2. Estimate the volatility of Citigroup.

a. Calculate the daily returns of Citigroup (file BigGameCitigroupData.cvs). (Link is as below)

b. Use the excel function STDEV to estimate the volatility of the daily returns within the last year (Jan 26, 2007 to Jan 25, 2008). Multiply the daily volatility by the square root of 252 (number of trading days per year) to get the annualized volatility. Further, estimate the annualized volatility within the last 6 months (July 26, 2007 to Jan 25, 2008).

c. Construct the volatility surface using the options in Exhibit 3. Assume the dividend yield for options with 1 year to maturity is 3.6% and for options with 2 years to maturity 2.6%. Use the Excel Option Pricing Tool from our class. Use the excel Solver Add-in to find a volatility (cell C6) such that the option prices in Exhibit 3 match the American option prices in cells R17 and R18 in a Binomial tree with n = 250 steps. How do the option implied volatilities compare to the volatility estimated from the past 1 year or 6 months of daily data?

d. Estimate the volatility of daily returns from Jan 28, 2008 to Jan 1, 2011. How does this volatility compare to the estimates in questions (b) and (c)?

#BigGameCitigroupData.cvs excel Link is as below:

https://docs.google.com/spreadsheets/d/1iAJvJq5LAl02wubXNvswQrZriWZskoSrntm_n4deB-o/edit?usp=sharing

#Exhibit3

Exhibit 3 Listed American Options on Citigroup Stock on January 25, 2008 Expiration Option Type Strike Price Bid Ask Open Date Symbol $ ($) Interest VRN.AE Call 25 4.70 4.70 39,297 17 Jan 2009 VRN.AF Call 30 2.60 2.61 87,923 VRN.ME Put 25 3.40 3.45 69,211 VRN.MF Put 30 6.25 6.25 105,537 WRV.AE Call 25 6.10 6.40 19,821 16 Jan 2010 WRV.AF Call 30 4.15 4.45 44,015 WRV.ME Put 25 4.75 4.90 23,785 WRV.MF Put 30 7.55 7.90 49,501 No options with a longer maturity were listed. The bid price or 'bid' (ask price or 'ask') is the price received (paid) by option sellers (buyers). The 'open interest' for a given option is the number of options outstanding, i.e., the number of long positions (which equals that of short positions)