CSV file link "StVolat.csv" : https://drive.google.com/file/d/1Sxlg_LZhHFM6RSk3BANX0HKVR9P-sTP5/view?usp=sharing

Plz do the problem using Rstudio

"StVolat.csv" contains the values of VIX and VXN (stochastic volatility indexes) between the dates 11/1/2012 and 10/1/2017.

VIX is the ticker symbol for the Chicago Board Options Exchange volatility index, which shows the market's expectation of a 30-day volatility. It is constructed using the implied volatilities of a wide range of SP500 index options. VXN is a measure of market expectations of 30-day volatility for the Nasdaq-100 market index, as implied by the price of near-term options on this index.

a) Consider modeling the VIX and VXN using continuous uniform, normal, exponential, and gamma random variables. For each case, estimate the model parameters using the data (you can use the maximum and minimum values for the uniform distribution and the method of moments for the rest). Which one provides the best fit (visually).

b) For each estimated model, compute the probability that VIX will exceed 15 points and the probability that VXN will exceed 15 points (separately)? Comment on your findings.

c) Assuming that VIX and VXN are exponentially distributed, compute the probability that each will exceed 15 points given that the index has already exceeded 10 points so far? Hint: You need to compute P(VXN>15|VXN>10) and P(VIX>15|VIX>10).