Computational Methods in Finance

Hirsa, Ali

doi:10.1201/b12755

Cited by 28 publications

(33 citation statements)

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“…A numerical technique is presented in [18,19] to calculate F Θ (θ) from φ Θ (ω). Its key idea is to calculate the Fourier transform of e −ηθ F Θ (x) where e −ηθ is a damping function with η > 0.…”

Section: Characteristic Function Of the Packet Loss Probabilitymentioning

confidence: 99%

Analysis of macro diversity based on maximum ratio combining in long range ALOHA networks

2019

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In low power wide area networks (LPWAN), packets transmitted by a device are not addressed to a specific base station : any surrounding station can receive them. This opens the way to several macro diversity schemes. As opposed to independent decoding of packets received by each base station, we propose using maximum ratio combining (MRC) to improve system performance. We use stochastic geometry to analyze the packet loss probability when MRC is implemented for both pure and slotted Aloha and obtain a closed formula when the path loss exponent γ is 4. However, the formula is valid when all base stations on an infinite plane participate in the MRC procedure, which gives the most optimistic evaluation. We developed simulations to get the performance when a finite number of receivers in the MRC is considered and focus on the case with only 2 receivers. We use a curve-fitting approach based on the simulation results to get a closed-form formula of the packet loss probability with 2 receivers. This curve-fitting approach is also applicable to other cases in which more receivers are leveraged by MRC. The formula is easy to use and accurate when γ ∈ [3.3, 4.5] and the loss probability is greater than 0.5%. For pure Aloha when advanced transmission techniques (e.g., interleaving, robust channel coding, etc.) are applied and when the capture ratio is 3 dB, the system capacity for a 10% packet loss probability is increased by a factor greater than 1.26 compared to a simple scheme in which each base station independently decodes packets.

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Section: Characteristic Function Of the Packet Loss Probabilitymentioning

confidence: 99%

Analysis of macro diversity based on maximum ratio combining in long range ALOHA networks

2019

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“…where the sum is over the number n S (= 5) of initial stock values, EC is the estimate price obtained via a FFT and EC is the exact price determined by MCS or FDMs. Note [15]. Hence, to determine an appropriate choice of these parameters, we adapt the methodology employed by Hurd and Zhou [18], where the average of the absolute value of the log price differences, as in equation 3.1, was minimized as…”

Section: Numerical Examplementioning

confidence: 99%

“…A two-step approach is taken to optimize the FFT parameters. First, α 1 and ∆ 1 are fixed at 0.75 and 0.1, respectively, which are reasonable parameters [15]. The outputs for α 2 and ∆ 2 are then employed (together with α 1 and ∆ 1 ) as initial inputs to minimize Err.…”

Section: Numerical Examplementioning

confidence: 99%

Pricing Holder-Extendable Call Options With Mean-Reverting Stochastic Volatility

Ibrahim¹,

Hernández²,

O’Hara³

et al. 2019

ANZIAM J.

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Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carlo simulation, and we determine the efficiency and accuracy of the Fourier method in pricing holder-extendable call options for Heston parameters calibrated from the subprime crisis. We show that the fast Fourier transform reduces the computational time required to produce a range of holder-extendable call option prices by at least an order of magnitude. Numerical results also demonstrate that when the Heston correlation is negative, the Black–Scholes model under-prices in-the-money and over-prices out-of-the-money holder-extendable call options compared with the Heston model, which is analogous to the behaviour for vanilla calls.

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“…However, directly using Gil-Pelaez Theorem needs long time. Applying mathematical techniques used in finance domain [19], we seek to calculate the Fourier…”

Section: Wide-band Imperfect Power Controlmentioning

confidence: 99%

An analytical model for S-ALOHA performance evaluation in M2M networks

Song¹,

Lagrange²,

Nuaymi³

2017

2017 IEEE International Conference on Communications (ICC)

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Abstract-The S-ALOHA (i.e. slotted-ALOHA) protocol is recently regaining interest in Lower Power Wide Area Networks (LPWAN) handling M2M traffic. Despite intensive studies since the birth of S-ALOHA, the special features of M2M traffic and requirements highlight the importance of analytical models taking into account performance-affecting factors and giving a thorough performance evaluation. Fulfilling this necessity is the main focus of this paper: we jointly consider the impact of capture effect, diversity of transmit power levels with imperfect power control. We propose a low-complexity but still accurate analytical model capable of evaluating S-ALOHA in terms of packet loss rate, throughput, energy-efficiency and average number of transmissions. The proposed model is able to facilitate dimensioning and design of S-ALOHA based LPWAN. The comparison between simulation and analytical results confirms the accuracy of our proposed model. The design guides about S-ALOHA based LPWAN deduced from our model are: the imperfect power control can be positive with capture effect and and appropriate transmit power diversity strategy. The transmit power diversity strategy should be determined by jointly considering network charges level, power control precision and capture ratio to achieve optimal performance of S-ALOHA.

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Computational Methods in Finance

Cited by 28 publications

References 0 publications

Analysis of macro diversity based on maximum ratio combining in long range ALOHA networks

Analysis of macro diversity based on maximum ratio combining in long range ALOHA networks

Pricing Holder-Extendable Call Options With Mean-Reverting Stochastic Volatility

An analytical model for S-ALOHA performance evaluation in M2M networks

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