CFA Level 2 - Derivatives

Explore the valuation of contingent claims by modeling call and put options under European and American styles, using no-arbitrage methods with binomial and Black-Scholes-Merton models.

Discover the one-period binomial model, up and down stock movements, and how delta hedging and the no-arbitrage principle price calls and puts by replication with shares and bonds.

The lecture presents the expectations approach to option pricing in a one-period binomial model, using risk-neutral probabilities, hedge ratios, and discounting to value call and put options.

Use the two-period binomial model to price call and put options, compute two-period share prices, determine payoffs, and derive risk-neutral probabilities and delta hedge ratios.

Apply the two-period binomial model using a shortcut to price european call options, determine risk-neutral up probability, and use put–call parity to derive put values from the computed call.

This lecture uses a two-period binomial model to price a european put and then extends to an american put, highlighting hedge ratios and early exercise premium.

Explore a two-period binomial model for an American call on stock with dividends, including ex-dividend price adjustment, payoff calculation, early exercise decision, and comparison to European pricing.

Apply the binomial valuation model to price european-style call and put options on one-year interest rates, using spot and exercise rates, 50/50 risk-neutral probability, and a one million notional.

The multiplier binomial model slices a two-year option into 100 time steps, showing how finer periods cause its value to converge to the Black-Scholes model.

Explore the Black-Scholes world where asset prices follow geometric Brownian motion with continuous, normal returns, no jumps, and no market frictions, enabling European option pricing.

Learn to value call and put options with the BSM model by forming a dynamic stock and zero-coupon bond portfolio using d1, d2, and continuous compounding.

Apply the BSM model with carry benefits by discounting the underlying price with the carry yield and adjusting the risk-free rate for calls and puts.

Explore carry benefit in foreign exchange options: the carry equals the foreign risk-free rate, with 135 yen per euro spot, at-the-money strike, using the BSN model for valuation.

Learn how the black option valuation model prices european options on futures by substituting the futures price for the underlying and applying the adjusted black-scholes framework.

Apply the Black model to pricing interest rate options, using forwards such as FRAs and the FRB rate. Explore caplets, caps and floors, and their relation to swaps and parity.

Apply the Black model to swaption valuation, distinguishing pay and receiver options on swaps, their fixed and floating legs, and parity relationships between long/short positions.

Understand how delta measures the change in option price for small stock moves, including call and put deltas, dividend yield effects, and delta hedging to achieve portfolio neutrality.

Use option delta to forecast changes in option prices by multiplying delta by the change in the underlying; this works for small moves but is biased low for larger moves.

Explore gamma, the second derivative of option price with respect to the underlying, showing how it measures curvature, affects delta hedging, and how delta-gamma approximations improve pricing accuracy.

Analyze theta, the rate at which an option's time value decays as calendar time passes toward expiration. Observe how this time decay accelerates as expiration nears, affecting calls and puts.

Vega measures how a small change in volatility affects a portfolio of options, raising call and put values when volatility rises, especially near the money.

Rho measures portfolio value change with shifts in risk-free rate; call rho is positive, put rho negative, and zero rates yield call and put values for at-the-money options via parity.

Derive implied volatility from current option prices via the Black–Scholes model, and use the term structure and volatility smile to compare options and guide trading.