Use the S&P 500 index options data for April 3, 2014 posted on BlackBoard.

1. Calculate the time to expiration of May 2014 SPX options as of the market close on April 3, 2014.[1] These options expire on May 3, 2014.
2. Obtain from http://finance.yahoo.com/ the historical values of the S&P 500 index (^GSPC) from January 2, 2014 to April 3, 2014. Use daily closing prices adjusted for stock splits and dividends to compute returns. Using this sample of returns, estimate the S&P 500 index volatility as the sample standard deviation of returns.
3. Use the binomial OPM with 30 periods to price the May 2014 SPX call and put with a strike price of 1890 (Note: the number of periods is independent to the days to expiration).

Assume the following:

• The dividend yield on the S&P 500 index is 2.02% per year.
• The riskless interest rate (one-month LIBOR) for April 3, 2014 is 0.15% per year.

Please show formulas on excel

18 1/2/2014 1845.86 1845.86 1827.74 1831.98 1831.98 3.08-09 3/2014 1833.21 1838.24 1829.13 183137 183137 2.77E+09 1/6/2014 1832.31 1837.16 1823.73 1826 77 1826.77 3.29-09 1/7/2014 1828.71 1840.1 1828.71 183788 1837.88 3.51E+09 1/8/2014 18379 1840.02 18314 1837 49 1837.49 3.65E+09 1/9/2014 1839 1843.23 1830.38 1838.13 1838.13 3.58E+09 1/10/2014 1840.06 1843.15 1832.43 184237 1842.37 3.34E+09 1/13/2014 1841.26 1843.45 1815.52 1819.2 1819.2 3.59E+09 1/14/2014 1821.36 1839.26 182136 1838.88 1838.88 3.35E 09 1/15/2014 1840.52 1850.84 1840.52 1848.38 1848.38 3.78E+09 1/16/2014 1847.99 1847.99 1840.3 184589 1845.89 3.49E+09 1/17/2014 1844.23 1846.04 1835.23 18387 1838.7 3.63E+09 /21/2014 184105 1849.31 1832.38 1843.8 1843.8 3.78E+09 1/22/2014 1844 71 1846.87 1840.88 184486 1844.86 3.37E+09 1/23/2014 1842.29 1842.29 1820.06 182846 182846 3.97E+09 1/24/2014 1826.96 1826.96 1790.29 1790.29 1790.29 4.62E+09 1/27/2014 1791.03 1795.98 1772.88 178156 1781.56 4.05E+09 1/28/2014 1783 1793.87 1779.49 17925 1792.5 3.445+09 1/29/2014 1790.15 1790.15 1770.45 17742 1774.2 3.96E+09 1/30/2014 1777.171798.771777.171794.19 1794.19 3.55E 09 1/31/2014 1790.88 1793.88 1772.26 1782 59 1782.59 4.06E+09 2/3/2014 1782.68 1784.83 1739.66 174189 1741.89 4.73E+09 2/4/2014 1743.82 1758.73 1743.82 17552 1755.2 4.07E+09 2/5/2014 1753.38 1755.79 1737.92 1751.64 1751.64 3.98[+09 2/6/2014 1752.99 1774.06 1752.99 1773.43 1773.43 3.83-09 /7/2014 1776.01 1798.03 1776.01 1797.02 1797.02 3.78E+09 2/10/2014 1796.2 1799.94 1791.83 1799.84 1799.84 3.31E+09 2/11/2014 1800.45 1823.54 1800.41 1819.75 1819.75 3.7E 09 2/12/2014 1820.12 1826.55 1815.97 1819.26 1819.26 3.33-09 2/13/2014 1814.82 1830.25 1809.22 182983 1829.83 3.29E+09 2/14/2014 1828.46 1841.65 1825.59 1838.63 1838.63 3.11E+09 2/18/2014 1839.03 1842.87 1835.01 1840.76 1840.76 3.42E 09 2/19/2014 1838.9 1847.5 1826.99 1828.75 1828.75 3.66-09 2/20/2014 1829.24 1842.79 1824.58 1839 78 183978 3.4+09 2/21/2014 1841.07 1846.13 1835.6 1836.25 1836.25 3.4E+09 2/24/2014 1836.78 1858.71 1836.78 1847.61 1847.61 4.01E 09 2/25/2014 1847 66 1852.91 1840.19 1845.12 1845.12 3.52E+09 /26/2014 1845.79 1852.65 1840.66 1845.16 1845.16 3.72E+09 2/27/2014 1844.9 1854.53 1841.13 1854.29 185429 3.55E+09 2/28/2014 1855.12 1867.92 1847.67 1859.45 1859.45 3.92E+09 /3/2014 1857.68 1857.68 1834.44 1845.73 1845.73 3.43E+09 3/4/2014 1849.23 1876.23 1849.23 1873 91 1873.91 3.77[+09 3/5/2014 1874.05 1876.53 187111 1873.81 1873.81 3.39E+09 /6/2014 1874.18 1881.94 1874.18 1877.03 1877.03 3.36E 09 /7/2014 1878.52 1883.57 1870.56 1878.04 1878.04 3.56E+09 3/10/2014 1877.86 1877.87 1867.04 1877.17 1877.17 3.02E+09 3/11/2014 1878.26 1882.35 1863.88 1867.63 1867.63 3.39E+09 3/12/2014 1866.15 1868.38 1854.38 1868.2 1868.2 3.27E 09 3/13/2014 186906 1874.4 184186 1846 34 184634 3.67-09 3/14/2014 1845.07 1852.44 1839.57 184113 1841.13 3.29E+09 3/17/2014 184281 1862.3 1842.81 1858.83 1858.83 2.36E+09 18/2014 1858.92 1873.76 1858.92 187225 1872.25 2.93E+09 3/19/2014 1872 25 1874.14 1850.35 186077 1860.77 3.29E+09 3/20/2014 1860.09 1873.49 1854.63 1872.01 1872.01 3.33E+09 3/21/2014 1874.53 1883.97 1863.46 1866.52 1866.52 5.27E 09 3/24/2014 1867.67 1873.34 1849.69 1857.44 1857.44 3.41-09 3/25/2014 1859.48 1871.87 1855.96 185562 1865.62 3.2E+09 3/26/2014 1867.09 1875.92 1852.56 185256 1852.56 3.48E+09 3/27/2014 1852 11 1855.55 1842.11 1849.04 1849.04 3.73E 09 /28/2014 1850.07 1866.63 1850.07 1857.62 1857.62 2.96E+09 3/31/2014 1859.16 1875.18 1859.16 187234 1872.34 3.27E+09 4/1/2014 1873.96 1885.84 1873.96 1885.52 1885.52 3.34[+09 4/2/2014 1886.61 1893.17 1883.79 1890.9 1890.9 3.13E 09 4/3/2014 1891.43 1893.8 1882.65 1888.77 1888.77: 306-09 18 1/2/2014 1845.86 1845.86 1827.74 1831.98 1831.98 3.08-09 3/2014 1833.21 1838.24 1829.13 183137 183137 2.77E+09 1/6/2014 1832.31 1837.16 1823.73 1826 77 1826.77 3.29-09 1/7/2014 1828.71 1840.1 1828.71 183788 1837.88 3.51E+09 1/8/2014 18379 1840.02 18314 1837 49 1837.49 3.65E+09 1/9/2014 1839 1843.23 1830.38 1838.13 1838.13 3.58E+09 1/10/2014 1840.06 1843.15 1832.43 184237 1842.37 3.34E+09 1/13/2014 1841.26 1843.45 1815.52 1819.2 1819.2 3.59E+09 1/14/2014 1821.36 1839.26 182136 1838.88 1838.88 3.35E 09 1/15/2014 1840.52 1850.84 1840.52 1848.38 1848.38 3.78E+09 1/16/2014 1847.99 1847.99 1840.3 184589 1845.89 3.49E+09 1/17/2014 1844.23 1846.04 1835.23 18387 1838.7 3.63E+09 /21/2014 184105 1849.31 1832.38 1843.8 1843.8 3.78E+09 1/22/2014 1844 71 1846.87 1840.88 184486 1844.86 3.37E+09 1/23/2014 1842.29 1842.29 1820.06 182846 182846 3.97E+09 1/24/2014 1826.96 1826.96 1790.29 1790.29 1790.29 4.62E+09 1/27/2014 1791.03 1795.98 1772.88 178156 1781.56 4.05E+09 1/28/2014 1783 1793.87 1779.49 17925 1792.5 3.445+09 1/29/2014 1790.15 1790.15 1770.45 17742 1774.2 3.96E+09 1/30/2014 1777.171798.771777.171794.19 1794.19 3.55E 09 1/31/2014 1790.88 1793.88 1772.26 1782 59 1782.59 4.06E+09 2/3/2014 1782.68 1784.83 1739.66 174189 1741.89 4.73E+09 2/4/2014 1743.82 1758.73 1743.82 17552 1755.2 4.07E+09 2/5/2014 1753.38 1755.79 1737.92 1751.64 1751.64 3.98[+09 2/6/2014 1752.99 1774.06 1752.99 1773.43 1773.43 3.83-09 /7/2014 1776.01 1798.03 1776.01 1797.02 1797.02 3.78E+09 2/10/2014 1796.2 1799.94 1791.83 1799.84 1799.84 3.31E+09 2/11/2014 1800.45 1823.54 1800.41 1819.75 1819.75 3.7E 09 2/12/2014 1820.12 1826.55 1815.97 1819.26 1819.26 3.33-09 2/13/2014 1814.82 1830.25 1809.22 182983 1829.83 3.29E+09 2/14/2014 1828.46 1841.65 1825.59 1838.63 1838.63 3.11E+09 2/18/2014 1839.03 1842.87 1835.01 1840.76 1840.76 3.42E 09 2/19/2014 1838.9 1847.5 1826.99 1828.75 1828.75 3.66-09 2/20/2014 1829.24 1842.79 1824.58 1839 78 183978 3.4+09 2/21/2014 1841.07 1846.13 1835.6 1836.25 1836.25 3.4E+09 2/24/2014 1836.78 1858.71 1836.78 1847.61 1847.61 4.01E 09 2/25/2014 1847 66 1852.91 1840.19 1845.12 1845.12 3.52E+09 /26/2014 1845.79 1852.65 1840.66 1845.16 1845.16 3.72E+09 2/27/2014 1844.9 1854.53 1841.13 1854.29 185429 3.55E+09 2/28/2014 1855.12 1867.92 1847.67 1859.45 1859.45 3.92E+09 /3/2014 1857.68 1857.68 1834.44 1845.73 1845.73 3.43E+09 3/4/2014 1849.23 1876.23 1849.23 1873 91 1873.91 3.77[+09 3/5/2014 1874.05 1876.53 187111 1873.81 1873.81 3.39E+09 /6/2014 1874.18 1881.94 1874.18 1877.03 1877.03 3.36E 09 /7/2014 1878.52 1883.57 1870.56 1878.04 1878.04 3.56E+09 3/10/2014 1877.86 1877.87 1867.04 1877.17 1877.17 3.02E+09 3/11/2014 1878.26 1882.35 1863.88 1867.63 1867.63 3.39E+09 3/12/2014 1866.15 1868.38 1854.38 1868.2 1868.2 3.27E 09 3/13/2014 186906 1874.4 184186 1846 34 184634 3.67-09 3/14/2014 1845.07 1852.44 1839.57 184113 1841.13 3.29E+09 3/17/2014 184281 1862.3 1842.81 1858.83 1858.83 2.36E+09 18/2014 1858.92 1873.76 1858.92 187225 1872.25 2.93E+09 3/19/2014 1872 25 1874.14 1850.35 186077 1860.77 3.29E+09 3/20/2014 1860.09 1873.49 1854.63 1872.01 1872.01 3.33E+09 3/21/2014 1874.53 1883.97 1863.46 1866.52 1866.52 5.27E 09 3/24/2014 1867.67 1873.34 1849.69 1857.44 1857.44 3.41-09 3/25/2014 1859.48 1871.87 1855.96 185562 1865.62 3.2E+09 3/26/2014 1867.09 1875.92 1852.56 185256 1852.56 3.48E+09 3/27/2014 1852 11 1855.55 1842.11 1849.04 1849.04 3.73E 09 /28/2014 1850.07 1866.63 1850.07 1857.62 1857.62 2.96E+09 3/31/2014 1859.16 1875.18 1859.16 187234 1872.34 3.27E+09 4/1/2014 1873.96 1885.84 1873.96 1885.52 1885.52 3.34[+09 4/2/2014 1886.61 1893.17 1883.79 1890.9 1890.9 3.13E 09 4/3/2014 1891.43 1893.8 1882.65 1888.77 1888.77: 306-09