Parisian options are barrier options for which the knock-in/knock-out feature is only activated after the price process has spent a certain prescribed, consecutive time beyond the barrier. This specification has two motivations: First, there is the need to make the option more robust against short-term movements of the share price. This is achieved in Parisian options where it is ensured that a...

This paper investigates the pricing formula for barrier options where underlying asset is driven by sub-mixed fractional Brownian motion with jump. By applying corresponding Ito^’s formula, B-S type PDE derived a self-financing strategy. Furthermore, explicit obtained through converting to Cauchy problem. Numerical experiments are conducted test impact of price, Hurst index, jump intensity and ...

Black-Scholes (BS) equations, which are in the form of stochastic partial differential fundamental equations mathematical finance, especially option pricing. Even though there exists an analytical solution to standard form, not straightforward be solved numerically. The effective and efficient numerical method will useful solve advanced non-standard forms BS future. In this paper, we propose a ...

In Foreign Exchange Markets Compound options (options on options) are traded frequently. Instalment options generalize the concept of Compound options as they allow the holder to prolong a Vanilla Call or Put option by paying instalments of a discrete payment plan. We derive a closed-form solution to the value of such an option in the Black-Scholes model and prove that the limiting case of an I...

Tunnel amplitudes of molecular configurations (like neuronal channel pores) may be very sensitive to thermal vibrations of the barrier width (vibration-assisted tunneling) resulting in pseudo-random spikes of widely varying sizes. An observer who “lives” behind the barrier would experience as an “event” an accidental minimum of the barrier width, the timing being determined by the microstate of...

In this work, we derive an analytical solution for the value of Parisian up-and-in calls by using the “moving window” technique developed by Zhu and Chen [15] for pricing European-style Parisian up-and-out calls. Our pricing formula can be applied to both European-style and American-style Parisian up-and-in calls, due to the fact that with an “in” barrier, the option holder cannot do or decide ...