© K. Cuthbertson and D. Nitzsche Figures for Chapter 17 ASSET PRICE DYNAMICS (Financial Engineering : Derivatives and Risk Management)

© K. Cuthbertson and D. Nitzsche Figure 17.1 : Finite difference grid T tt time, t (index k = T - k  t ) SS Current Stock Price: S = 4(  S). Hence value of f 4 0 will be solution for the option premium. f 3 6 is determined by the values of f at points A, B and C 0 Stock Price (index i) 4 A B C

© K. Cuthbertson and D. Nitzsche Figure 17.2 :Use of grid points Differential with respect to S (index for S is i ) Value of option, f(S,t) (index for t is k) Differential with respect to time (Note: as k increases t decreases) f i k+1   f i k f k i+1  f i k  f k i-1  Central difference forward difference backward difference  f k i+1  f i k  f k i-1 f i k+1 

© K. Cuthbertson and D. Nitzsche Figure 17.3 :Approximations for  f /  S S f SS SS Central difference Backward difference Forward difference Derivative required for this point f i+1 fifi f i-1