Long-term option pricing with a lower reflecting barrier

This paper considers the pricing of long-term options on assets such as housing, where either government intervention or economic nature asset is assumed to limit large falls in prices. The observed price modelled by a geometric Brownian motion (the 'notional price') reflected at lower barrier. resulting has standard dynamics but with localised barrier, which allows arbitrage interim losses; this funded government's unlimited powers intervention, and its exploitation subject credit constraints. Despite lack an equivalent martingale measure for price, can be expressed compound arbitrage-free notional risk-neutral arguments applied. Because option deltas tend zero when approaches hedging gives same results so exactly replicates payoffs. Hedging schemes are not unique, cheapest scheme any derivative being one best exploits interventions put clear: direct replication initial cost than synthetic replication, portfolio always positive value. call ambiguous: may give losses, preferred strategy (and hence price) depend what margin payments need made these losses.