Options Pricing Using Black Scholes Model

Document Sample
Options Pricing Using Black Scholes Model Powered By Docstoc
					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
 Reduces your return
 Limits your downside
 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.
 Then buy a $30 put to limit your downside.
 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