Given a single period binomial market (N=1), with a safe asset with return r=5% and a risky asset S with initial value S_0=1000 Dollars, and up-tick factor u=1.1 and down-tick factor d=0.9. An Arrow-Debreu security pays 1 Dollars, if the stock at t=1 ticks down, and zero else. In our Binomial model, this security, commonly used in economic modelling, is equivalent to the following derivative.

i. A European Put with strike 901 Dollars, as the only non-zero payoff at t=1 equals 901-900=1 Dollar.

ii. A European Call with strike 1099 Dollars, as the only non-zero payoff at t=1 equals 1100-1099=1 Dollar.

iii. An American Put with 1001 Dollars, as then by early exercise the value to the buyer equals 1001-1000=1 Dollar.

iv. An American Call with 999 Dollars, as then by early exercise, the value to the buyer equals 1000-999=1 Dollar.