Digital barrier option contract with exponential random time

Jun, Doobae; Ku, Hyejin

doi:10.1093/imamat/hxs013

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…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]. Hui [13] used the Black-Scholes environment and derived the analytical solution for knock-out binary option values.…”

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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“…Relying on the technique of hitting the probabilities of a Brownian motion, closed‐form expressions for European‐style double‐barrier options are derived in the work of Jun and Kun. () Luo() derived a closed‐form valuation formula for a digital constant barrier option, which is initiated at a random time with an exponential distribution. All exponential barriers mentioned previously have an arbitrarily fixed time coefficient on the exponent, ie, they are given by exp( a t ), a ≠0, which is different from .…”

Section: Introductionmentioning

confidence: 99%

Pricing and hedging barrier options

Rosalino

Silva

Baczynski

et al. 2018

Appl Stoch Models Bus & Ind

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European options are a significant financial product. Barrier options, in turn, are European options with a barrier constraint. The investor may pay less buying the barrier option obtaining the same result as that of the European option whenever the barrier is not breached. Otherwise, the option's payoff cancels. In this paper, we obtain closed-form expressions of the exact no-arbitrage prices, delta hedges, and gammas of a call option with a moving barrier that tracks the prices of the risk-free asset. Besides the interest in its own right, this class of options constitutes the core element to obtain, via an original and simple technique, the closed-form expressions for the estimates of the prices of call options with barriers of arbitrary shape. Equally important is the fact that a bound for the worst associated error is provided, so the investor can evaluate beforehand if the accuracy provided is according to his/her needs or not. Discrete monitored barrier provisions are also allowed in the estimates. Simulations are performed illustrating the accuracy of the estimates. A quality of the aforementioned procedures is that the time consumed in computations is very small. In turn, we observe that the approximate prices, delta hedges, and gammas of the barrier option associated to the risk-free asset, obtained via a PDE approach in conjunction with a good finite difference method, converge to the closed-form expressions of the prices, hedges, and gammas of the option. This attests the correctness of the analytical results. KEYWORDS barrier option, finite-difference method, hedging, no-arbitrage pricing, risk-neutral measure dS(u) = (u)S(u)du + (u)S(u)dW(u),Appl Stochastic Models Bus Ind. 2018;34:499-512. wileyonlinelibrary.com/journal/asmb

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Closed-form solutions for options with random initiation under asset price monitoring

Jun

2017

Finance Research Letters

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Digital barrier option contract with exponential random time

Abstract: In this paper, we derive a closed-form valuation formula for a digital barrier option which is initiated at random time τ with exponential distribution. We also provide a simple example and graphs to illustrate our result.

Cited by 5 publications

References 12 publications

The Barrier Binary Options

The Barrier Binary Options

Pricing and hedging barrier options

Closed-form solutions for options with random initiation under asset price monitoring

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