The number of possible final average prices in an Asian option for a four period binomial model is
A)8
B)4
C)16
D)32
E)none of the above

Question

Quizplus · Accepted Answer

In a four period binomial model, there are 5 possible final stock prices (because at each period, the stock can go up or down). Therefore, there are 5^4 = 625 possible combinations of final stock prices. However, for an Asian option, we are interested in the average of these final prices. This means that for each combination of final prices, we need to calculate the average and keep track of how many times each average appears. Since the final prices can take on any value between zero and twice the initial stock price, there are an infinite number of possible averages. However, in practice, we can calculate the averages for a large number of possible final price combinations (say, 10,000), and then group them into buckets of a certain width (say, 0.05). The number of buckets will depend on the width chosen, but let's say there are 16 buckets. Then, each of the 10,000 possible average prices falls into one of these 16 buckets. Therefore, the number of possible final average prices is 16.

The Number of Possible Final Average Prices in an Asian