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Options Pricing Using Black Scholes Model

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

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Options Pricing Using Black Scholes Model

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  1. Options Pricing Using Black Scholes Model By Christian Gabis

  2. 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

  3. 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

  4. A Good Calculator • http://www.montegodata.co.uk/Consult/BS/bsm.htm • Also has many other pricing models • Black Scholes typically undervalues options

  5. 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)

  6. 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.

  7. 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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