Options Strategies L2

Section: Options Strategies — Level 2 Estimated study time: 60 minutes Content: Options pricing and strategies at CFA Level 2 focus on the Black-Scholes-Merton (BSM) model, put-call parity, the Greeks, and the construction and analysis of options strategies in vignette scenarios. The BSM model provides a closed-form solution for European option prices: Call = S_0*N(d1) - X*e^(-rT)*N(d2); Put = X*e^(-rT)*N(-d2) - S_0*N(-d1), where d1 = [ln(S/X) + (r + sigma^2/2)*T] / (sigma*sqrt(T)) and d2 = d1 - sigma*sqrt(T). N(.) is the cumulative standard normal distribution. The five inputs to BSM are: S (underlying price), X (strike price), r (risk-free rate), T (time to expiration), and sigma (volatility). Notably, the expected return of the underlying asset does not appear in the BSM formula — options can be priced by constructing a risk-free hedge, eliminating the need for a risk premium. Put-call parity is a no-arbitrage relationship between European calls, puts, the underlying stock, and a risk-free bond: C + X*e^(-rT) = P + S_0, or equivalently P - C = X*e^(-rT) - S_0. This relationship holds because both sides represent portfolios with identical payoffs at expiration. A protective put (P + S_0) has the same payoff as a fiduciary call (C + X*e^(-rT)) — the portfolio consisting of a call plus an investment of the present value of the strike. Violations of put-call parity create arbitrage opportunities. At Level 2, put-call parity is used to derive the price of one option type given the other, and to construct equivalent positions synthetically. The Greeks measure the sensitivity of option prices to changes in underlying variables. Delta (Δ) = dC/dS, the sensitivity of the option price to changes in the underlying price.…