The Random Walk in Simple Terms

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.