I appreciate that both are the direct result of constricting a replicate portfolio using stock and bonds.
Are there deeper relationship between the two?
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There is a deeper relationship between the two risk-neutral measures. Take any event in the binomial model with a finite number of steps and calculate the risk-neutral probability of it. Take the same event in the Black Scholes model and calculate the risk-neutral probability of it. For most events, the two probabilities are different. Now let the number of steps in the binomial model become infinite and have the multiplicative binomial process converge to geometric Brownian motion. As a result, the risk-neutral probability in the binomial model converges to the risk-neutral probability of the same event in the Black Scholes model, no matter what the common event is. This is a deeper relationship.