Closed-form solutions for option pricing in the presence of volatility smiles: a density-function approach

2001 ◽  
Vol 3 (3) ◽  
pp. 5-25 ◽  
Author(s):  
Dariush Mirfendereski ◽  
Riccardo Rebonato
Keyword(s):  
Option Pricing ◽  
Closed Form ◽  
Density Function ◽  
Function Approach ◽  
Closed Form Solutions

scholarly journals CLOSED-FORM SOLUTIONS FOR THE PROBABILITY DENSITY OF WAVE HEIGHT IN THE SURF ZONE

1988 ◽  
Vol 1 (21) ◽  
pp. 60 ◽  
Author(s):  
William R. Dally ◽  
Robert G. Dean
Keyword(s):  
Probability Density Function ◽  
Shallow Water ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Wave Height ◽  
Surf Zone ◽  
Wave Steepness ◽  
Bottom Slope ◽  
Closed Form Solutions

By invoking the assumption that in the surf zone, random waves behave as a collection of individual regular waves, two closed-form solutions for the probability density function of wave height on planar beaches are derived. The first uses shallow water linear theory for wave shoaling, assumes a uniform incipient condition, and prescribes breaking with a regular wave model that includes both bottom slope and wave steepness effects on the rate of decay. In the second model, the shallow water assumption is removed, and a distribution in wave period (incipient condition) is included. Preliminary results indicate that the models exhibit much of the behavior noted for random wave transformation reported in the literature, including bottom slope and wave steepness effects on the shape of the probability density function.

scholarly journals Closed-form Solutions of the Time-fractional Standard Black-Scholes Model for Option Pricing using He-separation of Variable Approach

2020 ◽  
Vol 16 ◽  
Keyword(s):  
Option Pricing ◽  
Closed Form ◽  
Transformation Method ◽  
Pricing Model ◽  
Closed Form Solutions ◽  
Variable Approach ◽  
Black Scholes ◽  
Option Pricing Model ◽  
And Mathematics ◽  
Separation Of Variable

The Black-Scholes option pricing model in classical form remains a benchmark model in Financial Engineering and Mathematics concerning option valuation. Though, it has received a series of modifications as regards its initial constancy assumptions. Most of the resulting modifications are nonlinear or time-fractional, whose exact or analytical solutions are difficult to obtain. This paper, therefore, presents exact (closed-form) solutions to the time-fractional classical Black-Scholes option pricing model by means of the He-Separation of Variable Transformation Method (HSVTM). The HSVTM combines the features of the He’s polynomials, the Homo-separation variable, the modified DTM, which increases the efficiency and effectiveness of the proposed method. The proposed method is direct and straight forward. Hence, it is recommended for obtaining solutions to financial models resulting from either Ito or Stratonovich Stochastic Differential Equations (SDEs).

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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