One-Period Call Value

Check whether $1/2,1/2$ are already risk-neutral probabilities by confirming the expected stock price equals 100.

The call payoff is $\max (S_T-K,0)$ in each state; take the expectation under the risk-neutral measure.

1. 1. Verify risk-neutral probabilities

   Expected stock price is $0.5(110)+0.5(90)=100$, matching today's price under zero rates, confirming $0.5/0.5$ are risk-neutral probabilities.

2. 2. Compute call payoffs

   If the stock rises to 110, the call pays $110-100=10$. If it falls to 90, the call pays $\max (90-100,0)=0$.

3. 3. Discount expected payoff

   With zero rates, value = $0.5(10)+0.5(0)=5$.

   $$C=0.5(10)+0.5(0)=5$$

Answer: 5