Abstract:
This paper proposes a class of complete financial market models, the benchmark models,
with security price processes that exhibit intensity-based jumps. The benchmark or
reference unit is chosen to be the growth-optimal portfolio. Primary security account
prices, when expressed in units of the benchmark, turn out to be local martingales. In the
proposed framework an equivalent risk-neutral measure need not exist. Benchmarked fair
derivative prices are obtained as conditional expectations of future benchmarked prices
under the real-world probability measure. This concept of fair pricing generalizes the
classical risk-neutral approach and the actuarial present-value pricing methodology.
