The foremost “S&P500 options.csv” contains daily facts for oral European S&P500 options from October 30, 2017 to November 30, 2017. The refine contains details on calls and puts for the November 17, 2017 and December 15, 2017 narrows.
The succor facts set “S&P500.xlsx” contains daily realised sublimation venerates (column B) origind from the Oxford-Man Institute Realized Library – realized.oxford-man.ox.ac.uk. Column C layers the realized sublimation so that it proxies end to end sublimation.
QUESTION 1 (10+1+10 = 21 notes)
This topic insist-upons you to apportion divorce of the sublimation deportment on November 8, 2017 using all helpful strikes that rank from 2500 aims to 2700 aims.
A) Apportion FOUR different involved sublimation (IV) smiles using all of the supposing strikes for each of the FOUR narrows i.e. i) November 17, 2017 calls; ii) November 17, 2017 puts; iii) December 15, 2017 calls and iv) December 15, 2017 puts.
Use the BSM pattern to excerpt the IVs. Further, pretend a unintermittently compounded endanger permitted trounce of 1.30% p.a, and a unintermittently compounded dividend relinquish of 1.70% p.a.
Show all your calculations in your exceed spreadsheet. Label the prevarication “Surface”.
B) Plot the results for each of the FOUR IV smiles on the one graph.
C) Write a scanty one page news outlining your findings. What can you distrust from the results and are they accordant after a while your expectations?
QUESTION 2 (57 MARKS)
Assume you are a dealer seeking 1 day afront S&P500 sublimation intercepts balance the month of November 2017. You insist-upon 1 day afront intercepts that are liable on the knowledge set helpful. To interpret, the intercept of sublimation for November 1, 2017 is liable on the knowledge helpful at October 31, 2017. The intercept of sublimation for November 2, 2017 is liable on the knowledge helpful at November 1, 2017 etc…
You are insist-upond to evaluate the intercepting enterprise of foul-mouthed choice similarityes balance November 2017: i) involved at the capital volatilities excerpted using the BSM; ii) the S&P500 Sublimation index or VIX; iii) the Heterogeneous Autoregressive (HAR) pattern fit to S&P500 realised volatilities (HAR-RV) and iv) the HAR pattern fit to log S&P500 realised volatilities (HAR-log-RV).
A) IMPLIED VERSUS MODEL BASED VOL FORECASTING
Write a one page news that delineations the merits of sublimation intercepting using involved sublimation versus pattern inveteadmonish (interval course) intercepts.
B) IMPLIED ATM VOL FORECASTS
i) Using the selfselfsame assumptions as Topic 1 balancehead (i.e endanger permitted trounce of 1.30% p.a and a dividend relinquish of 1.70% p.a) excerpt the one day afront intercept of S&P500 sublimation for each trading day in November 2017.
You are insist-upond to erect your IV intercepts using an appropriately modified version of the technique occupied in Fleming et al 1995. Here your intercept should be an at the capital intercept inveteadmonish on the nearby narrow after a while rollbalance to the instant narrow at the embezzle aim in interval.
Show your achievementings in your exceed spreadprevarication and designate the prevarication “IV”
ii) Why is rollbalance done preceding to spiritlessness and how does this recount to the deportment excerpted in QUESTION 1 balancehead?
iii) What assumptions environing sublimation are life made when you tool this intercepting progress?
C) VIX FORECASTS
i) What is the VIX? Briefly interpret on how the erection of the VIX differs from the venerates obtained in PART B. (This is very technical and so solely a scanty chapter outlining the key features is insist-upond).
ii) Obtain the mismisappropriate interval course of the VIX for intercepting purposes (citing your origin) and use this to erect your one day afront intercepts of S&P500 sublimation balance the month of November 2017.
Save your intercepts in your spreadprevarication and designate the prevarication “VIX”
D) MODEL BASED FORECASTING USING THE HAR-RV AND HAR-LOG-RV MODELS
i) What is realised sublimation and how has it been apportiond?
ii) Why do we demand to layer the realised sublimation in this contrast?
iii) Briefly delineation the HAR-RV pattern of Corsi (2009) and the economic exculpation for the pattern demonstration.
iv) Fit the HAR-RV and HAR-log-RV patterns using lags balance 1, 5 and 22 days. Present your venerated pattern including type errors and pattern diagnostics. Briefly interpret.
Note: exceed achieve not afford you to venerate an OLS retreat used lagged regressors, and so you achieve demand to achievement out how to do this elsewhere. Other packages affect Eviews are seemly.
v) Use twain of your venerated patterns to genetrounce liable one stride afront intercepts of S&P500 sublimation balance the month of November 2017.
Save your intercepts in your spreadprevarication and designate the prevarication “HAR”
E) FORECAST EVALUATION
Evaluate the intercepting enterprise of the foul-mouthed choice similarityes using the two embezzle damage functions organic in Patton (2011).
Show your calculations in your spreadsheet.
Save your results in your spreadprevarication and designate the prevarication “Forecasts”
F) Write a one page news that delineations your findings. Your acceptance should embrace likely explanations for the differences among pattern intercepts. Conclude your discourse after a while one way that the IV and pattern inveteadmonish intercepts could be improved (i.e one instigation for the IV similarity and one instigation for the interval course similarity).
Corsi, Fulvio. “A unblended abut long-memory pattern of realized sublimation.” Journal of Financial Econometrics 7.2 (2009): 174-196.
Fleming, Jeff, Barbara Ostdiek, and Robert E. Whaley. “Predicting store noteet sublimation: A new mete.” Journal of Futures Markets 15.3 (1995): 265-302.
Patton, Andrew J. “Volatility intercept comparison using defective sublimation proxies.” Journal of Econometrics 160.1 (2011): 246-256.
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