An application of quasi Monte Carlo methods for the numerical assessment of maintenance strategies

Demgne, Jeanne; Lair, William; Lonchampt, Jérôme; Mercier, Sophie

doi:10.1201/b19094-122

Cited by 1 publication

(2 citation statements)

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“…where 𝑥 𝑖 = (𝑥 1 , 𝑥 2 , … , 𝑥 𝑑 ) taken from a uniform distribution on [0,1] 𝑑 that is normally distributed [16].…”

Section: 𝐸[𝑓(𝑥)] = ∫ 𝑓(𝑥)𝑑𝑥mentioning

confidence: 99%

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Pricing of Call Options Using the Quasi Monte Carlo Method

Oktaviani,

Sulistianingsih,

Satyahadewi

2023

BAREKENG: J. Math. & App.

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A call option is a type of option that grants the option holder the right to buy an asset at a specified price within a specified period of time. Determining the option price period of time within a certain period of time is the most important part of determining an investment strategy. Various methods can be employed to determine the prices of options, such as Quasi-Monte Carlo and Monte Carlo simulations. The purpose of this research is to determine the price of European-type call options using the Quasi-Monte Carlo method. The data used is daily stock closing price data on the Apple Inc. for the period October 1, 2021, to September 30, 2022. Apple Inc. stock options in this study were chosen because it is the largest technology company in the world in 2022. The steps taken in this study are to determine the parameters obtained from historical data such as the initial risk-free interest rate (r), stock price (, volatility , maturity time (T), and strike price (K). Next is to generate Halton’s quasi-randomized sequence and simulate the stock price by substituting the parameters by substituting the parameters. Then proceed to calculate the call option payoff and estimate the call option price by averaging the call option payoff values. The results showed that the call option price of the company Apple Inc. using the Quasi-Monte Carlo with Halton’s quasi-randomized sequence on the 1000000th simulation with a standard error of 0,045 is $90,163. The call option price obtained can be used as a reference for investors in purchasing options to minimize losses from call option investments in that period.

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“…where 𝑥 𝑖 = (𝑥 1 , 𝑥 2 , … , 𝑥 𝑑 ) taken from a uniform distribution on [0,1] 𝑑 that is normally distributed [16].…”

Section: 𝐸[𝑓(𝑥)] = ∫ 𝑓(𝑥)𝑑𝑥mentioning

confidence: 99%

“…In the Monte Carlo simulation, 𝑥 𝑖 is a pseudo-random sequence, while in the Quasi-Monte Carlo method, 𝑥 𝑖 is a quasi-randomized sequence [16].…”

Section: ∫ 𝑓(𝑥)𝑑𝑥 𝐶mentioning

confidence: 99%