The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VωAPut(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is...

This paper proposes the sample path generation method for the stochastic volatility version of the CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to the American style S&P 100 index options...

We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy-stable models with maximal negative asymmetry. Particular cases, efficiency testing, and some qualitative features of the model are also discussed.