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# A random walk under the risk-neutral measure

Under risk-neutral measure, with real probabilities 0.55 up, 0.45 down, what’s the expected next step in a random walk?

🔘 A. UP
🔘 B. DOWN
🔘 C. Cannot be determined

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To compute the expected next step in a random walk under the risk-neutral measure, we first need to determine the risk-neutral probabilities. Let's define the following:
- u = upward movement
- d = downward movement
- q = risk-neutral probability of an upward movement
- 1 - q = risk-neutral probability of a downward movement
- r = risk-free rate
- Δt = time step
The risk-neutral probability, q, is given by:
q = (e^(r * Δt) - d) / (u - d)
Without specific values for u, d, r, or Δt, we can't compute q hence Answer C.

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Registered Training Organization No. 24280185328

Contact: Florian CAMPUZAN Phone: 0680319332 Email:fcampuzan@finance-tutoring.fr