Pricing, no-arbitrage bounds and robust hedging of instalment options

An instalment option is a European option in which the premium, instead of being paid up-front, is paid in a series of instalments. If all instalments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these options, in particular the use of static hedges, and also study a continuous-time limit in which premium is paid at a certain rate per unit time.