Class Notes
These are the lecture notes for the derivatives topics. Each chapter is available in HTML and as a PDF for printing, ends with a set of practice problems, and comes with a deck in the slides.
Introduction
Financial Derivatives Derivatives with linear and nonlinear payoffs, contracts with periodic payments and assets with embedded derivatives, how derivatives complete the market, and who uses them, where they trade, and how they are priced and hedged.
Futures and Forwards
Interest Rates Treasury, LIBOR, OIS, and SOFR rates, compounding frequencies and the conversion between them, continuous compounding, and zero rates and the prices of zero-coupon bonds.
Forward and Futures Markets Forward and futures payoffs, margin and daily settlement, settlement and delivery, open interest, the nearby futures as the spot price of a commodity, hedging the basis, and SOFR futures and the end of LIBOR.
Forward and Futures Prices No-arbitrage forward prices for assets that can be carried, with cash dividends or a dividend yield, index futures and covered interest parity, what changes when the underlying cannot be carried, from non-deliverable forwards to commodity spreads as the price of storage, and futures prices against expected spot prices.
Crypto Futures Bitcoin futures on CME and crypto-native exchanges, why the bitcoin basis is far above the interest rate and arbitrage does not close it, perpetual futures and the funding rate that replaces an expiration date, why nearly identical Treasury bonds trade at different prices, and CME’s Spot-Quoted futures.
Options
Options Markets Calls and puts, their payoffs, moneyness, contract size, volume and open interest, and the split of an option premium into intrinsic and time value.
Options Strategies Covered calls, protective puts, straddles, strangles, and collars, with their payoffs, profits, and break-even prices.
Options Spreads Bull and bear spreads, butterflies, and condors, and what their payoffs reveal about how option prices change with the strike.
Properties of European Options Put-call parity and its links to covered calls, protective puts, and forwards, the bounds on European call and put prices, negative interest rates, and the factors that move option prices.
The Impact of Dividends How cash dividends and a continuous dividend yield change put-call parity and the bounds on European call and put prices.
Option Pricing in Discrete Time
Binomial Pricing The one-period binomial tree, pricing calls, puts, and any derivative by replication, and the same prices from risk-neutral probabilities and state prices.
Multiple Periods Binomial trees with several periods, recombining trees, dynamic replication, calibrating the tree to volatility, a shortcut for European options, and assets paying a dividend yield.
American Options Early exercise and when it pays, the bounds and put-call parity for American options, the factors that move their prices, and pricing an American put on a binomial tree.
Option Pricing in Continuous Time
The Lognormal Distribution The normal distribution and its probabilities and percentiles, the expected exponential of a normal variable, and the density, probabilities, moments, and partial expectations of the lognormal distribution.
Modeling Stock Prices in Continuous-Time From binomial trees to Brownian motion, geometric Brownian motion, Itô’s lemma, and the lognormal distribution, moments, expected return, and growth rate of the stock price.
The Black-Scholes Model Pricing by replication and the Black-Scholes equation, risk-neutral pricing, the call and put formulas and their deltas, vega and implied volatility, and the volatility surface of S&P 500 options.
Options on Assets Paying a Dividend Yield Replication and risk-neutral pricing with a continuous dividend yield, options on stock indices such as the SPX, and options on currencies with the Garman-Kohlhagen model.
Options on Futures Replicating a futures option with futures and bonds, the futures price as a martingale, Black’s model and how it is used for commodities, currencies, and indices, and futures-style options.
The Greeks Delta hedging at discrete times, gamma, theta, and the profit of a delta hedge, the volatility risk premium, transaction costs and deep hedging, vega and the demand for options, rho, and how the Greeks change with maturity.
Exotic Options Packages, binary and gap options, forward start and chooser options, lookback, Asian, and barrier options priced on binomial trees, and compound, exchange, basket, shout, and non-standard American options.