Answer: USD 954.81

## 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

Author: LeetQuiz .