scholarly journals PREFERENCES, LÉVY JUMPS AND OPTION PRICING

2007 ◽  
Vol 03 (01) ◽  
pp. 0750001 ◽  
Author(s):  
CHENGHU MA
Keyword(s):  
Option Pricing ◽  
Contingent Claims ◽  
Economic Variable ◽  
European Options ◽  
Jump Risk ◽  
Representative Agent ◽  
Potential Explanation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Lévy Jumps

This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black–Scholes, Naik–Lee, Cox–Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black–Scholes model is explored.

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 APPROPRIATE APPROACH TO PRICING EUROPEAN-STYLE OPTIONS WITH THE ADOMIAN DECOMPOSITION METHOD

2018 ◽  
Vol 59 (3) ◽  
pp. 349-369
Author(s):  
ZIWIE KE ◽  
JOANNA GOARD ◽  
SONG-PING ZHU
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
European Options ◽  
Black Scholes Model ◽  
Adomian Decomposition ◽  
Black Scholes ◽  
Interest Rate Model ◽  
Vasicek Interest Rate Model ◽  
Digital Options ◽  
Continuous Estimation

We study the numerical Adomian decomposition method for the pricing of European options under the well-known Black–Scholes model. However, because of the nondifferentiability of the pay-off function for such options, applying the Adomian decomposition method to the Black–Scholes model is not straightforward. Previous works on this assume that the pay-off function is differentiable or is approximated by a continuous estimation. Upon showing that these approximations lead to incorrect results, we provide a proper approach, in which the singular point is relocated to infinity through a coordinate transformation. Further, we show that our technique can be extended to pricing digital options and European options under the Vasicek interest rate model, in both of which the pay-off functions are singular. Numerical results show that our approach overcomes the difficulty of directly dealing with the singularity within the Adomian decomposition method and gives very accurate results.

Option pricing models

1989 ◽  
Vol 116 (3) ◽  
pp. 537-558 ◽  
Author(s):  
D. Blake
Keyword(s):  
Option Pricing ◽  
Binomial Model ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes

ABSTRACTThe paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.

scholarly journals A Note on Numerical Solution of a Linear Black-Scholes Model

2014 ◽  
Vol 33 ◽  
pp. 103-115 ◽  
Author(s):  
Md. Kazi Salah Uddin ◽  
Mostak Ahmed ◽  
Samir Kumar Bhowmilk
Keyword(s):  
Time Integration ◽  
Weighted Average ◽  
Financial Mathematics ◽  
European Options ◽  
Average Scheme ◽  
Put Options ◽  
Weighted Average Method ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Solution Methods

Black-Scholes equation is a well known partial differential equation in financial mathematics. In this article we discuss about some solution methods for the Black Scholes model with the European options (Call and Put) analytically as well as numerically. We study a weighted average method using different weights for numerical approximations. In fact, we approximate the model using a finite difference scheme in space first followed by a weighted average scheme for the time integration. Then we present the numerical results for the European Call and Put options. Finally, we investigate some linear algebra solvers to compare the superiority of the solvers. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 103-115 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17664

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

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