13.11 Gamma Gamma(r) is the rate of change of delta() with respect to the price of the underlying aa af as aS Figure 13.9(p. 325)[for a call or put Gamma Stock Price Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 13.11 Gamma • Gamma () is the rate of change of delta () with respect to the price of the underlying • Figure 13.9 (p. 325) [for a call or put] 2 2 S f S = = • Gamma X Stock Price
13.12 Equation for gamma The Gamma( f) for a European call or put paying a continuous dividend g is F N'(d, y o√T where N"(d1)=n(a1 e 2丌 Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 13.12 Equation for Gamma • The Gamma () for a European call or put paying a continuous dividend q is where S T N d qT 0 1 '( )e − = / 2 1 1 2 1 e 2 1 '( ) ( ) d N d n d − = = •
13.13 Gamma Addresses delta Hedging Errors Caused By curvature Figure 13.7(p. 322) C" Price Stock price Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University
Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University 13.13 Gamma Addresses Delta Hedging Errors Caused By Curvature • Figure 13.7 (p. 322) Call Price S C S' Stock Price C'' C' •