Pricing American Options under Azzalini Ito-McKean Skew Brownian Motions

被引：6

作者：

Hussain, Sultan ^{[1
]}

Arif, Hifsa ^{[1
]}

Noorullah, Muhammad ^{[1
]}

Pantelous, Athanasios A. ^{[2
]}

机构：

[1] COMSATS Univ Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan

[2] Monash Univ, Dept Econometr & Business Stat, Wellington Rd, Clayton, Vic 3800, Australia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2023年 / 451卷

关键词：

American option pricing; Skew Brownian motion; Non-normal distribution; Optimal stopping problem; Quadratic variation; STOCHASTIC VOLATILITY; VALUATION; TESTS; ARBITRAGE; MODEL;

D O I：

10.1016/j.amc.2023.128040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the pricing of American options whose asset price dynamics follow Azza-lini Ito-McKean skew Brownian motions is considered. The corresponding optimal stop-ping time problem is then formulated, and the main properties of its value function are provided. We show that if the payoff function is positive and decreasing, then the value function and its partial derivatives are continuous and locally bounded, and therefore sev-eral variational inequalities are derived. Furthermore, the Feyman-Kac formula is calcu-lated. Finally, under this more general as well as very versatile setting, the Black-Scholes option pricing model is nested as a special case. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：14

共 45 条

[1]

Arellano-Valle RB, 2004, SKEW-ELLIPTICAL DISTRIBUTIONS AND THEIR APPLICATIONS: A JOURNEY BEYOND NORMALITY, P113

[2]

AZZALINI A, 1985, SCAND J STAT, V12, P171

[3] Post-'87 crash fears in the S&P 500 futures option market [J].

Bates, DS .

JOURNAL OF ECONOMETRICS, 2000, 94 (1-2) :181-238

[4] Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options [J].

Bates, DS .

REVIEW OF FINANCIAL STUDIES, 1996, 9 (01) :69-107

[5]

Bingham N., 2001, RETURN DISTRIBUTIONS, P252

[6] PRICING OF OPTIONS AND CORPORATE LIABILITIES [J].

BLACK, F ;

SCHOLES, M .

JOURNAL OF POLITICAL ECONOMY, 1973, 81 (03) :637-654

[7] TESTS OF AN AMERICAN OPTION PRICING MODEL ON THE FOREIGN-CURRENCY OPTIONS MARKET [J].

BODURTHA, JN ;

COURTADON, GR .

JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS, 1987, 22 (02) :153-167

[8] American option pricing under two stochastic volatility processes [J].

Chiarella, Carl ;

Ziveyi, Jonathan .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 :283-310

[9]

Corns T.R.A., 2007, EUR J FINANC, V13

[10]

Corrado C.J., 1997, The Journal of Derivatives, V4, P8

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