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1. Consider 1-factor ane models for asset prices.
(a) What is the maximal A0(1) model? Derive formulas for futures prices and for
options on futures.
A0（1）应该是1 factor的gaussian model

(b) What is the maximal A1(1) model? What restrictive assumptions must be made
for the asset price and the parameters for the model to be admissible? Derive a
formula for futures prices and give a recipe for pricing options on futures (provide
as much detail as you can).

2. Consider the maximal A1(1) model for interest rates.
(a) Derive the PDE that bond prices must satisfy. Use our usual trick to show that
bond prices may be computed by solving a system of ODEs (write down the ODE
system, but you don't have to actually solve it).
(b) Show that the Vasicek model is a special case of the maximal A1(1) model, and
explicitly solve the ODE system in this case.