valuation using NPV

You can't use just a simple NPV calculation to value options. It is, however, part of option pricing models, such as the Binomial Option Pricing Model.
 
Correct.

The bog-standard Black-Scholes PDE contains two terms that have r (the risk-free rate) as the factor.

The solution, the -ve (the N(d2)) term has an exponential factor with -r(T-t) as the exponent, r being the risk free rate, and that sort of solution being the standard NPV representation in continuous time.

So to explain that in English, the risk free rate is used in an NPV type calculation as part of the solution, however, you cannot value an option using NPV alone.

Ask me again when I have not drunk any Finlandia Vodka :D
 
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