The Binomial Interpolated Lattice Method for Step Double Barrier Options

Appolloni, Elisa; Gaudenzi, Marcellino; Zanette, Antonino

doi:10.1142/s0219024914500356

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…The price at s 0 is obtained by a Lagrange four points interpolation in space of the prices denoted in Figure 1 with the empty circles, such prices are obtained by a linear interpolation in time of the prices at the nodes denoted by squares. For more details one can refer to Appolloni et al (2013). Then, we can easily adapt the BIL algorithm to the case of digital options with a single barrier.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The theoretical proof that the rate of convergence of the Adjusted BIL algorithm is of order 1 n is a direct consequence of Proposition 1 in Appolloni et al (2013), Theorem 3 and Theorem 5. In fact, in the Adjusted BIL algorithm we get the price in (0, s 0 ) by suitable interpolations of some selected CRR prices at times t 0 and t 2 , as in the standard version of the BIL algorithm (see Figure 1).…”

Section: Remarkmentioning

confidence: 91%

“…In this framework we treat the study of the CRR binomial approximation error in the case of digital options with a single barrier and we get a complete theoretical result that allows us to construct an efficient algorithm. In particular we fit the Binomial Interpolated Lattice (BIL) algorithm provided in Appolloni et al (2013) to this specific case. We recall that the BIL procedure is based on a backward induction on a binomial mesh with additionally suitable interpolations that allows one to get very precise option prices for call and put double barrier options.…”

Section: Introductionmentioning

confidence: 99%

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Efficient tree methods for pricing digital barrier options

Appolloni,

Ligori

2014

Preprint

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Efficient tree methods for pricing digital barrier options

Appolloni,

Ligori

2014

Preprint

Self Cite

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“…In 2006, a modified standard binomial method which can price the American type barrier option was introduced by Gaudenzi and Lepellere, 13 which is more efficient than the CRR model and can be used in the trinomial tree method as well. Appolloni et al 14 explored the binomial lattice method to evaluate the step double barrier options.…”

Section: Exotic Option With Monotonic Payoffs: the Barrier Optionmentioning

confidence: 99%

Pricing exotic options in the incomplete market: An imprecise probability method

Coolen

Coolen‐Maturi

2022

Appl Stoch Models Bus & Ind

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This article considers a novel exotic option pricing method for incomplete markets. Nonparametric predictive inference (NPI) is applied to the option pricing procedure based on the binomial tree model allowing the method to evaluate exotic options with limited information and few assumptions. As the implementation of the NPI method is greatly simplified by the monotonicity of the option payoff in the tree, we categorize exotic options by their payoff monotonicity and study a typical type of exotic option in each category, the barrier option and the look-back option. By comparison with the classic binomial tree model, we investigate the performance of our method either with different moneyness or varying maturity. All outcomes show that our model offers a feasible approach to price the exotic options with limited information, which makes it can be utilized for both complete and incomplete markets.

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“…Grosse-Erdmann and Heuwelyckx (2016) generalize Heuwelyckx (2014) to any given time after emission. Appolloni et al (2014) introduced the binomial interpolated lattice approach to deal with the 'near barrier' problem and improve the convergence of American option prices. Bock and Korn (2016) use Edgeworth expansions to construct a fast converging binomial tree for vanilla and barrier options.…”

Section: Introductionmentioning

confidence: 99%

Path independence of exotic options and convergence of binomial approximations

Leduc¹,

Palmer²

2019

JCF

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The analysis of the convergence of tree methods for pricing barrier and lookback options has been the subject of numerous publications aiming at describing, quantifying, and improving the slow and oscillatory convergence in such methods. For barrier and lookback options, we find path-independent options whose price is exactly that of the original path-dependent option. The usual binomial models converge at a speed of order 1/ √ n to the Black-Scholes price. Our new path-independent approach yields convergence of order 1/n. Furthermore, we derive a closed form formula for the coefficient of 1/n in the expansion of the error of our path-independent pricing when the underlying is approximated by the Cox, Ross, and Rubinstein (CRR) model. Using this we obtain a corrected model with a convergence of order n −3/2 to the price of barrier and lookback options in the Black-Scholes model. Our results are supported and illustrated by numerical examples.

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The Binomial Interpolated Lattice Method for Step Double Barrier Options

Cited by 6 publications

References 15 publications

Efficient tree methods for pricing digital barrier options

Efficient tree methods for pricing digital barrier options

Pricing exotic options in the incomplete market: An imprecise probability method

Path independence of exotic options and convergence of binomial approximations

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