An analytic expansion method for the valuation of double-barrier options under a stochastic volatility model

Jeon, Junkee; Yoon, Jihun; Park, Chang-Rae

doi:10.1016/j.jmaa.2016.11.061

Cited by 13 publications

(4 citation statements)

References 15 publications

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“…Example 2. Consider Equation (8), subject to conditions (12) for pricing double knock-in put options with the following parameters: K = 80, r = 0.05, σ = 0.015, T = 1, S max = 120, L = 100, N = 100, δ = 0.045 and 0.10, α = (0.5, 0.7, 0.9, 1.0), with lower barrier located at B l = 10 and upper barrier located at B u = 130.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Another style of barrier options is a double-barrier option, some references to which can be found in [11][12][13][14], among others. Under the double-barrier case, there is an upper and a lower barrier.…”

Section: Introductionmentioning

confidence: 99%

“…Consider Equation(8), subject to conditions(12) for pricing double knock-in put options with the following parameters: K = 80, r = 0.05, σ = 0.015, T = 1, S max = 120, L = 100, N = 100, δ = 0.045 and 0.10, α = (0.5, 0.7, 0.9, 1.0), with lower barrier located at B l = 10 and upper barrier located at B u = 130.Option maturity payoff curves for the two considered examples (Examples 1 and 2, above) are presented in Figures1 and 2below.…”

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confidence: 99%

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An Efficient Numerical Method for Pricing Double-Barrier Options on an Underlying Stock Governed by a Fractal Stochastic Process

2023

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After the discovery of the fractal structures of financial markets, enormous effort has been dedicated to finding accurate and stable numerical schemes to solve fractional Black-Scholes partial differential equations. This work, therefore, proposes a numerical scheme for pricing double-barrier options, written on an underlying stock whose dynamics are governed by a non-standard fractal stochastic process. The resultant model is time-fractional and is herein referred to as a time-fractional Black-Scholes model. The presence of the time-fractional derivative helps to capture the time-decaying effects of the underlying stock while capturing the globalized change in underlying prices and barriers. In this paper, we present the construction of the proposed scheme, analyse it in terms of its stability and convergence, and present two numerical examples of pricing double knock-in barrier-option problems. The results suggest that the proposed scheme is unconditionally stable and convergent with order O(h2+k2).

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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An Efficient Numerical Method for Pricing Double-Barrier Options on an Underlying Stock Governed by a Fractal Stochastic Process

2023

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“…One-factor stochastic volatility models can generate "smile, " leverage effects, and term structure effects which cannot be explained by the Black-Scholes model [1,2]. Consequently many papers [3][4][5][6][7][8][9] evaluate barrier options under one-factor stochastic volatility models.…”

Section: Introductionmentioning

confidence: 99%

Efficient Simulation for Pricing Barrier Options with Two‐Factor Stochastic Volatility and Stochastic Interest Rate

Jieqiong

2017

Mathematical Problems in Engineering

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This paper presents an extension of the double Heston stochastic volatility model by combining Hull-White stochastic interest rates. By the change of numeraire and quadratic exponential scheme, this paper develops a new simulation scheme for the extended model. By combining control variates and antithetic variates, this paper provides an efficient Monte Carlo simulation algorithm for pricing barrier options. Based on the differential evolution algorithm the extended model is calibrated to S&P 500 index options to obtain the model parameter values. Numerical results show that the proposed simulation scheme outperforms the Euler scheme, the proposed simulation algorithm is efficient for pricing barrier options, and the extended model is flexible to fit the implied volatility surface.

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A Study of Controlling Shareholders’ Equity Pledge Rate Based on Dividend Policy and Barrier Option

Wang,

He,

Liu

2024

Comput Econ

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An analytic expansion method for the valuation of double-barrier options under a stochastic volatility model

Cited by 13 publications

References 15 publications

An Efficient Numerical Method for Pricing Double-Barrier Options on an Underlying Stock Governed by a Fractal Stochastic Process

An Efficient Numerical Method for Pricing Double-Barrier Options on an Underlying Stock Governed by a Fractal Stochastic Process

Efficient Simulation for Pricing Barrier Options with Two‐Factor Stochastic Volatility and Stochastic Interest Rate

A Study of Controlling Shareholders’ Equity Pledge Rate Based on Dividend Policy and Barrier Option

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