# Options Pricing Using Black Scholes Model

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```					Options Pricing Using
Black Scholes Model

By Christian Gabis
Variables
 C = price of the call option
 S = price of the underlying stock
 X = option exercise price
 r = risk-free interest rate
 T = current time until expiration
 N() = area under the normal curve
 σ =standard deviation of stock return
The Formula
 C = S N(d1) - X e-rT N(d2)
 d1 = [ ln(S/X) + (r + σ2/2) T ] / σ T1/2
 d2 = d1 - σ T1/2
A Good Calculator
 http://www.montegodata.co.uk/Consult/BS
/bsm.htm
 Also has many other pricing models
 Black Scholes typically undervalues
options
Using Options to Hedge
 Using options as a kind of insurance
 Will not work well with small amounts of
capital ( too few shares for one option)
Example
 You buy 100 shares of WAG for \$36.00 for
a position of \$3600.
 The put option costs you \$105 and is good
until October.
 There are 3 possible outcomes for this
situation.
Outcomes
   The stock goes to \$30 leaving you with a position worth
\$3000 and a worthless option. Outcome: -\$600-\$105=-
\$705
   The stock climbs higher to \$40 leaving you with a
worthless put option and a \$4000 position. Outcome :
-\$105+\$400=\$295
   The stock falls to \$25 leaving you with a loss of \$1100
and a gain on your option of roughly \$500( market price
will vary slightly). Your loss was limited because of the
insurance effect of the option. Outcome : -\$600

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 views: 21 posted: 2/24/2010 language: English pages: 7