Derivatives and risk management
This domain tests pricing by no-arbitrage, payoff construction and hedge design. Questions typically combine a payoff diagram with a cost-of-carry or Greek calculation.
Core rules
- Forward price with no income: F = S0(1 + r)^T. With income or dividends, subtract the future value of the income; with storage cost, add it.
- Call payoff at expiry = max(ST − K, 0). Premium is paid upfront, so profit = payoff − premium.
- Delta is the hedge ratio; a delta-neutral position must be rebalanced because gamma changes delta as the underlying moves.
- Put-call parity for European options on a non-dividend stock: C − P = S0 − K/(1 + r)^T.
Worked example
Spot is 100, the one-year risk-free rate is 5% and the asset pays no income. F = 100 × 1.05 = 105.00. A one-year forward struck at 103 is worth (105 − 103)/1.05 = 1.90 to the long at initiation. Reasoning: the payoff arrives in one year, so it is discounted; comparing 105 with 103 without discounting gives 2.00 and overstates value.
Traps that cost marks
- Adding dividends instead of subtracting their future value from the forward price.
- Confusing option payoff with profit; the premium is sunk at expiry.
- Assuming a static delta hedge stays neutral after the underlying moves.
- Forgetting that American calls on dividend-paying stocks may be exercised early.