Figure 1 Smile on SP 500 on March 19, 1999 from 1-Month Options01020304050600.700.750.800.850.900.951.001.051.101.151.20Figure 2 Smile on SP 500 on March 19, 1999 from 6-Month Options051015202530354045500.500.600.700.800.901.001.101.20Figure 3Bounds on the Slope of the Smile on 1-Month Options with ATM Vol. 21.8% and RRA Coefficient 0.8-30-20-10010203040500.90 0.91 0.92 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.02 1.03 1.04 1.05 1.06 1.08 1.11ProposedNon-ArbitrageProposedNon-ArbitrageObservedFigure 4Bounds on the Slope of the Smile on 6-Month Options with ATM Vol. 24.3% and RRA Coefficient 0.8-3-2-1012340.91 0.92 0.92 0.93 0.93 0.94 0.95 0.95 0.96 0.98 1.00 1.02 1.04 1.06 1.10 1.12ProposedNon-ArbitrageProposedNon-ArbitrageObservedFigure 5Bounds on the Slope of the Smile on 1-Month Options with ATM Vol. 21.8% and RRA Coefficient 0.2-30-20-10010203040500.90 0.91 0.92 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.02 1.03 1.04 1.05 1.06 1.08 1.11ProposedNon-ArbitrageProposedNon-ArbitrageObservedFigure 6Bounds on the Slope of the Smile on 6-Month Options with ATM Vol. 24.3% and RRA Coefficient 0.2-3-2-10123450.89 0.91 0.92 0.92 0.93 0.93 0.94 0.95 0.95 0.96 0.98 1.00 1.02 1.04 1.06 1.10ProposedNon-ArbitrageProposedNon-ArbitrageObserved