Pricing geometric Asian rainbow options under the mixed fractional Brownian motion

Ahmadian, Davood; Ballestra, Luca Vincenzo

doi:10.1016/j.physa.2020.124458

Cited by 18 publications

(7 citation statements)

References 26 publications

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“…For practical application, the Ito formula plays an important role, which in the case of fBm takes the form of [9,11,13,14,20,23] df (τ, B(τ…”

Section: Stochastic Differential Equation Based On Fbmmentioning

confidence: 99%

“…In comparison to Brownian motion, for which increments on time intervals that do not intersect do not correlate, whereas, for fBm, a correlation takes place, which is also called a strong after action. Properties of fBm and its application to a number of applied problems were researched in many works [11][12][13][14][15][16]. In particular, in works [11,12], a generalized Ito formula for fBm is given.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, in works [11,12], a generalized Ito formula for fBm is given. Based on it, a Fokker-Planck equation for the transition probability density of stochastic process based on fBm was received [13][14][15]17]. In the given works, solutions were found for the Fokker-Planck equation for transition probability for which option price was obtained, as well as equations were built for option price dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Fractional Brownian motion in financial engineering models

Yanishevskyi¹,

Nodzhak²

2023

Math. Model. Comput.

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An application of fractional Brownian motion (fBm) is considered in stochastic financial engineering models. For the known Fokker–Planck equation for the fBm case, a solution for transition probability density for the path integral method was built. It is shown that the mentioned solution does not result from the Gaussian unit of fBm with precise covariance. An expression for approximation of fBm covariance was found for which solutions are found based on the Gaussian measure of fBm and those found based on the known Fokker–Planck equation match.

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“…For practical application, the Ito formula plays an important role, which in the case of fBm takes the form of [9,11,13,14,20,23] df (τ, B(τ…”

Section: Stochastic Differential Equation Based On Fbmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional Brownian motion in financial engineering models

Yanishevskyi¹,

Nodzhak²

2023

Math. Model. Comput.

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“…The analysis of risk management of rainbow option is also included, which is presented is the research of Dockendorf (2010) and Topper (2001) [5,6]. Milanesi (2021), D.Ahmadian & L.V.Ballestra (2020), Wang & Zhang (2018) analyzes the application of rainbow option in the Economics [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Research On The Pricing Of Rainbow Option Based On The Geometric Brownian Motion Model: Case Of Pfizer & Walmart

Guo¹

2022

BCPBM

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Trading financial derivatives become more and more popular in the modern life. The investor wants to purchase the financial derivative to receive more benefits. However, Option is the important component in the financial derivatives. Compared with Futures, Option can let investor feel more convenance since it acts as the contract. This research analyzes the price of the Rainbow Option in the Stock market. The Stock market includes two companies which are Pfizer and Walmart. The results shows that the Rainbow Option should be priced between max of call options and the sum of the options. It can testify the theory of rainbow Options‘ price successfully. Based on this research, the investor can understand the background and process of the rainbow Options‘ working. Combine with the feature of the rainbow options, the investor can make the proper investment decision in the different situations.

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“…options whose payoff depends on the average, either geometric or arithmetic, of the underlying asset over the whole option's lifespan [18]. In particular, [16] obtained an exact closed-form solution for geometric Asian options, [27] derived an exact analytical formula for geometric Asian power options, [25] proposed an exact closed-form solution for geometric Asian rainbow options on two underlying assets, which was generalized to the case on an arbitrarily large number of underlying assets in [1]. Furthermore, [15] considered a mf Bm with jumps and obtained an exact analytical formula for valuing geometric Asian power options.…”

Section: Introductionmentioning

confidence: 99%

Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps

Shokrollahi¹,

Ahmadian²,

Ballestra³

2021

Preprint

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The mixed fractional Brownian motion ( mf Bm ) has become quite popular in finance, since it allows one to model long-range dependence and selfsimilarity while remaining, for certain values of the Hurst parameter, arbitragefree. In the present paper, we propose approximate closed-form solutions for pricing arithmetic Asian options on an underlying described by the mf Bm . Specifically, we consider both arithmetic Asian options and arithmetic Asian power options, and we obtain analytical formulas for pricing them based on a convenient approximation of the strike price. Both the standard mf Bm and the mf Bm with Poisson log-normally distributed jumps are taken into account.

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Pricing geometric Asian rainbow options under the mixed fractional Brownian motion

Cited by 18 publications

References 26 publications

Fractional Brownian motion in financial engineering models

Fractional Brownian motion in financial engineering models

Research On The Pricing Of Rainbow Option Based On The Geometric Brownian Motion Model: Case Of Pfizer & Walmart

Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps

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