NO.PZ2023091601000089
问题如下：
A portfolio manager has asked
each of four analysts to use Monte Carlo simulation to price a path-dependent
derivative contract on a stock. The derivative expires in nine months and the
risk-free rate is 4% per year compounded continuously. The analysts generate a
total of 20,000 paths using a geometric Brownian motion model, record the
payoff for each path, and present the results in the table shown below.
What is the estimated
price of the derivative?
选项：
A.USD 43.33
USD 43.77
USD 44.21
USD 45.10
解释：
Following the risk
neutral valuation methodology, the price of the derivative is obtained by
calculating the weighted average nine month payoff and then discounting this
figure by the risk free rate.
Average payoff
calculation: (2000*43 + 4000*44 + 10000*46 + 4000*45)/20000 = 45.10
Discounted payoff
calculation: 45.10* e-0.04*(5/12) = 43.77
折现的时候T为啥不是9/12啊？
