict small changes in option prices due to small changes in the price of the underlying asset (in preparation for delta and delta-gamma hedging).
• More detailed discussion of theta θ and associated concept of time decay, and how it relates to moneyness.
• Basic ideas and examples of static delta hedging, static delta-gamma hedging, and dynamic delta hedging.
• Implied volatility and the volatility smile and term structure, and related VIX index enabling volatility to be directly traded.
• Trading strategies and their payoff and profit/loss diagrams.

• Delta/gamma hedging questions
• not realistic to ask questions on dynamic delta hedging
• Basic questions may be asked
• Implied volatility
  • volatility smile - what does it mean? VIX index

Trading strategies

• on a bull spread e.g., what is the payoff?
• Simple stuff around the basics, basic strategies
• Know what a bear spread, etc

• Binomial and Monte Carlo numerical option pricing methods:
  • The need for numerical methods:
  • Price more complex derivative securities.
  • More complex pricing methods than the Black-Scholes model, in particular because returns are not normally distributed.
• 1-period binomial model for European option price and delta.
• Multi-period binomial model for European option price and delta.
• More rigorous introduction of risk-neutral pricing via binomial model.
• Monte Carlo pricing of European options.
  • Simple method that simulates only final asset price.
  • More general method that simulates entire asset price paths in preparation for Monte Carlo pricing of path dependent options.

• representative in the practise exam
  • All the i questions
  • Will be given the values in the tree - will not be asked to build one
  • Calculate their delta's
  • choosers option IMPORTANT (given a tree)
• Binomial risk-neutral probability
  • work through the tree, use the risk-neutral approach to calculate the binomial prices in the tree
• chooser options and other options with the binomial model
• five asset price paths with a few dates - MAKE SURE YOU CAN DO THIS
  • Will be given the tree or the asset price paths

Lec 9 CDS

• Basic definitions and concepts for credit default swaps.
• More precise description of mechanics, including notions of:
• Analogy with insurance contracts.
• Parties: protection buyer and seller.
• Reference entity, assets and events.
• Payout, including physical vs cash delivery.
• Recovery rate and loss given default.
• CDS coupon or spread or premium.
• Single name vs multi name, basket, CDS indices.
• Idea that CDS spreads reflect credit risk perceptions, and relation between breakeven CDS spread and reference entity’s risk premium.
• Survival and default probabilities.

• CDS calculations
  • Table with dates, given survival prob, and default prob
    • Breakeven CDS spread
    • Upfront exchange of money
• CDS spread increases
  • Speculate in credit risk perceptions
  • conceptual understanding of CDS - be prepared and understand them

• CDS pricing:
  • Calculating the breakeven CDS spread.
  • Or calculating the upfront cashflow given a fi xed CDS spread.
• Speculating and hedging with CDS.
• Idea that CDS opened up credit risk as “just another” asset class that can be directly traded, like VIX indices did for volatility.

• Numerical options, credit rate swaps and credit default swaps

Lec 10 Interest rate swaps

• Floating rate notes (FRN) definition, concepts and pricing in preparation for fixed-for-floating interest rate swap pricing.
• Fixed-for-floating interest rate swap definitions and concepts.
• Calculating the net cashflows on each coupon or interest date.
• The idea that a position in a fixed-for-floating interest rate swap can be replicated via positions in a FRN and a fixed coupon bond.
• Interest rate swap pricing: calculating the fi xed rate.
• Hedging and speculating with interest rate swaps.

• interest rate swaps question - representative of what is in the final exam

Lec 12 VaR and ES

• Basic concepts relating to risk, including:
  • Types: market, default, liquidity, operational.
  • Portfolio expected return and standard deviation (volatility).
• Concepts related to the normal distribution in preparation for calculating value at risk (VaR) and expected shortfall (ES).
• The need for simple, single measures of market risk like VaR and ES.
• VaR and ES definitions, basic concepts, and differences.
• Potential shortcoming of VaR and consequent need for ES.
• Calculating VaR and ES via 2 methods:
  • Parametric approach assuming normally distributed returns.
  • Nonparametric approach directly using historical data.
• Parametric portfolio VaR, worst case VaR, diversification benefits.

• What is risk, calculate the portfolio
• Worst case VAR, benefits of diversification
• Proficient of normal distribution
• VaR
• Know how to use normal distribution
• Why do we need VaR
  • simple measures of risk
  • Basic definitions and what they are
• expected definition of VaR and expected shortfall?

Parametric and non-parametric

• Calculate a parametric approach for a portfolio
• non-parametric is not possible
• no VaR formulas - need to remember these
• confidence interval to the left of it
• no portfolio VaR formula