So the lognormal distribution should not have a bias, and so (assuming £/$ exchange rate= 1) the present value (in dollars) of unconditionally receiving 1 pound sterling should be greater than 1, and similarly for the present value (in sterling) of unconditionally receiving 1 dollar. Both will be greater than 1.

]]>The (risk adjusted) probability that the option will be in the money and will be exercised when it expires is \(-XQ(S_T > X) = N(d_2)\). The delta of the option is \(N(d_2)\), which is different from \(N(d_1)\). I tried to explain this in the paper.

]]>Risk-Adjusted Probabilities in the

Black-Scholes Model 1

The expected future

payoff is

EC1T = −XP{ ST > X}.

where P is the risk-adjusted probability, and so the value is

−e−rτ XP{ST > X}.

This implies that e−rτ is equal to 1.

I believe this is incorrect. Please tell me what I am missing.

What I am actually looking for is the probability the option will be exercised before it expires. I have some literature that states that probability is equal to delta, one of the Greeks associated with the Black Scholes model. Can you tell me if delta is indeed that probability?

Yours truly,

Benjamin Roscoe PhD

God journalistik

]]>—Lars ]]>

I am a masters student in applied finance in Australia and I would just like to show you my gratitude as you have successfully showed me how to understand nd1 and nd2 in the BS model. Many papers and sites are too hard to understand but your brief paper has finally done it it a very simplistic nature. You have save me a lot of time and I thank you.

Keep up the good work.

Amish

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