NO.PZ2023040701000055
问题如下：
Tandon asks Geng how pathwise valuation compares with the Monte Carlo method. Geng responds with the following statements:
Statement 1: “Pathwise valuation calculates the present value of the bond’s cash flows for each possible interest rate path, whereas the Monte Carlo method calculates present values for randomly selected interest rate paths.”
Statement 2: “Interest rate paths for both the pathwise valuation and the Monte Carlo method are based on an assumption of interest rate volatility and an interest rate model that is calibrated to the current benchmark term structure of interest rates.”
Statement 3: “In pathwise valuation, a constant is added to all interest rate paths so that the resulting present value for each benchmark bond is equal to its market value. No such adjustment is made in the Monte Carlo method.”
Which of Geng’s statements to Tandon is least likely correct?
选项：
A.
Statement 1
B.
Statement 2
C.
Statement 3
解释：
Correct Answer: C
Statement 3 is incorrect. Because the Monte Carlo model calculates the present value of the bond’s cash flows over randomly selected interest rate paths (unlike the pathwise valuation method, which uses all interest rate paths) and then averages the present values across these paths, the resulting present value will only match benchmark bond market values by chance. The addition of a constant to all interest rate paths (a drift term) ensures the average present value for each benchmark bond will equal its market value.
请问pathwise valuation 也是一种二叉树吗 如何假设all possible paths呢？那岂不是无穷多了？也要假设波动率吗
