Using options algebra, long straddle, X = 1020, S1 = 1080. What is the investment? Profit? Breakeven points? And what is the position delta of this problem?

The following is for AT MATURITY only.

+ means long, no sign means long, - means short.

Max (S1 X, 0) means take the higher of the two expressions in the ( ).

Max (S1 X, 0) means take the higher of the two expressions in the ( ) and then negate the number.

Payoff excludes the cost of the option or the short proceeds.

Profit (or loss) includes the premium (+ or -).

One option will be referred to as a simple position.

A combination of options will be referred to as a complex position (this is purely my terminology for use in the class.)

Covered means that no margin is needed. Uncovered means that margin is needed.

Short calls are covered with long stock. Short puts are covered with short stock.

S1 refers to stock price at maturity, S0 is stock price at inception.

X is strike price, Xc is call strike, Xp is put strike, Xh is the higher strike price, Xl is the lower strike price.

C is the call premium, P is the put premium.

Max expressions can not be negative. They can be negated however outside of the Max.

Options are in units of 100. An option quoted at $5 is really $500.

The gross cost of a CC is S, the net cost is S C.

Objectives are to:

Determine breakeven point (s)

Maximum gains/ losses

Probable gains/ losses

Strategy

Calculate ROI

When only X is used it is assumed to be the same for calls and puts and same maturity.

There are vertical and calendar spreads. The horizontal/ vertical refers to how it is read in the newspaper or internet. Strikes move up and down so they are vertical spreads when different strike prices are used. Maturities move left to right so they are horizontal spreads. Examples are Bull call spreads and bear put spreads.

Very advanced: some positions can essentially pay for themselves: zero cost collars, selling 2 calls and buying a put while using the call proceeds to buy the put, excluding margin.

The books uses K for strike, I have used X. They are interchangeable. The book uses Min expressions on page 185, we will not be using that expression.

Simple Positions

Long Call Payoff (PO): Max (S1 X, 0)

Long Call Profit (PR): Max (S1 X, 0) C (1)

Long Put PR: Max (X S1, 0) P (2)

Short Call PR: - Max (S1 X, 0) + C (3)

Short Put PR: - Max (X S1, 0) + C (4)

Simple/ Complex Positions

Covered Call (CC) (S1 S0) + - Max (S1 X, 0) + C (5)

Protective Put (PP) (S1 S0) + Max (X S1, 0) P (6)

Complex Positions

Long Straddle Max (S1 X, 0) C + Max (X S1, 0) P (7)

Short Straddle - Max (S1 X, 0) + C+ - Max (X S1, 0) + P (8)

Long Strangle Max (S1 Xcl, 0) C + Max (Xph S1, 0) P (9)

Short Straddle -Max (S1 Xch, 0) + C + -Max (Xpl S1, 0) + P (10)

Bullish.

Bearish.

Bearish.

Bullish.

NOT a good hedge, This is an income position.

Weak hedge.

Volatility bet, either way.

NO volatility bet.

Volatility bet, like a straddle, though it widens the range.

No volatility bet, though it widens the range.