Continuously Paying Options (CPOs) form a very natural class of derivatives for hedging risks coming from adverse movements of a continuously traded asset. We study the rate of convergence of CPOs evaluated under the ...

This article examines the martingale difference hypothesis (MDH) and the random walk hypothesis (RWH) for nine conventional and nine Islamic stock indices: Asia-Pacific, Canadian, Developed Country, Emerging, European, ...

Considering a general class of regime-switching geometric random walks and a broad class of piecewise twice differentiable payoff functions, we show that convergence of option prices occurs at a speed of order 𝒪 (𝑛-ᵝ), ...

The martingale problem for superprocesses with parameters (𝛏, Ф, 𝑘) is studied where 𝑘(𝒹𝑠) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of ...

The valuation of American options is an optimal stopping time problem which typically leads to a free boundary problem. We introduce here the randomization of the exercisability of the option. This method considerably ...

This paper examines the random walk hypothesis (RWH) and the martingale difference hypothesis (MDH) for the Australian dollar and five Asian emerging currencies relative to three benchmark currencies. We use Wright’s (2000) ...

We study the value of European security derivatives in the Black-Scholes model, when the underlying asset 𝛏 is approximated by random walks 𝛏(𝑛). We obtain an explicit error formula, up to a term of order 𝒪(𝑛⁻³/² ), ...

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 ...

The analysis of the convergence of tree methods for pricing barrier and lookback options has been the subject of numerous publications aiming at describing, quantifying, and improving the slow and oscillatory convergence ...