# EWMA using Monte-Carlo simulation

Im trying to forecast volatility using an EWMA model in python. Where i have return(t-1) and variance(t-1). n is number of days. for every Monte-carlo simulation N:

• t=1: Forecast the variance using: var(t+1)=(1-λ)*return(t-1)**2 + λ*variance(t-1) then calculating y(t+1)=sqrt(var(t+1))*gauss(0,1.0)

• t=2: forecast var(t+2)=(1-λ)*y(t+1) + λ * var(t+1) continue the process until t=n. then obtaining a (n,N) matrix taking the average column wise, to get an average daily variance.

Dataframe which i want to apply the simulation to:

Date
2015-01-02    0.005735
2015-01-05   -0.024288
2015-01-06    0.007963
2015-01-07    0.005912
2015-01-08    0.011647


Code:

def MC_simulation(y):
sim_df=pd.DataFrame
l=0.94
simulations= 1000
count=0
v=df1['variance'][-1]
v_list=[]
y_list=[]
v1=(1 - l)*(y**2) + (l*v)
v_list.append(v1)
y1=sqrt(v1)*gauss(0,1.0)
y_list.append(y1)

for t in range(simulations):

v1=(1-l)*(y_list[count]**2) + l * v_list[count]
y1=sqrt(v1)*gauss(0,1.0)
v_list.append(v1)
y_list.append(y1)
count +=1
sim_df= (sum(v_list)/simulations)
return sim_df

def annu(x):
return x*252

df3=pd.DataFrame()
df3=df1['ret'].apply(MC_simulation)
df3=df3.apply(annu)
df3=df3.to_frame()
df3=df3.rolling(window=63,center=False).mean()
df3=df3.apply(np.sqrt)


plot: The result I'm getting running this code does not seem to be correct. When I plot it against the realized volatility its completely off. I'm sure my loop is wrong, but I can not figure it out.

• Hi there and welcome. 1) Your question is close to being off-topic. Because it is about code. 2) Please include a plot of the predicted vs realized volatilities. – Jim Jun 18 '18 at 9:54
• In your case I would run a GARCH Modell and benchmark against this model. – Ferdi Jun 18 '18 at 10:13
• Yes, but what i try to do is compare the models against the realised volatility as i want to check which model would be the best predictor, for an optimal strike, for a variance/volatility swap. So using the GARCH as a benchmark would not give me any new information. – Vegard Jun 18 '18 at 10:15