On the dependence between a Wiener process and its running maxima and running minima processes

09/05/2021

∙

We study a triple of stochastic processes: a Wiener process W_t, t ≥ 0, its running maxima process M_t=sup{W_s: s ∈ [0,t]} and its running minima process m_t=inf{W_s: s ∈ [0,t]}. We derive the analytical formulas for the joint distribution function and the corresponding copula. As an application we draw out an analytical formula for pricing double barrier options.

READ FULL TEXT

On the dependence between a Wiener process and its running maxima and running minima processes

Efficient inverse Z-transform and pricing barrier and lookback options with discrete monitoring

Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation

Exact asymptotic characterisation of running time for approximate gradient descent on random graphs

Applications of multivariate quasi-random sampling with neural networks

Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression

Analytical calculation formulas for capacities of classical and classical-quantum channels

Correlators of Polynomial Processes

On the dependence between a Wiener process and its running maxima and running minima processes

Related Research

Efficient inverse Z-transform and pricing barrier and lookback options with discrete monitoring

Efficient Pricing of Barrier Options on High Volatility Assets using Subset Simulation

Exact asymptotic characterisation of running time for approximate gradient descent on random graphs

Applications of multivariate quasi-random sampling with neural networks

Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression

Analytical calculation formulas for capacities of classical and classical-quantum channels

Correlators of Polynomial Processes