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Hi there!
They are different models:
1. Binomial model – Uses up and down risk-adjusted probabilities
Up probability = 1+Rf-D/U-D
2. When you say the “no-arbitrage,” model I’m assuming you mean the European Put-Call Parity equation from which you could derive the price of a call or a put.
C0 + PV(Bond)=P0 + Long Stock
3. Expectation approach – It is the Black-Scholes-Merton Model
Yes, they are different models and the vignettes will generally tell you which model to use to calculate the value of the call or put.