Algorithm design.
1.
a) Price series simulation: Assume that the asset simple return obeys a normal random variable with an initial price of 1. Please simulate the price series for the next 100 days based on this return distribution. (Note: simple return on day t = price on day t / price on day t-1 - 1)
b) Design a function with an input of price series X to calculate the maximum retracement. and use this function to calculate the maximum retracement of the above simulated series.
c) Improve the performance of the next algorithm so that the time complexity is O(n) and the space complexity is O(1). (Hint: only one loop is needed to find the local maximum first, then calculate the retracement, and finally the maximum retracement)
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