Explanation

To solve for P(1,1), we need to use the risk-neutral pricing approach with the given interest rate tree and probability structure.

Step 1: Set up the equations

From the price tree structure, we have:

Equation 1 (from t=0 to t=0.5): $\frac{0.72 \times P(1,1) + 0.28 \times P(1,0)}{1 + \frac{0.042}{2}} = 937.49$

Equation 2 (from t=0.5 to t=1 for the upper path): $\frac{975.13 \times q + 979.43 \times (1-q)}{1 + \frac{0.0465}{2}} = P(1,1)$

Equation 3 (from t=0.5 to t=1 for the lower path): $\frac{979.43 \times q + 983.77 \times (1-q)}{1 + \frac{0.0375}{2}} = P(1,0)$

Step 2: Solve for q

Substituting Equations 2 and 3 into Equation 1: $\frac{0.72 \times \left(\frac{975.13q + 979.43(1-q)}{1.02325}\right) + 0.28 \times \left(\frac{979.43q + 983.77(1-q)}{1.01875}\right)}{1.021} = 937.49$

Solving this system yields: q = 0.563

Step 3: Calculate P(1,1)

Substitute q = 0.563 into Equation 2: $P(1,1) = \frac{975.13 \times 0.563 + 979.43 \times (1-0.563)}{1 + \frac{0.0465}{2}}$ $P(1,1) = \frac{975.13 \times 0.563 + 979.43 \times 0.437}{1.02325}$ $P(1,1) = \frac{548.998 + 428.011}{1.02325} = \frac{977.009}{1.02325} = 954.81$

Therefore, the correct estimate of price P(1,1) is USD 954.81.

Why other options are incorrect:

• A (954.15): Incorrect calculation, likely using wrong probability or discount factor
• C (956.25): Too high, doesn't properly account for the risk-neutral probabilities
• D (956.92): Even higher, likely using incorrect interest rates or probabilities