Bernstein’s inequalities and their extensions for getting the Black–Scholes option pricing formula

2016 ◽  
Vol 111 ◽  
pp. 86-92 ◽  
Author(s):  
Anna Glazyrina ◽  
Alexander Melnikov
Keyword(s):  
Option Pricing ◽  
Black Scholes ◽  
Pricing Formula

AN ANALYTICAL OPTION PRICING FORMULA FOR MEAN-REVERTING ASSET WITH TIME-DEPENDENT PARAMETER

2021 ◽  
Vol 63 (2) ◽  
pp. 178-202
Author(s):  
P. NONSOONG ◽  
K. MEKCHAY ◽  
S. RUJIVAN
Keyword(s):  
Option Pricing ◽  
Option Price ◽  
Time Dependent ◽  
Initial Time ◽  
Agricultural Commodity ◽  
Time Integral ◽  
Long Run ◽  
Black Scholes ◽  
Dependent Parameter ◽  
Pricing Formula

AbstractWe present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided.

Derivative Assets Analysis

1987 ◽  
Vol 1 (2) ◽  
pp. 73-93 ◽  
Author(s):  
Mark Rubinstein
Keyword(s):  
Economic Theory ◽  
Economic Analysis ◽  
Option Pricing ◽  
Portfolio Insurance ◽  
Equity Options ◽  
Index Options ◽  
Index Futures ◽  
The Core ◽  
Black Scholes ◽  
Pricing Formula

Derivative assets analysis enjoys an unusual status; it is a recently developed, relatively complex tool of economic analysis, faithful to the core of economic theory, and widely used to make reallife decisions. This paper, discusses derivative assets based on buy-and-hold strategies; derivative assets based on dynamic replicating strategies; valuing and replicating other derivative assets; and the Black-Scholes option pricing formula. Then it takes a detailed look at four applications: index futures, equity options, index options, and portfolio insurance.

scholarly journals The Performance of Skewness and Kurtosis Adjusted Option Pricing Model in Emerging Markets

2016 ◽  
Vol 5 (3) ◽  
pp. 70-84
Author(s):  
Özge Sezgin Alp
Keyword(s):  
Emerging Markets ◽  
Option Pricing ◽  
Option Prices ◽  
Pricing Model ◽  
European Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Skewness And Kurtosis ◽  
Pricing Formula

In this study, the option pricing performance of the adjusted Black-Scholes model proposed by Corrado and Su (1996) and corrected by Brown and Robinson (2002), is investigated and compared with original Black Scholes pricing model for the Turkish derivatives market. The data consist of the European options written on BIST 30 index extends from January 02, 2015 to April 24, 2015 for given exercise prices with maturity April 30, 2015. In this period, the strike prices are ranging from 86 to 124. To compare the models, the implied parameters are derived by minimizing the sum of squared deviations between the observed and theoretical option prices. The implied distribution of BIST 30 index does not significantly deviate from normal distribution. In addition, pricing performance of Black Scholes model performs better in most of the time. Black Scholes pricing Formula, Carrado-Su pricing Formula, Implied Parameters

An analytical option pricing formula for mean-reverting asset with time-dependent parameter

2021 ◽  
Vol 63 ◽  
pp. 178-202
Author(s):  
Piyapoom Nonsoong ◽  
Khamron Mekchay ◽  
Sanae Rujivan
Keyword(s):  
Option Pricing ◽  
Option Price ◽  
Time Dependent ◽  
Initial Time ◽  
Agricultural Commodity ◽  
Time Integral ◽  
Long Run ◽  
Black Scholes ◽  
Dependent Parameter ◽  
Pricing Formula

We present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided. doi:10.1017/S1446181121000262  

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