We apply the multilevel Monte Carlo method for option pricing problems using exponential Lévy models with a uniform timestep discretisation. For lookback and barrier options, we derive estimates of the convergence rate of the error introduced by the discrete monitoring of the running supremum of a broad class of Lévy processes. We then use these to obtain upper bounds on the multilevel Monte Ca...

Abstract Introduction Community Conservation Initiatives o Two Regions with Special Partnerships and Selective Strategies o Example 1: West Coast Vancouver Island (WCVI) o Example 2: Lower Fraser River Summary Analysis of Key Barriers to Community Conservation Initiatives and Options for Overcoming Identified Barriers o Category 1 Barriers  Barrier: Government's Desire to Control Data  Option...

In the present paper we explore the problem for pricing discrete barrier options utilizing the Black–Scholes model for the random movement of the asset price. We postulate the problemas a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number...

An external barrier of an option contract is a stochastic variable which determines whether the option is knocked in or out when the value of the variable is above or below some predetermined level, but itself is not the price of an asset which underlies the option. In this paper, we present analytic formulation for the valuation of European options on one or multiple assets with single externa...

A time-dependent double-barrier option is a derivative security that delivers the terminal value φ(ST ) at expiry T if neither of the continuous time-dependent barriers b± : [0, T ]→R+ have been hit during the time interval [0, T ]. Using a probabilistic approach, we obtain a decomposition of the barrier option price into the corresponding European option price minus the barrier premium for a w...

The double barrier option is characterized by pay-off with strike K, maturity T, upper Su and lower Sd barrier levels and the corresponding rebates φu and φd which can be time dependent. We divide last four quantities by strike K and introduce new variables x = ln(S/K), xu = ln(Su/K), xd = ln(Sd/K). The value of European double barrier call option U(t, x) satisfies the extended Black-Scholes eq...