Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions

Hussain, Sultan; Arif, Hifsa; Noorullah, Muhammad; Pantelous, Athanasios A.

doi:10.1016/j.amc.2023.128040

Cited by 6 publications

(1 citation statement)

References 33 publications

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“…As the random driving source of the risk asset price in the BS model is Brownian motion, it cannot capture many of the characteristic features of the risk asset price, including long-range dependence, heavy tails, and periods of constant values, etc. In order to overcome these shortcomings, scholars adopt other stochastic processes as the random source of the option pricing model, such as fractional Brownian motion [2-7], mixed fractional Brownian motion [8][9][10][11][12], time-changed Brownian motion [13][14][15][16], skew Brownian motion [17][18][19][20][21], etc.…”

Section: Introductionmentioning

confidence: 99%

European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

Guo,

Liu,

Dai

2023

Fractal Fract

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In this paper, the approximate stationarity of the second-order moment increments of the sub-fractional Brownian motion is given. Based on this, the pricing model for European options under the sub-fractional Brownian regime in discrete time is established. Pricing formulas for European options are given under the delta and mixed hedging strategies, respectively. Furthermore, European call option pricing under delta hedging is shown to be larger than under mixed hedging. The hedging error ratio of mixed hedging is shown to be smaller than that of delta hedging via numerical experiments.

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Section: Introductionmentioning

confidence: 99%

European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

Guo,

Liu,

Dai

2023

Fractal Fract

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Modelling the Chinese crude oil futures returns through a skew‐geometric Brownian motion correlated with the market volatility index process for pricing financial options

Bufalo,

Fanelli

2024

Appl Stoch Models Bus & Ind

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In this paper we model the dynamics of the Chinese crude oil futures returns by using a skew‐geometric Brownian motion correlated with the market volatility, which is taken as a square‐root stochastic process. We use the OVX index data as proxy for market volatility. We validate the proposed model in terms of accuracy of its calibrations through an in‐sample simulation. Instead, out‐of‐sample simulations are used to show that a correlated skew‐geometric Brownian motion is more appropriate for modelling the Chinese returns compared to a single skew‐geometric Brownian motion in terms of forecasts. Furthermore, we price an American call option on the Chinese futures by using a recursively scheme based on a closed‐form formula, and an alternative Monte Carlo approach, for the related European call option. We show that our call price estimates are very close to market values and our model generally outperforms many benchmarks in literature, such as the Barone‐Adesi and Whaley formula and its generalizations.

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Daily and Weekly Geometric Brownian Motion Stock Index Forecasts

Sinha

2024

JRFM

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In this manuscript, daily and weekly geometric Brownian motion forecasts are obtained and tested for reliability for three indexes, DJIA, NASDAQ and S&P 500. A twenty-year rolling window is used to estimate the drift and diffusion components, and applied to obtain one-period-ahead geometric Brownian motion index values and associated probabilities. Expected values are estimated by totaling up the product of the index value and its associated probabilities, and test for reliability. The results indicate that geometric Brownian-simulated expected index values estimated using one thousand simulations can be reliable forecasts of the actual index values. Expected values estimated using one or ten simulations are not as reliable, while those obtained using at least one hundred simulations could be useful.

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Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions

Cited by 6 publications

References 33 publications

European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

Modelling the Chinese crude oil futures returns through a skew‐geometric Brownian motion correlated with the market volatility index process for pricing financial options

Daily and Weekly Geometric Brownian Motion Stock Index Forecasts

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