Knock‐in American options

Dai, Min; Kwok, Yue Kuen

doi:10.1002/fut.10101

Cited by 28 publications

(9 citation statements)

References 6 publications

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“…Haug [9] has presented analytic valuation formulas for American up-and-input and down-and-in call options in terms of standard American options. It was extended by Dai and Kwok [10] to more types of American knock-in options in terms of integral representations. Jun and Ku [11] derived a closed-form valuation formula for a digit barrier option with exponential random time and provided analytic valuation formulas of American partial barrier options in [12].…”

Section: Introductionmentioning

confidence: 99%

The Barrier Binary Options

Gao¹,

Wei²

2020

JMF

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We extend the binary options into barrier binary options and discuss the application of the optimal structure without a smooth-fit condition in the option pricing. We first review the existing work for the knock-in options and present the main results from the literature. Then we show that the price function of a knock-in American binary option can be expressed in terms of the price functions of simple barrier options and American options. For the knockout binary options, the smooth-fit property does not hold when we apply the local time-space formula on curves. By the properties of Brownian motion and convergence theorems, we show how to calculate the expectation of the local time. In the financial analysis, we briefly compare the values of the American and European barrier binary options.

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Section: Introductionmentioning

confidence: 99%

The Barrier Binary Options

Gao¹,

Wei²

2020

JMF

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“…Then Gao, Huang and Subrahmanyam [4] pushed forward the pricing analysis of the American barrier option by using the decomposition technique, and Dai and Kwok [5] has got the pricing formula of American down and in call option.…”

Section: Introductionmentioning

confidence: 99%

Numerical Methods for Discrete Double Barrier Option Pricing Based on Merton Jump Diffusion Model

Li¹

2017

OJS

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As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others impose underlying assets on some strong assumptions, for example, a lot of calculations are based on the Black-Scholes model. This thesis considers Merton jump diffusion model as the basic model to derive the pricing formula of discrete double barrier option; numerical calculation method is used to approximate the continuous convolution by calculating discrete convolution. Then we compare the results of theoretical calculation with simulation results by Monte Carlo method, to verify their efficiency and accuracy. By comparing the results of degeneration constant parameter model with the results of previous models we verified the calculation method is correct indirectly. Compared with the Monte Carlo simulation method, the numerical results are stable. Even if we assume the simulation results are accurate, the time consumed by the numerical method to achieve the same accuracy is much less than the Monte Carlo simulation method.

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“…Subsequently, barrier options in American style were investigated by other researchers. Similar to vanilla American options, analytic solutions are available only for limited cases, such as, a closed-form solution of a perpetual American up-and-out put [9], an integral representation of the knock-in American option pricing formula [6]. Thus, both numerical and analytical approximation methods have been developed for the valuation of finite maturity American barrier options.…”

Section: Introductionmentioning

confidence: 99%

Finite maturity margin call stock loans

Putri

2016

Operations Research Letters

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Knock‐in American options

Cited by 28 publications

References 6 publications

The Barrier Binary Options

The Barrier Binary Options

Numerical Methods for Discrete Double Barrier Option Pricing Based on Merton Jump Diffusion Model

Finite maturity margin call stock loans

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