High-order accurate implicit methods for barrier option pricing

Ndogmo, J. C.; Ntwiga, Davis Bundi

doi:10.1016/j.amc.2011.07.037

Cited by 14 publications

(20 citation statements)

References 31 publications

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“…It should be noted that the method has simple computer implementations and permits also observing of the entire life of the option for a reasonable time, i.e we could evaluate the option price simultaneously for different values of the underlying asset price. This property is characterized for the finite difference approach used in [20,11].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…when L = 95 and U = 125, we have compared our results with the finite difference scheme of Zvan, [22], and the implicit scheme applied in [20], denoted with HOBIS, where the computational domain is adjusted in advance under some probabilistic hypothesis for the boundaries. Table 1 Prices of discrete double knock-out call option in 5 monitoring dates.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Formally, there are three examples respectively when the two barriers are L = 95 and U = 110, as it is explored in [21], when L = 95 and U = 125 used in [20,22], and the third case is when L = 95 and U = 140, [13].…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The second relation (20) of Theorem 3.1 is proved in an analogous way using formulas (11) and (12), and presenting K = U + (K − U) in Eq. (21).…”

Section: Algorithm For Numerical Valuationmentioning

confidence: 99%

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Numerical valuation of discrete double barrier options

Milev

Tagliani

2010

Journal of Computational and Applied Mathematics

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a b s t r a c tIn the present paper we explore the problem for pricing discrete barrier options utilizing the Black-Scholes model for the random movement of the asset price. We postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number of the monitoring dates.We propose a fast and accurate numerical algorithm for its valuation. Our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in Finance and literature. A desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers.The method has a simple computer implementation and it permits observing the entire life of the option.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

“…The second relation (20) of Theorem 3.1 is proved in an analogous way using formulas (11) and (12), and presenting K = U + (K − U) in Eq. (21).…”

Section: Algorithm For Numerical Valuationmentioning

confidence: 99%

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Numerical valuation of discrete double barrier options

Milev

Tagliani

2010

Journal of Computational and Applied Mathematics

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“…The main numerical methods in the literature are the tree method [2,5,16] and the finite difference method [3,15,19]. However, although easy to implement pure numerical methods can prove to be time consuming and restrictive in applications.…”

Section: Introductionmentioning

confidence: 99%

Finite maturity margin call stock loans

Putri

2016

Operations Research Letters

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A numerical method for pricing discrete double barrier option by Lagrange interpolation on Jacobi nodes

Sobhani

Milev

2022

Math Methods in App Sciences

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In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock‐out call options is presented. With regard to the well‐known Black‐Scholes model, the price of an option in each monitoring date could be calculated by computing a recursive integral formula that is based on the heat equation solution. We have approximated these recursive solutions with the aid of Lagrange interpolation on Jacobi polynomial nodes. After that, an operational matrix, which makes our computation significantly fast, has been derived. In some theorems, the convergence of the presented method has been shown and the rate of convergence has been derived. The most important benefit of this method is that its complexity is very low and does not depend on the number of monitoring dates. The numerical results confirm the accuracy and efficiency of the presented numerical algorithm.

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High-order accurate implicit methods for barrier option pricing

Cited by 14 publications

References 31 publications

Numerical valuation of discrete double barrier options

Numerical valuation of discrete double barrier options

Finite maturity margin call stock loans

A numerical method for pricing discrete double barrier option by Lagrange interpolation on Jacobi nodes

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