题目
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.「huixue_img/importSubject/1564169523173658624.png」What is the estimated price of the derivative?
选项
A.USD 43.33
B.USD 43.77
C.USD 44.21
D.USD 45.10
答案
B
解析
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-0.04×9/12=43.77 根据风险中性估值方法，衍生品的价格是通过计算9个月的加权平均收益，然后用无风险利率折现得出的。平均收益计算:(2000×43＋4000×44＋10000×46＋4000×45)/ 20000 = 45.10。收益的折现值:45.10×e^(－0.04×9/12)=43.77