11.9 Is Normality realistic? >If returns are normal and thus prices are lognormal and assuming that volatility is at 20%(about the historical average) On 10/19/87 the 2 month s&P 500 Futures dropped 29% This was a-27 sigma event with a probability of occurring of once in every 10160 days On 10/13/89. the s&P 500 index lost about 6% This was a-5 sigma event with a probability of 0.00000027 or once every 14, 756 years Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University11.9 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University Is Normality Realistic? ➢ If returns are normal and thus prices are lognormal and assuming that volatility is at 20% (about the historical average) – On 10/19/87, the 2 month S&P 500 Futures dropped 29% • This was a -27 sigma event with a probability of occurring of once in every 10160 days – On 10/13/89, the S&P 500 index lost about 6% • This was a -5 sigma event with a probability of 0.00000027 or once every 14,756 years