Drawbacks and Limitations of Black-Scholes Model for Options Pricing

Janková, Zuzana

doi:10.5171/2018.79814

Cited by 18 publications

(17 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, it assumes that during the lifetime of the option no dividend is paid, that risk-free rate and volatility are constant, and the movement of the market cannot be predicted but in the real world, usually, this cannot happen. Likewise, Janko has studied the drawbacks and limitations of the Black-Scholes model and concluded that "another strong prerequisite necessary for the derivation of the Black-Scholes model is the perfect derivative replication by the share and a risk-free instrument; however, this cannot be achieved without transaction costs" [12][13]. This means B-S formula does not consider the transaction cost.…”

Section: Discussionmentioning

confidence: 99%

The Valuation of European Option on Underlying Stock Price Based on AAPL index

Wu¹,

Zhang²

2022

Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022)

View full text Add to dashboard Cite

Simulating option prices is one of the most commonly used arbitrage investment methods by financial investors at present. In this paper, the Black-Scholes model is used to simulate option price, which is widely used in option valuation. At the same time, taking the European option as an example, this paper selects the daily underlying stock price data of Apple Inc. from November 2018 to October 2021 and obtains a total of 745 observed values. Secondly, by searching and calculating the value of relevant parameters, the simulated option value and the price of call and put options are obtained. The results were in line with expected price movements. Finally, considering that the single target data cannot explain the robust results, sensitivity tests of different strike prices, different risk-free interest rates, and different maturity dates are carried out. The results show that the option prices under different conditions are consistent with the expected prices. To sum up, in this paper it is of theoretical and practical significance to simulate European option price based on the underlying stock price.

show abstract

Section: Discussionmentioning

confidence: 99%

The Valuation of European Option on Underlying Stock Price Based on AAPL index

Wu¹,

Zhang²

2022

Proceedings of the 2022 7th International Conference on Financial Innovation and Economic Development (ICFIED 2022)

View full text Add to dashboard Cite

show abstract

“…For Al-Zhour et al [2] investigated pricing using a nonlinear volatility model. Jankova [6] focused on the methods of derivative contract pricing, and derived the basic differential equation of the Black-Scholes model for option contract pricing. He also referred to the significant drawbacks and limitations of other option pricing models which are based on unrealistic assumptions.…”

Section: Preliminariesmentioning

confidence: 99%

Dynamic investment portfolio optimization using a Multivariate Merton Model with Correlated Jump Risk

Afhami,

Rezapour,

Madadi

et al. 2021

Preprint

View full text Add to dashboard Cite

In this paper, we are concerned with the optimization of a dynamic investment portfolio when the securities which follow a multivariate Merton model with dependent jumps are periodically invested and proceed by approximating the Condition-Value-at-Risk (CVaR) by comonotonic bounds and maximize the expected terminal wealth. Numerical studies as well as applications of our results to real datasets are also provided.

show abstract

“…Nowadays many different option contracts are traded. They are divided into call and put contracts giving the owner the right to buy or sell an asset (Hull et al, 1987;Jankova, 2018), respectively. The option contract may be signed for a few days as well as for a several months.…”

Section: Introductionmentioning

confidence: 99%

“…This approach includes also linear Black-Scholes option pricing model (Ivancevic, 2011;Wróblewski, 2017) having the form of the linear parabolic boundary value problem with constant coefficients. The option trading practice indicates, that the assumptions of linear Black-Scholes option pricing model are simplification (Hull et al, 1987;Jankova, 2018) of the real market conditions. Assuming in this linear model stochastic volatility or interest rate we can extend and transform it into non-linear model.…”

Section: Introductionmentioning

confidence: 99%

Quantum Dynamics approach for non-linear Black-Scholes option pricing

Wróblewski

Myśliński

2023

Preprint

View full text Add to dashboard Cite

Option pricing models are formulated based on mathematical theories. They are applied to estimate the fair value of an option. Among different pricing models, the linear Black-Scholes equation is very frequently used as option pricing model. Since assumptions of this linear model do not match precisely the real market conditions and do not allow to estimate the option price precisely there are developed more complicated non-linear Black-Scholes option pricing models. In these models volatility of underlying asset price or market risk free interest rate are assumed stochastic or time dependent. Moreover transaction costs are also taken into account. Quantum mechanics provides other approach to calculate option values using non-linear models. This approach is based on the similarity between the evolution of elementary particles in space and the volatility of the stock prices. In previous paper the authors have proposed non-linear Black-Scholes model to calculate option price based on quantum dynamics approach. This model has been obtained by suitable transformation of variables in non-linear Schrödinger equation with the external potential term. In this paper the non-linear quantum based option pricing model is numerically tested and verified. Based on this model, the calculation of European, Asian and American call option prices for market data is provided. The model parameters, especially the adaptive market potential, have been estimated based on market prices of European call options listed on Warsaw Stock Exchange as well as American call options prices based on the selected NYSE stock prices. The sensitivity of this model with respect to risk free interest rate has been investigated. For the sake of comparison non-linear Heston option pricing model has been also solved and calibrated using Monte Carlo method. The comparison of option pricing using the developed quantum based model, linear Black-Scholes model, Heston model, indicates higher precision and lower computational costs of the proposed enhanced non-linear model.

show abstract

Drawbacks and Limitations of Black-Scholes Model for Options Pricing

Cited by 18 publications

References 9 publications

The Valuation of European Option on Underlying Stock Price Based on AAPL index

The Valuation of European Option on Underlying Stock Price Based on AAPL index

Dynamic investment portfolio optimization using a Multivariate Merton Model with Correlated Jump Risk

Quantum Dynamics approach for non-linear Black-Scholes option pricing

Contact Info

Product

Resources

About