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Spreads and Collars

  • SSP 

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:
    1. Long call [K1,T] + Short call [K2,T]
    2. Long put [K1,T] + Short put [K2,T]
    3. Perform well when the price of the underlying asset goes up
  • Bear Spread:
    1. Short call [K1,T] + Long call [K2,T]
    2. Short put [K1,T] + Long Put [K2,T]
    3. Perform well when the price of the underlying asset goes down
  • Box Spread:
    1. Synthetic Long forward + Synthetic short forward
    2. Strategy guarantees a cash flow in the future
    3. 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
    4. Costly but no stock price risk
    5. Payoff $=K_{2} – K_{1}$ – IRRESPECTIVE of the underlying asset
  • Ratio Spread:
    1. m Long call [K1,T] + n Short call [K2,T]  [SAME underlying asset]
    2. m Long put [K1,T] + n Short put [K2, T]


  • 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:
    1. Pick the desired put strike below or at the forward price
    2. Find a strike above the forward price such that a call has the same premium
  • Collared Stock:
    1. This position entails buying the stock, buying a put, and selling a call.
    2. It is an insured position because we own the asset and buy a put.
    3. 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.


  • 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


  • 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]