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CFA1: Derivatives

  • derives its value from the price of another underlying asset or an interest rate
    • cons: risky, zero-sum game
    • pros: provide price information, lower transaction costs, allow the transfer of risk
  • arbitrage exists when identical future payoffs, but different market prices

Forward contracts

  • customized: no active secondary market
  • long: obligated to buy; short: obligated to sell
  • specified date of future
  • if asset price > forward price, long gains
  • if asset price < forward price, short gains
  • contract settlement
    • delivery: short delivers underlying to long for payment of the forward price
    • cash settlement
  • early termination
    • cash settlement (buy out)
    • enter into an offsetting contract, with a different/same counterparty
  • end user: typically a corporation or institution seeking to transfer an existing risk
  • Forward Rate Agreement
    • FRA settlement payment to long


  • Currency forward contracts: commitments to buy/sell foreign currency for a fixed amount of another currency for specified exchange rate

Futures contracts

  • exchange traded:minimum price fluctuation(tick), daily price limit
  • standardized, regulated contract: quality and quantity of good, delivery time, manner of delivery
  • clearinghouse acts as counterparty on all contracts, no default risk
  • margin requirements
    • initial margin: deposited before trade occurs
    • maintenance margin: minimum margin that must be maintained in a future account
    • variation margin: funds needed to restore future account to initial margin
    • settlement price: average of trades during closing period, used to calculate margin
  • marking to market: process of adjusting margin balance in a futures account each day for the change in the futures price (add gains, subtract losses)
  • termination methods: reversal(offsetting trade), asset delivery, cash settlement, exchange for physicals(off exchange)
  • Eurodollar futures: add-on yield based on 90-day LIBOR
    • minimum price change = one 'tick' = price change of 0.01% = $25 per $1 million contract
  • S&P 500 index futures: 250 times the level of the index, $250 per change in index point

Option contracts

  • Call option: right to buy
  • Put option: right to sell
    • American put option- may be exercised on any trading day on or before expiration
    • European put option- may only be exercised on expiration
  • Moneyness
    • at the money : current price = strike price
    • in the money : high prices relative to original price
    • out of the money : option has no intrinsic value
  • option value = intrinsic value + time value
    • intrinsic value = payoff at expiration
    • time value = option premium - intrinsic value
  • Interest rate options: payoff based on the difference between a floating rate(LIBOR) and the strike rate
    • payoff on interest rate call = Max[0, (LIBOR-strike rate)] x notional amount (long gains when rates rise)
    • payoff on interest rate put = Max[0, (strike rate-LIBOR)] x notional amount (long gains when rates fall)
    • payoffs made at the end of the interest rate term, after expiration
  • cap: maximum on an issuer's payments on a floating rate debt
    • equivalent to series of long interest rate calls
    • makes payments to issuer when floating rate > cap rate
  • put: minimum on an issuer's payments on a floating rate debt
    • equivalent to series of short interest rate puts
    • receives payments from issuer when floating rate < floor rate
  • Put-Call parity S+P = C+X(discounted)
  • Option values increase when
  1. time to expiration increases
  2. greater price volatility
  3. increase in RFR
  • if the asset has positive cash flows, cost of the asset is reduced by the PV of the cash flows


  • equivalent to a series of forward contracts
    • notional principal: used to calculate periodic payments
    • floating rate: usually LIBOR
    • tenor: time period covered by swap
    • settlement dates: payment due dates
  • Interest rate swap : one party exchanges a stream of interest payments for another party's stream of cash flows
  • Plain Vanilla Interest Swap
    • fixed interest rate payments in exchange for floating rate psyments
    • notional amount not exchanged
    • interest payments are netted
    • payment is made at end of period based on beginning of period LIBOR
  • Equity swap: equity returns exchanged with fixed/floating rate payments
    • equity return payer: receives interest payment, pays on positive equity return
    • interest payer: pays interest payment, pays any negative equity return
  • Total return swap : party A pays the total return of an asset, and party B makes periodic interest payments
  • Currency swap : a foreign exchange agreement between two parties to exchange a given amount of one currency for another and, after a specified period of time, to give back the original amounts swapped

Option strategies

  • covered call: writer owns the stock and sells a call, any loss will be reduced by premium received; writer trades the stock's upside potential for the fixed option premium
  • protective put: put buyer owns the stock and a put; put buyer pays for protection against any stock price below the strike price