Option pricing in the Black Scholes model: a fair price of a European call

Derivative trading, started in mid-2000, has become an integral and significant part of Indian stock market. The tremendous increase in trading volume in Indian stock market has reflected into high volatility in the option prices. The pricing of options is very complex aspect of applied finance and has been subject of extensive research. Black–Scholes option model is a scientific pricing model which is applied for determining the fair price for option contracts. This article examines if Black–Scholes option pricing model (BSOPM) is a good indicator of option pricing in Indian context. The literature review highlights that various studies have been conducted on BSOPM in various stock exchange across the world with mixed outcome on its relevance and applicability. This article is an empirical study to test the relevance of BSOPM for which 10 most popular industry’s stock listed on National Stock Exchange have been taken. Then the BSOPM has been applied using volatility and risk-free rate. Furthermore, t-test has been used to test the hypothesis and determine the significant relationship between BS model values and actual model values. This study concludes that BSOPM involves significant degree of mispricing. Hence, this model alone cannot be adopted as an indicator for option pricing. The variation from market price is synchronised with respect to moneyness and time to maturity of the option.

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Black-Scholes Model and Option Pricing

Simulation Techniques in Financial Risk Management ◽

10.1002/0471789496.ch3 ◽

2006 ◽

pp. 31-48

Keyword(s):

Option Pricing ◽

Black Scholes Model ◽

Black Scholes

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Pricing resettable convertible bonds using an integral equation approach

IMA Journal of Management Mathematics ◽

10.1093/imaman/dpz015 ◽

2019 ◽

Vol 31 (4) ◽

pp. 417-443

Author(s):

Sha Lin ◽

Song-Ping Zhu

Keyword(s):

Integral Equation ◽

Convertible Bonds ◽

Convertible Bond ◽

Equation Approach ◽

Fair Price ◽

Bond Price ◽

Black Scholes Model ◽

Black Scholes ◽

Integral Equation Approach ◽

Increasing Function

Abstract In this paper, the fair price of an American-style resettable convertible bond (CB) under the Black–Scholes model with a particular reset clause is calculated. This is a challenging problem because an unknown optimal conversion price needs to be determined together with the bond price. There is also an additional complexity that the value of the conversion ratio will change when the underlying price touches the reset price. Because of the additional reset clause, the bond price is not always a monotonically increasing function with the underlying price, which is impossible for other types of the CBs. Of course, the problem can be dealt with using the Monte-Carlo simulation. But, a partial differential equation (PDE)/integral equation approach is far superior in terms of computational efficiency. Fortunately, after establishing the PDE system governing the bond price, we are able to present an integral equation representation by applying the incomplete Fourier transform on the PDE system.

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PREFERENCES, LÉVY JUMPS AND OPTION PRICING

Annals of Financial Economics ◽

10.1142/s2010495207500017 ◽

2007 ◽

Vol 03 (01) ◽

pp. 0750001 ◽

Cited By ~ 1

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.

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Option pricing models

Journal of the Institute of Actuaries ◽

10.1017/s0020268100036696 ◽

1989 ◽

Vol 116 (3) ◽

pp. 537-558 ◽

Cited By ~ 2

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.

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Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2009.09.041 ◽

2010 ◽

Vol 389 (3) ◽

pp. 438-444 ◽

Cited By ~ 41

Author(s):

Xiao-Tian Wang

Keyword(s):

Option Pricing ◽

Transaction Costs ◽

Long Range ◽

Long Range Dependence ◽

European Option ◽

Black Scholes Model ◽

Black Scholes

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

Journal of Mathematics Research ◽

10.5539/jmr.v10n6p108 ◽

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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Finite Difference/Fourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing

Mathematical Problems in Engineering ◽

10.1155/2020/1393456 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Juan He ◽

Aiqing Zhang

Keyword(s):

Option Pricing ◽

Dynamic Behavior ◽

Numerical Scheme ◽

Step Size ◽

Spatial Direction ◽

Discrete Method ◽

Black Scholes Model ◽

Black Scholes ◽

Difference Fourier ◽

The Impact

We study the fractional Black–Scholes model (FBSM) of option pricing in the fractal transmission system. In this work, we develop a full-discrete numerical scheme to investigate the dynamic behavior of FBSM. The proposed scheme implements a known L1 formula for the α-order fractional derivative and Fourier-spectral method for the discretization of spatial direction. Energy analysis indicates that the constructed discrete method is unconditionally stable. Error estimate indicates that the 2−α-order formula in time and the spectral approximation in space is convergent with order OΔt2−α+N1−m, where m is the regularity of u and Δt and N are step size of time and degree, respectively. Several numerical results are proposed to confirm the accuracy and stability of the numerical scheme. At last, the present method is used to investigate the dynamic behavior of FBSM as well as the impact of different parameters.

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