Unformatted text preview: Option Styles
European option – Holder can exercise the option only on the
expiration date
American option – Holder can exercise the option anytime during the
life of the option
Bermuda option – Holder can exercise the option during certain prespecified dates before or at the expiration date Call
Put Buy
↑
↓ Short Forward Long Call Write
↓
↑ Long Forward Short Call Payoff Floor – own + buy put
Cap – short + buy call
Covered Call – stock + write call = write put
Covered Put – short +write put = write call Profit
Price at Maturity CashandCarry – buy asset + short forward contract
Synthetic Forward – a combination of a long call and a short put with
the same expiration date and strike price Long Put Short Put Fo,T = no arbitrage forward price
Call(K,T) = premium of call
PutCall Parity Derivative
Position
Long
Forward
Short
Forward
Long Call
Short Call
Long Put
Short Put Maximum Loss Maximum Gain Strategy Payoff Unlimited Position wrt
Underlying Asset
Long(buy) Forward Price Guaranteed price PTK Unlimited Forward Price Short(sell) Guaranteed price KPT FV(Premium)
Unlimited
FV(Premium)
FV(Premium) – Strike Price Unlimited
FV(Premium)
Strike Price – FV(Premium)
FV(Premium) Long(buy)
Short(sell)
Short(sell)
Long(buy) Insures against high price
Sells insurance against high price
Insures against low price
Sells insurance against low price max{0,PTK}
max{0,PTK}
max{0,KPT}
max{0,KPT} (Buy index) + (Buy put option with strike K) = (Buy call option with strike K) + (Buy zerocoupon bond with par value K)
(Short index) + (Buy call option with strike K) = (Buy put option with strike K) + (Take loan with maturity of K) Spread Strategy
Creating a position consisting of only calls or only puts, in which some
options are purchased and some are sold Bull Spread
o Investor speculates stock price will increase
o Bull Call Buy call with strike price K1, sell call with strike
price K2>K1 and same expiration date
o Bull Put Buy put with strike price K1, sell put with strike
price K2>K1 and same expiration date
o Two profits are equivalent (Buy K1 call) + (Sell K2
call) = (Buy K1 put) + (Sell K2 put)
o Profit function Bear Spread
o Investor speculates stock price will decrease
o Exact opposite of a bull spread
o Bear Call Sell K1 call, buy K2 call, where 0<K1<K2
o Bear Put Sell K1 put, buy K2 put, where 1<K1<K2 Long Box Spread
Bull Call Spread Bear Put Spread
Synthetic Long Forward
Buy call at K1
Sell put at K1
Synthetic Short Forward
Sell call at K2
Buy put at K2
Regardless of spot price at expiration, the box spread guarantees a cash
flow of K2K1 in the future.
Net premium of acquiring this position is PV(K2K1)
If K1<K2, then lending money
Invest PV(K2K1), get K2K1
If K1>K2, then borrow money
Get PV(K1K2), pay K1K2
Butterfly Spread
An insured written straddle Let K1<K2<K3
o Written straddle Sell K2 call, sell K2 put
o Long strangle Buy K1 call, buy K3 put Profit
o Let F
o Profit Payoff
K2K1 K2K1FV[…
PT
PT
K1 K2 FV[… Asymmetric Butterfly Spread Collar
Used to speculate on the decrease of the price of an asset Buy K1strike atthemoney put Sell K2strike outofthemoney call K2>K1 K2K1 = collar width Profit Function Collared Stock
Collars can be used to insure assets we own Buy index Buy atthemoney K1 put Buy outofthemoney K2 call K1<K2 Profit Function Zerocost Collar
A collar with zero cost at time 0, i.e. zero net premium Straddle
A bet on market volatility Buy Kstrike call Buy Kstrike put Strangle
A straddle with lower premium cost Buy K1strike call Buy K2 strike put K1<K2 Profit Function Profit Function Equitylinked CD (ELCD) Can financially engineer an equivalent by Buy zerocoupon bond at discount Use the difference to pay for an atthemoney call option Prepaid Forward Contracts on Stock Let FP0,T denote the prepaid forward price for an asset bought
at time 0 and delivered at time T If no dividends, then FP0,T = S0, otherwise arbitrage
opportunities exist If discrete dividends, then
o If continuous dividends, then
o Let δ=yield rate, then the
and 1 share at time 0 grows to eδT shares at
time T
Forward Contracts Discrete dividends
o Continuous dividends
o Forward premium = F0,T / S0 The annualized forward premium α satisfies
o If no dividends, then α=r
If continuous dividends, then α=rδ Financial Engineering of Synthetics (Forward) = (Stock) – (Zerocoupon bond)
o Buy eδT shares of stock
o Borrow S0eδT to pay for stock
o Payoff = PT – F0,T (Stock) = (Forward) + (Zerocoupon bond)
o Buy forward with price F0,T = S0e(rδ)T
o Lend S0eδT
o Payoff = PT (Zerocoupon bond) = (Stock) – (Forward)
o Buy eδT shares
o Short one forward contract with price F0,T
o Payoff = F0,T
o If the rate of return on the synthetic bond is i, then S0e(iδ)T = F0,T or Implied repo rate ...
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This note was uploaded on 03/02/2012 for the course MATH 172 taught by Professor Kong during the Fall '09 term at UCLA.
 Fall '09
 kong

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