Choosing the Lognormal Mean for Black Scholes

destriero · Sep 26, 2021

Kevin Schmit said:
A number of posters have pointed out that pricing options off anything other than the risk-free rate would allow arbitrage, but I don't think anyone has actually explained that arbitrage to you. If you understood the arb, you would never have asked the question, so here is the explanation:

Price an ATM put and call (same expiry and underlying). Then simulate selling the call and simultaneously buying 100 shares of the stock, financed at the current risk-free rate, and buying the put. Then check what happens at expiry. You will find that in all situations, you have made money from the excess differential between the (overprices) call and the (comparatively underpriced) put.

Before you delve into the intricacies of BSM, and way before you dive into Shreve (not an undergraduate text!), you should learn about put-call parity and other basics.
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Hit me up in email when you get a chance. B

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Choosing the Lognormal Mean for Black Scholes

destriero