دانلود مقاله ISI انگلیسی شماره 99572
ترجمه فارسی عنوان مقاله

نوسان به عنوان اثر نسبیتی

عنوان انگلیسی
Volatility smile as relativistic effect
کد مقاله سال انتشار تعداد صفحات مقاله انگلیسی
99572 2017 18 صفحه PDF
منبع

Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : Physica A: Statistical Mechanics and its Applications, Volume 475, 1 June 2017, Pages 59-76

ترجمه کلمات کلیدی
نوسان نوسان دم پا چربی توزیع احتمال، نسبیتی، حرکت براونیا، قانون برج،
کلمات کلیدی انگلیسی
Volatility smile; Fat tails; Probability distribution; Relativistic; Brownian motion; Tower law;
پیش نمایش مقاله
پیش نمایش مقاله  نوسان به عنوان اثر نسبیتی

چکیده انگلیسی

We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution (1) is properly normalized and (2) obeys the tower law (semigroup property), so we can construct martingales and self-financing hedging strategies and price claims (options). This model is a 1-constant-parameter extension of the Black–Scholes–Merton model. The new parameter is the analog of the speed of light in Special Relativity. However, in the financial context there is no “speed limit” and the new parameter has the meaning of a characteristic diffusion speed at which relativistic effects become important and lead to a much softer asymptotic behavior, i.e., fat tails, giving rise to volatility smiles. We argue that a nonlocal stochastic description of such (Lévy) processes is inadequate and discuss a local description from physics. The presentation is intended to be pedagogical.