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Published byGary Wigglesworth Modified about 1 year ago

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Options Pricing Using Black Scholes Model By Christian Gabis

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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

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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

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A Good Calculator /bsm.htm /bsm.htm Also has many other pricing models Black Scholes typically undervalues options

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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)

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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.

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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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