Simulating a Random Walk in pandas is easy enough (this link gives a guide on one way to do so).
I am interested in taking things a step further, finding optimal entry/exit points for a set of random walks. The easiest way to explain this is to think of it like buying stocks. For a provided random walk, our "Entry Point" is our buy price - that is, if the random walk reaches a value less than or equal to our entry, we will "Buy" there. (This value is denoted B, for ease).
We are also able to select 2 exit points that work fairly similarly (denoted E0 and E1, for ease, with E0 < B < E1). If we have already bought, and the random walk reaches a value less than or equal to E0, we will "Sell" there. If we have bought and the random walk reaches a value greater than or equal to E1, we will "Sell" there.
The benefit gained from each random walk is:
- 0 if we never buy
- (The last value in the walk) - B if we buy but do not sell
- E0 - B if we sell at E0
- E1 - B if we sell at E1
I am looking for to determine the values E0, B, and E1 that maximize total benefit gained from a set of random walks. My current plan to use scipy to approach this is as follows:
from scipy.optimize import minimize
def BenefitFromOneRandomWalk(R, E0, B, E1):
#Returns the benefit gained with the entry/exit points provided
#This works by going through the series one value at a time
#I question whether it could be made more efficient
Bought = False
for price in R:
if (not Bought) and price <= B:
Bought = True
elif Bought and price <= E0:
return E0 - B
elif Bought and price >= E1:
return E1 - B
LastValue = R[-1]
if Bought:
return LastValue - B
return 0
def TotalBenefits(RandomWalks, ExitPoints):
#Return the total benefit of all random walks, using the same entry/exits
E0, B, E1 = ExitPoints
return sum([BenefitFromOneRandomWalk(R, E0, B, E1) for R in RandomWalks])
def FindOptimalEntryAndExitPoints(RandomWalks):
#Use scipy's minimize feature to estimate optimal entry/exit points
x0 = [1, 1, 1]
def ScoreExitPoints(e):
return -1*TotalBenefits(RandomWalks, e)
res = minimize(ScoreExitPoints, x0, method='Nelder-Mead', tol=1e-2)
return res.x
Is there a more efficient way to go about this, or is this the optimal solution?
EDIT: For the sake of simplicity, we can buy and sell only once each per random walk.
