Derivatives and Risk Management
What you must know
Option payoffs and classic strategies (covered call, protective put, collar, straddle, strangle, bull and bear spreads), put-call parity, the Greeks, binomial and Black-Scholes assumptions, delta hedging and dynamic replication, interest rate derivatives (swaps, swaptions, caps and floors), currency management (hedge ratio, minimum-variance hedge ratio, overlay versus asset-level hedging, forwards versus options), carry trades, volatility and variance swaps, and credit derivatives.
Traps
- Hedging notional value is not the same as hedging exposure. Beta-hedging an equity portfolio and currency-hedging a foreign asset both require scaling by sensitivity.
- A forward hedge locks the hedged return; the forward premium or discount merely reflects the interest-rate differential, so the domestic-currency outcome can still fall short of the local return.
- In currency options the roles of the two risk-free rates reverse depending on whether the option is written on the exchange rate or on a foreign asset.
- A delta hedge is instantaneous and must be rebalanced; gamma measures how quickly the hedge drifts out of line.
- Variance swaps give a linear payoff in variance and trade pure volatility (vega); they are not a cap on volatility.
Worked example: minimum-variance hedge ratio
A foreign equity holding worth EUR 10 million. Sigma of the asset in EUR = 18%, sigma of the futures = 15%, correlation = 0.85. Then h = rho x sigma_S / sigma_F = 0.85 x 18/15 = 1.02, so hedge EUR 10.2 million of notional. But if the mandate is to eliminate currency risk, hedge 100% of the value regardless of correlation; the correlation-based ratio minimises variance of the hedged value, not currency exposure.