Derivatives Analysis and Valuation
What the exam tests
Derivatives analysis and valuation covers forwards, futures, options and swaps: fair pricing, payoffs, arbitrage bounds, put-call parity, binomial and Black-Scholes models, and Greeks.
Core rules
- Forward/futures fair price: F = S(1+r)^T for no income; with income yield q, F = S e^{(r−q)T}; with storage and convenience yield, adjust carry.
- Option value = intrinsic value + time value. European put-call parity: C − P = S − K e^{−rT}.
- Black-Scholes assumes lognormal prices, constant volatility, no arbitrage, continuous trading and no early exercise.
- Delta is the change in option price per unit change in underlying; delta-hedging neutralises small moves, not large jumps.
- Swaps are portfolios of forwards; value by discounting expected net cash flows or by comparing fixed and floating legs.
Worked example
S = ₹100, K = ₹100, r = 10%, T = 1 year, call = ₹12. Put-call parity gives P = C − S + K/(1+r)^T = 12 − 100 + 100/1.10 = 12 − 100 + 90.909 = ₹2.909. If the market put trades at ₹3.50, the put is rich: buy the call, sell the put and sell the stock, or execute the reverse arbitrage depending on cash-flow signs. The parity value is the no-arbitrage anchor.
Traps
Applying European parity to American options with early-exercise value; forgetting dividends in index options; mixing continuous and discrete rates; treating delta as the probability of exercise; ignoring counterparty credit and margin in futures.