Assume the stock price follows a geometric Brownian motion Then in Black-Scholes pricing model, N(d2) is the risk-neutral probability that the option expires in-the-money. However, it is said that N(d1) is also the probability that the option expires in-the-money under the measure that uses the stock itself as the numeraire.
I understand that risk-neutral measure uses discounted stock price SB as the numeraire, but how do you use the stock itself as the numeraire?
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