Reliability index and option pricing formulas of the first-hitting time model based on the uncertain fractional-order differential equation with Caputo type

T Jin, X Yang, H Xia, HUI Ding - Fractals, 2021 - World Scientific
Since the ability to control the investor's income or loss within a certain range, barrier option
has been among the most popular path-dependent options where its payoff depends on …

Discrete barrier and lookback options

SG Kou - Handbooks in operations research and management …, 2007 - Elsevier
Discrete barrier and lookback options are among the most popular path-dependent options
in markets. However, due to the discrete monitoring policy almost no analytical solutions are …

Continuously monitored barrier options under Markov processes

A Mijatović, M Pistorius - Mathematical Finance: An …, 2013 - Wiley Online Library
In this paper, we present an algorithm for pricing barrier options in one‐dimensional Markov
models. The approach rests on the construction of an approximating continuous‐time …

Barrier option pricing of mean-reverting stock model in uncertain environment

M Tian, X Yang, Y Zhang - Mathematics and Computers in Simulation, 2019 - Elsevier
The barrier options become activated or extinguished only if the underlying asset's price
reaches a predetermined level. Options of the former case are the knock-in options, and …

Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation

JL Kirkby - European Journal of Operational Research, 2023 - Elsevier
Hybrid equity-rate derivatives are commonly traded between financial institutions, but are
challenging to price with traditional methods. Especially challenging are those contracts …

An exact analytical solution for discrete barrier options

G Fusai, ID Abrahams, C Sgarra - Finance and Stochastics, 2006 - Springer
In the present paper we provide an analytical solution for pricing discrete barrier options in
the Black-Scholes framework. We reduce the valuation problem to a Wiener-Hopf equation …

[BOOK][B] Continuous-time Markov chain and regime switching approximations with applications to options pricing

Z Cui, J Lars Kirkby, D Nguyen - 2019 - Springer
In this chapter, we present recent developments in using the tools of continuous-time Markov
chains for the valuation of European and path-dependent financial derivatives. We also …

A double-exponential fast Gauss transform algorithm for pricing discrete path-dependent options

M Broadie, Y Yamamoto - Operations Research, 2005 - pubsonline.informs.org
This paper develops algorithms for the pricing of discretely sampled barrier, lookback, and
hindsight options and discretely exercisable American options. Under the Black-Scholes …

Analysis of quadrature methods for pricing discrete barrier options

G Fusai, MC Recchioni - Journal of Economic Dynamics and Control, 2007 - Elsevier
In the present paper we provide an analysis of a quadrature method combined with an
interpolation procedure for the valuation of discrete barrier options. The convergence of the …

An improved Markov chain approximation methodology: Derivatives pricing and model calibration

CC Lo, K Skindilias - … Journal of Theoretical and Applied Finance, 2014 - World Scientific
This paper presents an improved continuous-time Markov chain approximation (MCA)
methodology for pricing derivatives and for calibrating model parameters. We propose a …