Double Barrier Options

Alternative models for FX: pricing double barrier options in regime-switching Lévy models with memory ArXiv ID: 2402.16724 “View on arXiv” Authors: Unknown Abstract This paper is a supplement to our recent paper Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models". We introduce the class of regime-switching Lévy models with memory, which take into account the evolution of the stochastic parameters in the past. This generalization of the class of Lévy models modulated by Markov chains is similar in spirit to rough volatility models. It is flexible and suitable for application of the machine-learning tools. We formulate the modification of the numerical method in Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models", which has the same number of the main time-consuming blocks as the method for Markovian regime-switching models. ...

Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models ArXiv ID: 2312.03915 “View on arXiv” Authors: Unknown Abstract We analyze the qualitative differences between prices of double barrier no-touch options in the Heston model and pure jump KoBoL model calibrated to the same set of the empirical data, and discuss the potential for arbitrage opportunities if the correct model is a pure jump model. We explain and demonstrate with numerical examples that accurate and fast calculations of prices of double barrier options in jump models are extremely difficult using the numerical methods available in the literature. We develop a new efficient method (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied to the Bromwich integral; the SINH-acceleration and simplified trapezoid rule are used to evaluate perpetual double barrier options for each value of the spectral parameter in GWR-algorithm. The program in Matlab running on a Mac with moderate characteristics achieves the precision of the order of E-5 and better in several several dozen of milliseconds; the precision E-07 is achievable in about 0.1 sec. We outline the extension of GWR-SINH method to regime-switching models and models with stochastic parameters and stochastic interest rates. ...