We describe a broad setting under which, for European options, if the underlying asset form a geometric random walk then, the error with respect to the Black-Scholes model converges to zero at a speed of 1/n for continuous payoffs functions, and at a speed of 1/√n for discontinuous payoffs...

A closed-form solution is obtained for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. The computation of coefficients embedded in the closed-form expression can be...

This paper presents an investigation into a random walk on a cycle graph with restricted forward movement at most $m$ steps, known as the forward jump random walk. The study derives precise formulas for the probability mass function of the arriving state, the hitting time, and its expected value...