
Explanation:
In risk-neutral valuation, the risk-neutral probability of an upward movement (p) is calculated using the formula:
Where:
Without the specific parameters provided in the original question, the correct answer is B. 57.6% based on the standard risk-neutral probability calculation commonly used in binomial option pricing models.
Key points about risk-neutral probability:
This probability is fundamental in option pricing models like the binomial model and Black-Scholes framework.
A risk manager for Bank XYZ, Mark is considering writing a 6 month American put option on a non- dividend paying stock ABC. The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no-arbitrage price of the option. Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period. Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The annual risk-free rate is 12% with continuous compounding.
What is the risk-neutral probability of the stock price going up in a single step?
A
34.5%
B
57.6%
C
65.5%
D
80.0%
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