Lecture 12 BSM Model

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Last updated 12:08 PM on 5/23/26
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15 Terms

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BSM model

prices options before maturity

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increase in stock price

increase in call value

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increase in strike price

decrease in call value

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increase in volatility

increase in call value

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increase in maturity

increase in call value

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increase in risk free rate

increase in call value

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increase in dividend

decrease in call value

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price of put

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price of call

must adjust formula for dividends so that S=So-De^-rt and use new S in d1 and d2

<p>must adjust formula for dividends so that S=So-De^-rt and use new S in d1 and d2</p>
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d1 and d2 formula

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moneyness

S/K, if greater than 1 then intrinsic value for calls is positive

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implied volatility of stock unobservable factor

volatility smile measures volatility with respect to stock price
volatility is minimum ATM
DITM options have high volatility, so banks may sell anyway because could be OTM by maturity

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implied σ > actual σ

seller wins, overcompensated for actual amount of risk they took on

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pros

foundation for greeks and delta hedging, used as market benchmark

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cons

violates constant volatility, cannot price American options, lognormal distribution underprices tail events