If δ = 0 (for any value of ˜ c), the pricing formula (35) reduces to the Black–Scholes
pricing formula with square-volatility σ2m
β2 + σ2 as it should be since that case
corresponds to the linear CAPM model described in Sect. 2.1. This reduction
is actually not straightforward. One needs to remark that A2 = 0, and a + ˜c
recombines, so that Ψ± becomes x + A1T + σmw + σ z.