1. Intro to Derivatives

Derivative: instrument whose value depends on value of some other asset. Serve to provide Price Discovery (liquidity) and Risk Management (hedging)

Derivative Contracts are zero-sum, counterparty refers to other side of contract.

Notional Principal = value of underlying asset in derivative. More accurate…less meaningful. Based on actual cash flows of asset

Market value: based on price of contract.

E-mini futres most liquid security in world. Small leveraged contract of S&P.

Derivative uses: Heding, Speculation (leverage), change the nature of asset or liability arbitrage trading (Ex. When S&P stocks to not line up with S&P Futures).

Unlike Gambling, Derivatives do no CREATE risk.

Forward contract: agreement between buyer (long) and seller (short) to trade. Specified quantity, price, and time in future
Futures: forward contracts that are standardized, more heavily regulated, and trade on exchanges
Spot Price: what asset is worth now
Borrow rate: how much can I borrow
Time until delivery: time frame

Call option: Buyer pays premium (strike/exercise price) for the right to BUY an asset at or before maturity.

Put option: right to SELL an asset at a stated exercise/strike price on or before a stated maturity date.

Options sell for 100 shares standard.

2. Mechanics of Futures Markets

Spot market (normal) : agree today, pay today, deliver tomorrow
Forward: agree today, pay at maturity, deliver at maturity
Futures: agree today, mark-to-market everyday, pay spot at maturity, deliver at maturity

Forward contracts: t = start time
T = delivery time
Buyer = long ; Payoff is “St - K
Seller = short ; payoff is “K – St”
St = spot at time T
K delivery price

Futures contracts: same as ^ except more formalized and go through “Clearing house” and post daily gains, losses though “daily settlement”. Traded on Exchanges

Must state delivery. Where, what, when. Only 3% of contracts result in delivery

Margin:
Margin account: required to pay futures (“down payment”)
Initial margin needed as security deposit

FORMULAS:
Forward contracts pay off:
Buyer = long ; Payoff is “St - K
Seller = short ; payoff is “K – St”
Time value of money:
FV = CFe^(T in yrs * r)
PV = CFe^-(T in yrs * r)
# coupon payments = CF*(semiannual)(.5) ; B0 = #Coupe^(r*T) + …
Notation for pricing forward contracts
St = spot price at time (t=0 origination, t=T is maturity)
Ft = Futures or Forward price at time (recall… Ft=St)
K = Futures or forward settlement price agreed at origination (K=F0)
T = Maturity
R = Risk free interest for Maturity T
Vt = Value of contract at time t
DETERMINES FAIR PRICE IN FUTURE (arbitrage opportunities)
F0 = S0*e^r(T)
IF F0 > S0e6(rT) … arbitrage is possible guaranteeing positive payoff in SELLING
IF F0 < S0e6(rT) … arbitrage is possible guaranteeing positive payoff in BUYING
Long and short on underlying assets, doesn't’t matter if asset goes up or down, you