Complete the binomial tree to price ATM European and American put options on a non-dividend-paying index with 3-month maturity in three steps. The index is currently priced at $470 with 17.5% volatility and the risk-free rate is 0.25%.

S0= 470. K = 470. r= 0.25% T=0.25 Sigma= 0.175

What is Delta T, u, and d for the binomial tree

Suuu fuuu 0.00 Suu f_uu 0.00 Suud S_u fu 0.00 f uud 0.00 470.00 0.00 S_ud f_ud 0.00 s_d fd S_udd f_udd 0.00 0.00 S_dd f dd 0.00 S_ddd f_ddd 0.00 Suuu fuuu 0.00 Suu f_uu 0.00 Suud S_u fu 0.00 f uud 0.00 470.00 0.00 S_ud f_ud 0.00 s_d fd S_udd f_udd 0.00 0.00 S_dd f dd 0.00 S_ddd f_ddd 0.00