Re: Common Sense Black-Scholes
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Just to be clear. In the real market where the Black-Scholes theoretical modeling after brownian motion applies, if the stock price is $60 would a Call with Strike 62 be in parity - ie. equally valued - with a Put with strike $58? Or not?
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Not. In the simplest setting, we'll take a unit bond (so interest is zero) and a unit volatility. Also assume our expiration time is 1. Then a call with strike price K is valued at
60*F(ln(60/K) + 1/2) - K*F(ln(60/K) - 1/2),
where F is the cdf of a normal. Take K=62 and get 22.37. Take K=58 and get 23.60.
So the call with strike price 62 has value 22.37. By put-call parity, the put with strike price 58 has value
23.60 + 58 - 60 = 21.60.
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