European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

Guo, Zhidong; Liu, Yang; Dai, Linsong

doi:10.3390/fractalfract8010013

Cited by 3 publications

(2 citation statements)

References 34 publications

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“…Any missing parameters are provided in the figure captions. Additionally, all models are solved using the BGMRES(4) method with settings of N = 2 12 and M = 2 10 . The figures demonstrate that the stock loan prices, similar to American call options, are positioned above the pay-off function.…”

Section: Stock Loanmentioning

confidence: 99%

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A Preconditioned Policy–Krylov Subspace Method for Fractional Partial Integro-Differential HJB Equations in Finance

Chen,

Gong,

Sun

et al. 2024

Fractal Fract

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To better simulate the prices of underlying assets and improve the accuracy of pricing financial derivatives, an increasing number of new models are being proposed. Among them, the Lévy process with jumps has received increasing attention because of its capacity to model sudden movements in asset prices. This paper explores the Hamilton–Jacobi–Bellman (HJB) equation with a fractional derivative and an integro-differential operator, which arise in the valuation of American options and stock loans based on the Lévy-α-stable process with jumps model. We design a fast solution strategy that includes the policy iteration method, Krylov subspace method, and banded preconditioner, aiming to solve this equation rapidly. To solve the resulting HJB equation, a finite difference method including an upwind scheme, shifted Grünwald approximation, and trapezoidal method is developed with stability and convergence analysis. Then, an algorithmic framework involving the policy iteration method and the Krylov subspace method is employed. To improve the performance of the above solver, a banded preconditioner is proposed with condition number analysis. Finally, two examples, sugar option pricing and stock loan valuation, are provided to illustrate the effectiveness of the considered model and the efficiency of the proposed preconditioned policy–Krylov subspace method.

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Section: Stock Loanmentioning

confidence: 99%

“…Hawkes jump diffusion models [6], mixed fractional Brownian model [7], two-factor nonaffine stochastic volatility model [8], and sub-fractional Brownian model [9,10]. The model based on the Lévy process, notable for its ability to model price jumps and transform into a fractional diffusion equation [11], is among these.…”

Section: Introductionmentioning

confidence: 99%

A Preconditioned Policy–Krylov Subspace Method for Fractional Partial Integro-Differential HJB Equations in Finance

Chen,

Gong,

Sun

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

Pricing European option under the generalized fractional jump-diffusion model

Guo,

Wang,

Kang

2024

Fract Calc Appl Anal

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Pricing geometric average Asian options in the mixed sub-fractional Brownian motion environment with Vasicek interest rate model

Wang,

Wang

2024

MATH

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<p>Considering the characteristics of long-range correlations in financial markets, the issue of valuing geometric average Asian options is examined, assuming that the variations of the underlying asset follow the mixed sub-fractional Brownian motion, and the dynamics of short-term interest rate satisfies the mixed sub-fractional Vasicek model. Based on the principle of no arbitrage, the definite solution of PDE of a zero-coupon bond for geometric average Asian options under the circumstance of the mixed sub-fractional is given by the delta hedging technique. The derivation of the explicit pricing formula for geometric average Asian options with fixed strike price is achieved through the utilization of multiple variable substitutions. Furthermore, we perform numerical calculations to analyze the performance of the model.</p>

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European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

Cited by 3 publications

References 34 publications

A Preconditioned Policy–Krylov Subspace Method for Fractional Partial Integro-Differential HJB Equations in Finance

A Preconditioned Policy–Krylov Subspace Method for Fractional Partial Integro-Differential HJB Equations in Finance

Pricing European option under the generalized fractional jump-diffusion model

Pricing geometric average Asian options in the mixed sub-fractional Brownian motion environment with Vasicek interest rate model

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