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; th...

This paper considers the problem of evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993). We develop a method of lines approach as it conveniently delivers not only the price, but also the delta and gamma of the option. The method is able to efficiently handle both continuously monitored and d...