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…