18.11 Calculation of gamma Gamma is calculated from the nodes at time 2st 064-3.77 3.77-1036 △ 024:△,= 064 6299-50 50-3969 Gamma= 003 1165 Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.11 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull Calculation of Gamma Gamma is calculated from the nodes at time 2dt 1 2 2 0 64 377 62 99 50 0 24 377 10 36 50 39 69 0 64 1165 0 03 = − − = − = − − = − − = . . . . ; . . . . . Gamma = . 1
18.12 Calculation of Theta Theta is calculated from the central nodes at times o and 2st 3.77-4.49 Theta =4.3 per year 0.1667 or-0.012 per calendar day Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.12 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull Calculation of Theta Theta is calculated from the central nodes at times 0 and 2dt or . per calendar day Theta = per year 0 012 4.3 0.1667 3.77 4.49 - = − −
18.13 Calculation of Vega o We can proceed as follows Construct a new tree with a volatility of 41% instead of 40% Value of option is 4.62 ° Vega is 4.62-449=0.13 per 1% change in volatility Options, Futures, and Other Derivatives, 5th edition C 2002 by John C Hull
18.13 Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull Calculation of Vega • We can proceed as follows • Construct a new tree with a volatility of 41% instead of 40%. • Value of option is 4.62 • Vega is 4.62 − 4.49 = 0.13 per 1% change in volatility