Bachelier Model for a Stock and Brownian motion Estimation

Question

Consider the Bachelier model for the stock (St)t0:

St = S0 + a t + bWt;

where (Wt)t0 is a Brownian motion and a; b > 0:

(a) Download daily data for the S&P 500 index for the twenty year period beginning in January 1994 until the end of 2013 (e.g., from yahoo finance). Use the data to estimate a and b for this model.

(b) Use Excel or another spreadsheet software to simulate a (discretized) sample path of a the Bachelier model over the year 2014 using 250 equidistant time steps, and compare it to the realized path. Just hand in the resulting plot.

Summary

This question belongs to finance and discusses about Bachelier model for the stock and to determine Brownian motion a and b from the given equation.

Total word count: 85