Assignment 1

Assignment 1

Imagine you are a gold trader and specifically, you trade gold options. As such you are very aware that volatility is critical to your understanding of option pricing. Your immediate supervisor asks you some questions concerning volatility in the market. Your supervisor has provided you with a time series of gold prices and the volume of gold trading. The data runs from Jan 2003 to May 2006 and can be found in Gold.xls in Assignment 1 folder.

He has asked you to estimate volatilities for gold. As a good student of Fina6282, you first proceed with identifying the appropriate time series process for the gold futures prices. Question 1

1A) Provide a time series plot (chart) of the gold futures price.

Discuss

1B) Test the gold futures price time series fora) Stationarity

b) Plot ACF and PACF functions

Discuss the results of these tests and any implications for your modeling process

1C) First-difference the gold prices and plot again.

Compare to the original undifferenced plots.

1D) Test the differenced gold price time series for

c) Stationarity

d) Plot ACF and PACF

Discuss the results of these tests and any implications for your modeling process.

1D) Identify the appropriate time series model for the gold prices; a) Determine the appropriate p, d, q.b) Estimate the ARIMA model(s) you determined above.

c) Test residuals for white noise.

d) In case you have multiple candidate models, pick the best one from the well behaved models. Explain your reasoning why you think this is the right way to model Gold price series.

e) Write out the final model (with coefficients). Interpret the results.

1E) Forecast changes in gold futures prices 6 periods ahead using your final ARIMA model. Question 2

2A) Estimate an AR(p,d,q) GARCH(1,1) model depending on the p, d, q you determined above. Provide the output from the model. 2B) From the AR(p,d,q) GARCH(1,1) output answer the following: What is the GARCH1 parameter estimate and ARCH1 parameter estimate in the GARCH volatility equation? Are they statistically significant (what p value do each of them have)?

SUPPORT YOUR ANSWERS WITH APPROPRIATE EXCERPTS FROM SAS OUTPUT.

Attach your SAS code with the answers. Append it to the end of file and save as pdf. Submit via Blackboard.