# Derivatives Ch. 3

FINA0301 Derivatives Faculty of Business and Economics University of Hong Kong Dr. Tao Lin

Chapter Outline

Options and basic insurance strategies Spreads and collars: bull and bear spreads; box spreads; ratio spreads; collars Speculating on volatility: straddles; butterfly spreads; asymmetric butterfly spreads

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Long / Short Call / Put Options

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Strategies: Based on Price Directions & Volatility Movements The simple call and put options reflect the following views on the price directions. Price to Increase Volatilities to Increase Volatilities to Decrease Long Call Short Put Price to Decrease Long Put Short Call

Other things being equal, buying options often benefit when volatility increases. 4

Basic Insurance Strategies

Buying insurance: buying options Selling insurance: selling options Buyer’s Perspective Short in Underlying Price to Increase Buy Insurance Sell Insurance Long Call (Cap) Producer’s Perspective Long in Underlying Price to Decrease Long Put (floor)

Short Put (Covered Put) Short Call (Covered Call)

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Other Option Strategies

Combined option positions can also express views on price directions and volatilities changes. Strategies on price direction views: Bullish: bull spread Bearish: bear spread

Strategies on volatility views:

Higher volatility: long straddle/strangle Lower volatility: short straddle/strangle; Butterfly spread

Box spread

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Bull Spreads

A bull spread is a position with the following profit shape.

It is a bet that the price of the underlying asset will increase, but not too much

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Bull Spreads (cont’d)

A bull spread is to buy a call/put and sell an otherwise identical call/put with a higher strike price Bull spread using call options: Long a call with no downside risk, and Short a call with higher strike price to eliminate the upside potential

Bull spread using put options:

Short a put to sacrifice upward potential, and Long a put with lower strike price to eliminate the downside risk 8

Bull Spread with Calls

Value K2

Long a call (strike price K1, premium c1) Value = 0 when ST ≤ K1 = - K1 + [1]ST when ST > K1 Short a call (K2>K1, c2 K2 Portfolio Value = 0 = -K1+ [1]ST = K2-K1

K2-K1 K2

FV(-c1+c2)

K1

ST

when ST ≤ K1 when K1K2

-K1

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c1>c2 Initial cash flows = -c1 + c2 K1

Value

K1

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Initial cash flow – p1+ p2 >0 Value = – K2 + K1 +FV(– p1 + p2) when ST ≤ K1 = – FV(c1 – c2) -K2 +K1+ =… FV(-p1+p2) Portfolio -K2+K1 Value = – K2 + K1 when ST ≤ K1 = – K2 + ST when K1 K2 Short a put (strike price K2, premium p2) -K2 when ST ≤ K2 Value = – K2 +ST =0 when ST > K2

K1

K2

Spreads (cont’d)

A bear spread is a position in which one sells a call and buys an otherwise identical call with a higher strike price. Opposite of a bull spread. A box spread is accomplished by using options to create a synthetic long forward at one price and a synthetic short forward at a different price A box spread is a means of borrowing or lending money: It has no stock price risk

A ratio spread is constructed by buying m calls / puts at one strike and selling n calls / puts at a different strike, with all options having the same time to maturity and same underlying asset 11

Box Spread

Synthetic Short: sell Call and buy Put with K2 Value = – ST + K2 Initial CF: c2 – p2 Portfolio Payoff = K2 – K1 Initial CF = c2 – p2 – c1 + p1 = PV(K1 – K2 )

Value K2

K2 – K1

Synthetic long: buy Call and sell Put with K1 Value = ST – K1 Initial CF: – c1 + p1

K1

K2

-K1

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Ratio Spread - Exercise

Create a ratio spread that has the following payoff:

Value K2

K1

K2

-K1

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Collars (Revisit)

A collar is a long put combined with a short call with same maturity but different strike price It resembles a short forward with a flat middle To bet that the price of the underlying asset will decrease significantly A zero-cost collar can be created...

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