Derivative Cheatsheet

Note 1 Derivative Securities:

Hedging with forward or futures:

To reduce risk and uncertainty of;

• Uncertainty in price
• Uncertainty in quantity

Price Elasticity of Supply (Quantity)

If elasticity is 1 –    ; [pic 1]

Don’t need to short/long cause revenue remains the same.

If Elasticity > 1 –    [pic 2]

Write (short) a future contract for people to buy at S0 Price. [Sell at S0 Price in the future]. Party who agrees to deliver the item in the future (Short Position)

If Elasticity < 1 – [pic 3]

Long (buy) future contract to buy at S0 Price. Party who agrees to take delivery of item in future (Long position)

Forward – Locking in paper profits only (No money changes hand)

Futures – Mark to Market mechanism (Money changes hand everyday)

Once Margin Account goes below Maintenance Margin, have to top up to initial margin amount.

Future contract on non-dividend stock

Cash and Carry

Avoid Arbitrage: F (Upper bound)[pic 4]

Reverse Cash and Carry

Avoid Arbitrage: F (Lower bound)[pic 5]

F=$107 for no arbitrage

Profit = Future price – spot $ + Carrying cost

For no Arbitrage to happen:[pic 6]

[pic 7]

Future Contracts on Dividend paying Stock (when income reinvested)
Cash and Carry: 1) Borrow buy one share. [pic 8]

2) Deposit Incomes. 3)Short future price F.

[pic 9]

[pic 10]

[pic 11]

To avoid Arbitrage (Cash and Carry):
[pic 12]

To avoid Arbitrage (Reverse Cash and Carry):

[pic 13]

[pic 14]

Future Contracts on a Dividend Paying stock (when income proportional to price of underlying Asset.) No Arbitrage; F=[pic 15]

q – continous dividend (income)
Investor who hold one share will hold  amount after end of T years.[pic 16]

Cash and Carry (Dividend are reinvested)

Reverse Cash and Carry F[pic 24]

Futures’ prices with different maturity

Cash & Carry: 1)(F1) Long units of futures contract maturing at T1. 2) Short one unit of futures contract that matures at T2, F2. C is carrying cost other than interest rate like dividend. F2 = F1[pic 33][pic 34]