I am reading Options, Futures, and other derivatives by John C. Hull. In the chapter on Binomial trees, he remarks:
A risk-neutral world has two features that simplify the pricing of derivatives:
- The expected return on a stock (or any other investment) is the risk-free rate.
- The discount rate used for the expected payoff on an option (or any other instrument) is the risk-free rate.
I understood the first point. The second point seems easier and almost obvious, though when I tried to come up with a written justification for it, I was at a lack of words. I am hoping someone could justify the second point for me. Thank you!
Edit: On further thought, it seems that in a world with only two possible investments - a risky stock and a riskless bond - it is the riskless bond that will represent the time value of money, hence we should use that as the discount rate.
But this raises another question: Based on the above argument, the fact that we use the risk-free rate for discounting is not a consequence of the risk neutral world, but this is not what Hull suggests.