The First Sp500 Optionscsv Contains Daily Data For Tradition

The First Sp500 Optionscsv Contains Daily Data For Traditional Eur The first “S&P500 options.csv” contains daily data for traditional European S&P500 options from October 30, 2017 to November 30, 2017. The file contains details on calls and puts for the November 17, 2017 and December 15, 2017 contracts. The second data set “S&P500.xlsx” contains daily realised volatility estimates sourced from the Oxford-Man Institute Realized Library – realized.oxford-man.ox.ac.uk.

Column B contains realized volatility estimates, and column C scales the realized volatility to proxy close-to-close volatility.

QUESTION 1 (10+1+10 = 21 marks) This question requires you to calculate part of the volatility surface on November 8, 2017, using all available strikes ranging from 2500 points to 2700 points.

A) Calculate four separate implied volatility (IV) smiles using all of the provided strikes for each of the four contracts: i) November 17, 2017 calls; ii) November 17, 2017 puts; iii) December 15, 2017 calls; and iv) December 15, 2017 puts. Use the Black-Scholes-Merton (BSM) model to extract the IVs. Assume a continuously compounded risk-free rate of 1.30% p.a. and a continuously compounded dividend yield of 1.70% p.a. Show all your calculations in your Excel spreadsheet, labeling the sheet “Surface.”

B) Plot the results for each of the four IV smiles on a single graph.

C) Write a brief one-page report outlining your findings. Discuss what you can infer from the results and whether they are consistent with your expectations.

QUESTION 2 (57 marks) Assume you are a trader seeking one-day-ahead S&P 500 volatility forecasts over November 2017. You require forecasts conditional on the information set available each day. For example, the forecast for November 1, 2017, is based on information available at October 31, 2017.

A) Write a one-page report contrasting the merits of volatility forecasting using implied volatility versus model-based (time series) forecasts.

B) Implied ATM Volatility Forecasts: i) Using the assumptions from Question 1, extract the one-day-ahead forecast of S&P 500 volatility for each trading day in November 2017. Use an appropriately modified version of Fleming et al.'s (1995)

technique for at-the-money implied volatility. Construct your forecasts based on the nearby contract with rollovers to the next contract at suitable times. Show your workings in your Excel sheet labeled “IV.” ii) Explain why rollovers are performed prior to expiration and how this relates to the surface in Question 1. iii) Discuss the assumptions about volatility inherent in this forecasting procedure.

C) VIX Forecasts: i) Briefly explain what the VIX is and how its construction differs from the estimates obtained in Part B. ii) Obtain the VIX time series data for the relevant period, citing your source, and use it to construct one-day-ahead forecasts of S&P 500 volatility for November 2017. Save these forecasts in your spreadsheet labeled “VIX.” D) Model-Based Forecasting using HAR-RV and HAR-Log-RV: i) Define realized volatility and describe how it has been calculated. ii) Explain why scaling realized volatility is necessary in this context. iii) Summarize the HAR-RV model of Corsi (2009) and its economic rationale. iv) Fit the HAR-RV and HAR-Log-RV models using lags of 1, 5, and 22 days. Present your estimates with standard errors and diagnostics. v) Use your models to generate one-step-ahead volatility forecasts for November 2017, saving results in your sheet “HAR.” E) Forecast Evaluation: Evaluate the performance of the four methods using two appropriate loss functions per Patton (2011).

Document your calculations in the spreadsheet, saving the results in a sheet labeled “Forecasts.”

F) Write a one-page report discussing your findings, possible reasons for differences between forecasts, and suggesting improvements for the implied volatility and model-based approaches.

References: - Corsi, F. (2009). A simple approximate long-memory model of realized volatility. Journal of Financial

Econometrics.

- Fleming, J., Ostdiek, B., & Whaley, R. E. (1995). Predicting stock market volatility: A new measure.

Journal of Futures Markets.

- Patton, A. J. (2011). Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics.