Put-Call Parity Equation:
$Call [K,T] – Put [K,T] = PV [ F_{0,T} – K ] = {F_{0,T} }^P – Ke^{-rT}$
Spread: Position consisting of only calls or only puts.
- Bull Spread:
- Long call [K1,T] + Short call [K2,T]
- Long put [K1,T] + Short put [K2,T]
- Perform well when the price of the underlying asset goes up
- Bear Spread:
- Short call [K1,T] + Long call [K2,T]
- Short put [K1,T] + Long Put [K2,T]
- Perform well when the price of the underlying asset goes down
- Box Spread:
- Synthetic Long forward + Synthetic short forward
- Strategy guarantees a cash flow in the future
- A means of borrowing or lending money
- Option market-makers have low transaction costs and can sell box spreads which is equivalent to borrowing
- They’re alternatives to buying a bond
- Costly but no stock price risk
- Payoff $=K_{2} – K_{1}$ – IRRESPECTIVE of the underlying asset
- Ratio Spread:
- m Long call [K1,T] + n Short call [K2,T] [SAME underlying asset]
- m Long put [K1,T] + n Short put [K2, T]
Collars:
- Purchase Collar: [AM/OM] Long Put [K1,T] + [OM]Short Call [K2,T] , K2> K1
- Collar width = Diff. of strike prices
- Written Collar: [AM] Short Put [K1,T] + [OM] Long Call [K2,T] , K2> K1
- Zero cost collar:
- Pick the desired put strike below or at the forward price
- Find a strike above the forward price such that a call has the same premium
- Collared Stock:
- This position entails buying the stock, buying a put, and selling a call.
- It is an insured position because we own the asset and buy a put.
- The collared stock looks like a bull spread; however, it arises from a different set of transactions. The bull spread is created by buying one option and selling another. The collared stock begins with a position in the underlying asset that is coupled with a collar.
Straddles:
- Non directional speculations – Holder does not care whether the stock price goes up or down, but only how much it moves.
- Long call [K1,T] + Long put [K1,T]
- Advantage: Benefits from stock price movement in either direction
- Disadvantage: High premium
- Bet on High volatility – Investor believes volatility is HIGHER than the market’s assessment
- Cost of straddle will be greater when markets perception is that volatility is greater
Written Straddle:
- Short call [K1,T] + Short put [K1,T]
- Bet on low volatility – Investor believes volatility is LOWER than the market’s assessment
- Highly risky since a large change in the stock price leads to potentially unlimited loss
Strangle:
- Investor holds a position in both a call and a put with different strike prices but with the same maturity and underlying asset.
- [OM] Long Call [K1,T] + [OM] Long Put [K2,T]
- Reduced premium as compared to the Straddle
- This option strategy is profitable only if there are large movements in the price of the underlying asset.
- Use this strategy when you speculate a large price movement in the near future but unsure which way the movement will be.
Butterfly Spread:
- Written straddle [K2,T] + Strangle [K1,T and K3,T]