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
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.