Pricing American continuous-installment options under stochastic volatility model

Deng, Guohe

doi:10.1016/j.jmaa.2014.11.049

Cited by 7 publications

(2 citation statements)

References 26 publications

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“…As such, a number of revised models have been suggested, leading to the development of more sophisticated models, those which are well suited in explaining unusual markets dynamics. A few examples of these revised models are but not limited to regime-switching and jump diffusion models [4][5][6], stochastic volatility models [7][8][9], and stochastic interest rates models [10][11][12] just to mention but a few.…”

Section: Introductionmentioning

confidence: 99%

“…The front-fixing method has been applied successfully to a wide range of problems arising in population dynamics [27] and finance [28][29][30][31][32][33][34]. There are numerous other similar techniques used in solving American option problems, for example singularity separating method [32,35] and Penalty methods [9,34]. The idea behind the front-fixing approach is to use some change of variables to transform the problem from a moving boundary problem to a fixed boundary problem.…”

Section: Introductionmentioning

confidence: 99%

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A Robust Numerical Simulation of a Fractional Black–Scholes Equation for Pricing American Options

Nuugulu,

Gideon,

Patidar

2024

J Nonlinear Math Phys

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After the discovery of fractal structures of financial markets, fractional partial differential equations (fPDEs) became very popular in studying dynamics of financial markets. Available research results involves two key modelling aspects; firstly, derivation of tractable asset pricing models, those that closely reflects the actual dynamics of financial markets. Secondly, the development of robust numerical solution methods. Often times, most the effective models are of a nonlinear nature, and as such, reliable analytical solution methods are seldomly available. On the other hand, the accurate value of American options strongly lies on the unknown free boundaries associated with these types of derivative contracts. The free boundaries emanates from the flexibility of the early exercise features with American options. To the best of our knowledge, the approach of pricing American options under the fractional calculus framework has not been extensively explored in literature, and an obvious wider research gap still exist on the design of robust solution methods for pricing American option problems formulated under the fractional calculus framework. Therefore, this paper serve to propose a robust numerical scheme for solving time-fractional Black–Scholes PDEs for pricing American put option problems. The proposed scheme is based on the front-fixing algorithm, under which the early exercise boundaries are transformed into fixed boundaries, allowing for a simultaneous computation of optimal exercise boundaries and their corresponding fair premiums. Results herein indicate that, the proposed numerical scheme is consistent, stable, convergent with order $${\mathcal {O}}(h^2,k)$$ O ( h 2 , k ) , and also does guarantee positivity of solutions under all possible market conditions.

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