ADVANCED OPTION STRATEGIES

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ADVANCED OPTION STRATEGIES
Straddles
A straddle is the purchase of one call option
and one identical put option. P Max(0, ST
-E) - C Max(0, E-ST ) - P P E - ST - C -
P if ST lt E P ST - E - C - P if ST
gt E Break-even points (Solving for ST which
yield P 0) ST E - C - P for ST lt E
ST E C P for ST gt E
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ADVANCED OPTION STRATEGIES
Straddles
P
Buy a put
Buy a call
0
ST
E
Straddle
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ADVANCED OPTION STRATEGIES
Straps
A strap is the purchase of two call options and
one identical put option. P 2Max(0, ST -E) -
2C Max(0, E-ST ) - P P E - ST - 2C -
P if ST lt E P 2ST - 2E - 2C - P if
ST gt E Break-even points (Solving for ST which
yield P 0) ST E - 2C - P for ST lt E
ST (2E 2C P)/ 2 for ST gt E
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ADVANCED OPTION STRATEGIES
Straps
P
Buy two calls
Buy one put
0
E
ST
Strap
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ADVANCED OPTION STRATEGIES
Strips
A strip is the purchase of one call options and
two identical put option. P Max(0, ST -E) -
C 2Max(0, E-ST ) - 2P P 2E - 2ST - C -
2P if ST lt E P ST - E - C - 2P if
ST gt E Break-even points (Solving for ST which
yield P 0) ST (2E - C - 2P)/ 2 for ST
lt E ST E C 2P for ST gt E
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ADVANCED OPTION STRATEGIES
Strips
P
Buy two puts
Buy one call
0
E
ST
Strip
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BLACK-SCHOLES OPTION PRICING MODEL
The Models Assumption
1. The rate of return on the stock follows a
lognormal distribution. 2. The risk-free rate
and variance of the returns are constant. 3.
There are no taxes or transaction costs. 4.
The stock pays no dividends. 5. The options
being priced are European call options.
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BLACK-SCHOLES OPTION PRICING MODEL
The Model
where
N(d1), N(d2) cumulative normal probabilities
s2 variance of stock return (annualized)
rc continuously compounded risk-free rate
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BLACK-SCHOLES OPTION PRICING MODEL
Example
Find the theoretical value of a European call
option with exercise price of 165 and 35 days to
expiration. The stock is currently priced at 164
and has the return standard deviation of 29.
Assume the annual risk-free rate equals to 5.35.
S 164 E 165 T 35/365
0.0959 s 0.29 s2 0.0841 rf
0.0535 erC (1 rf ) rC
ln(1 rf ) ln(1.0535) 0.0521
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BLACK-SCHOLES OPTION PRICING MODEL
Example
d1 0.0328
d2 -0.057
N(d1) N(0.0328) 0.512
N(d2) N(-0.057) 1 - N(0.057) 1 -
5239 0.4761
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BLACK-SCHOLES OPTION PRICING MODEL
Example
C 5.803
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BLACK-SCHOLES OPTION PRICING MODEL
The Hedge Ratio The call price increase with an
increase in stock price. The call Delta measures
the sensitivity of call price to the change in
stock price and is calculated by Call Delta
N(d1) The call Delta is also known as the hedge
ratio which is the number of stocks held per
number of calls written.
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BLACK-SCHOLES OPTION PRICING MODEL
Estimating the Volatility
Using Historical Volatility This assumes that
the historical volatility is a good approximation
for current and future volatility.
Implied Volatility This approach uses the market
prices to infer the volatility as is perceived by
the market. The implied volatility is calculated
by solving the Black-Scholes model for the
theoretical price which is equal to the observed
market price. The volatility which yield such
equality is the implied volatility.