  We propose an extension of the Cox-Ross-Rubinstein (CRR) model based on
q-binomial (or Kemp) random walks, with application to default with logistic
failure rates. This model allows us to consider time-dependent switching
probabilities varying according to a trend parameter, and it includes tilt and
stretch parameters that control increment sizes. Option pricing formulas are
written using q-binomial coefficients, and we study the convergence of this
model to a Black-Scholes type formula in continuous time. A convergence rate of
order O(1/N) is obtained when the tilt and stretch parameters are set equal to
one.
