Derivative (finance) Study Guide

📖 Core Concepts Derivative – a contract whose value comes from an underlying asset, rate, index, or currency. Four essential elements – (1) underlying asset, (2) future act (buy/sell), (3) agreed price, (4) future date. Notional amount – reference size of the underlying used to calculate cash‑flows; it does not change hands. Lock products – forwards, futures, swaps; valued at zero at initiation, become assets or liabilities as the underlying moves. Option products – give a right (not an obligation); have intrinsic value + time value; buyer pays a premium up front. Market structures – OTC (private, customized, higher counter‑party risk) vs exchange‑traded (standardized, cleared, margin‑protected). Primary purposes – hedge risk, obtain speculative exposure, access hard‑to‑trade markets, create optionality, enable leverage. Risk transfer – derivatives shift risk from risk‑averse participants to those willing to bear it. --- 📌 Must Remember Forward vs Futures – forwards are private, no daily cash‑flows; futures are exchange‑traded, marked‑to‑market daily, require margin. Option styles – European: exercise only at expiry; American: exercise any time up to expiry. Intrinsic value = max(spot − strike, 0) for calls, max(strike − spot, 0) for puts. Time value = option premium − intrinsic value; decays to zero at expiry. Leverage – small underlying moves produce large derivative P/L because exposure is scaled to notional, not cash outlay. CDS payoff – buyer receives compensation if a credit event occurs; seller receives periodic premiums. Arbitrage‑free price – for forwards/futures equals spot + cost of carry; for European options given by Black‑Scholes (assumes constant volatility, risk‑free rate). Margin call – triggered when a futures account falls below the required maintenance margin. --- 🔄 Key Processes Mark‑to‑Market Futures At each trading day end, compute the contract’s market value. Settle the daily profit/loss in cash; adjust margin account accordingly. If margin < maintenance level → margin call → deposit additional cash. Option Valuation (Black‑Scholes) Input: spot price \(S\), strike \(K\), time to expiry \(T\), volatility \(\sigma\), risk‑free rate \(r\). Compute \(d1 = \frac{\ln(S/K)+(r+\sigma^2/2)T}{\sigma\sqrt{T}}\) and \(d2 = d1-\sigma\sqrt{T}\). Call price = \(S N(d1) - K e^{-rT} N(d2)\); Put price = \(K e^{-rT} N(-d2) - S N(-d1)\). Swap Cash‑Flow Exchange Determine each leg’s payment formula (e.g., fixed rate \(\times\) notional vs floating rate \(\times\) notional). On each payment date, net the two legs; only the net amount changes hands. CDS Mechanics Buyer pays periodic premium (usually quarterly). If a credit event occurs, seller pays the par value of the reference obligation (or delivers the defaulted asset) to the buyer. Hedging with a Forward Rate Agreement (FRA) Borrower with floating‑rate loan buys FRA to lock in a fixed rate for the future period, eliminating exposure to rising rates. --- 🔍 Key Comparisons Forward vs Futures Customization: Forward – fully customizable; Futures – standardized. Settlement: Forward – single settlement at maturity; Futures – daily cash settlement (MTM). Counter‑party risk: Forward – higher (no clearing house); Futures – mitigated by clearing house and margin. American vs European Options Exercise: American – any time before expiry; European – only at expiry. Valuation: American often needs binomial/tree models; European has closed‑form Black‑Scholes. OTC vs Exchange‑Traded Transparency: OTC – private quotes, limited price info; Exchange – real‑time published prices. Regulation: OTC – less regulated, higher systemic risk; Exchange – central clearing, margin requirements. Calls vs Puts Payoff: Call – benefits from price rise; Put – benefits from price fall. Typical use: Call – bullish speculation or buying insurance against rising price; Put – bearish speculation or protecting against price drop. --- ⚠️ Common Misunderstandings “Notional amount is exchanged.” – It is only a calculation base; the actual cash flows are based on it. “Futures require no cash upfront.” – They require initial margin and daily cash settlements. “Options have no value at inception.” – They have time value even when out‑of‑the‑money. “A forward’s price equals the spot price.” – It includes a forward premium/discount for cost of carry. “CDS can only be bought by owners of the reference loan.” – Naked CDS are allowed (buyer holds no underlying loan). --- 🧠 Mental Models / Intuition Derivative as a “shadow” of the underlying – think of it as a mirror that reflects the underlying’s price movements, but you only pay for the right to move with it (option) or promise to move (forward/future). Leverage = “magnifying glass.” Small underlying change × large notional = big P/L on a tiny capital outlay. Mark‑to‑Market = “daily balance check.” The contract’s value is always reset to zero‑sum; you never sit on a large unrealized gain/loss overnight. Swap netting = “two‑way bridge.” Each leg is a road; only the net traffic (difference) actually crosses. --- 🚩 Exceptions & Edge Cases Naked CDS – buyer has no exposure to the reference loan; regulatory scrutiny because of systemic risk. Cash‑settled futures – no physical delivery; settlement is the cash difference between contract price and spot at expiry. Partial margin calls – some exchanges allow “partial” calls where only a portion of the shortfall must be funded immediately. Early exercise of American options – may be optimal for deep‑in‑the‑money calls on dividend‑paying stocks (not covered in outline but a known edge case). --- 📍 When to Use Which Hedge vs Speculate – Use forwards/futures or swaps when you must offset an existing exposure; use options when you want upside potential with limited downside. Choose OTC vs Exchange – Pick OTC for bespoke terms, exotic payoffs, or when the market is illiquid; pick exchange‑traded for transparency, lower counter‑party risk, and ease of entry/exit. Select Forward vs Futures – Use forwards for customized settlement dates or when you cannot post margin; use futures for standardized contracts with daily MTM and clearing‑house protection. Option style – Use European options when you only need protection at a known future date; use American when flexibility to exercise early is valuable (e.g., dividend capture). --- 👀 Patterns to Recognize Payoff diagram “V” shape – call option (upward), put option (downward). Leverage effect – P/L of lock products scales roughly linearly with underlying price change times notional. Convergence at expiry – futures/forward prices converge to spot; option intrinsic value equals payoff at expiration. Risk‑transfer chain – a risk‑averse party → derivative → risk‑tolerant party; look for the “risk‑absorber” in the transaction. --- 🗂️ Exam Traps Distractor: “Futures require no upfront cash.” → Wrong; they require initial margin and daily settlement. Distractor: “The notional amount is exchanged at maturity.” → Wrong; it is only a calculation reference. Distractor: “All options have time value at expiration.” → Wrong; time value decays to zero; only intrinsic value may remain. Distractor: “A forward’s price equals spot plus risk‑free rate.” → Incomplete; must add cost of carry (storage, dividends, financing). Distractor: “CDS can only be purchased by holders of the underlying loan.” → Wrong; naked CDS exist. Distractor: “Mark‑to‑market means the contract’s value is paid in full each day.” → Wrong; only the daily profit or loss is settled, keeping the contract alive. ---