scholarly journals European Option Pricing Formula in Risk-Aversive Markets

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Shujin Wu ◽  
Shiyu Wang
Keyword(s):  
Risk Measure ◽  
European Option ◽  
Underlying Asset ◽  
No Arbitrage ◽  
European Option Pricing ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Risk Neutral ◽  
Arbitrage Opportunity ◽  
Weaker Conditions

In this study, using the method of discounting the terminal expectation value into its initial value, the pricing formulas for European options are obtained under the assumptions that the financial market is risk-aversive, the risk measure is standard deviation, and the price process of underlying asset follows a geometric Brownian motion. In particular, assuming the option writer does not need the risk compensation in a risk-neutral market, then the obtained results are degenerated into the famous Black–Scholes model (1973); furthermore, the obtained results need much weaker conditions than those of the Black–Scholes model. As a by-product, the obtained results show that the value of European option depends on the drift coefficient μ of its underlying asset, which does not display in the Black–Scholes model only because μ = r in a risk-neutral market according to the no-arbitrage opportunity principle. At last, empirical analyses on Shanghai 50 ETF options and S&P 500 options show that the fitting effect of obtained pricing formulas is superior to that of the Black–Scholes model.

Comparison of European Option Pricing Models at Multiple Periods

2021 ◽  
pp. 149-166
Author(s):  
Amir Ahmad Dar ◽  
N. Anuradha ◽  
Ziadi Nihel
Keyword(s):  
Option Pricing ◽  
Graphical Representation ◽  
European Option ◽  
Pricing Models ◽  
European Option Pricing ◽  
Black Scholes Model ◽  
Time Period ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Anderson Darling

The point of this chapter is to think about the correlation of two well-known European option pricing models – Black Scholes Model and Binomial Option Pricing Model. The above two models not statistically significant at one period. In this examination, it is shown how the above two European models are statistically significant when the time period increases. The independent paired t-test is utilized with the end goal to demonstrate that they are statistically significant to vary from one another at higher time period and the Anderson Darling test being used for the normality test. The Minitab and Excel programming has been utilized for graphical representation and the hypothesis testing.

Block-pulse operational matrix method for solving fractional Black-Scholes equation

2017 ◽  
Vol 44 (3) ◽  
pp. 489-502 ◽  
Author(s):  
Farshid Mehrdoust ◽  
Amir Hosein Refahi Sheikhani ◽  
Mohammad Mashoof ◽  
Sabahat Hasanzadeh
Keyword(s):  
Design Methodology ◽  
Operational Matrix ◽  
Initial Condition ◽  
European Option ◽  
Content Type ◽  
Operational Matrix Method ◽  
European Option Pricing ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Alternative Algorithm

Purpose The purpose of this paper is to evaluate a European option using the fractional version of the Black-Scholes model. Design/methodology/approach In this paper, the authors employ the block-pulse operational matrix algorithm to approximate the solution of the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Findings The fractional derivative will be described in the Caputo sense in this paper. The authors show the accuracy and computational efficiency of the proposed algorithm through some numerical examples. Originality/value This is the first paper that considers an alternative algorithm for pricing a European option using the fractional Black-Scholes model.

Arbitrage Pricing

2019 ◽  
pp. 95-118
Author(s):  
Tomas Björk
Keyword(s):  
Continuous Time ◽  
Implied Volatility ◽  
Futures Contracts ◽  
Martingale Measures ◽  
Bank Account ◽  
No Arbitrage ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Financial Derivative ◽  
Delta Hedging

The chapter starts with a detailed discussion of the bank account in discrete and continuous time. The Black–Scholes model is then introduced, and using the principle of no arbitrage we study the problem of pricing an arbitrary financial derivative within this model. Using the classical delta hedging approach we derive the Black–Scholes PDE for the pricing problem and using Feynman–Kač we also derive the corresponding risk neutral valuation formula and discuss the connection to martingale measures. Some concrete examples are studied in detail and the Black–Scholes formula is derived. We also discuss forward and futures contracts, and we derive the Black-76 futures option formula. We finally discuss the concepts and roles of historic and implied volatility.

scholarly journals The Extended Black-Scholes Model with-LAGS-and “Hedging Errors”

2003 ◽  
Author(s):  
Mondher Bellalah
Keyword(s):  
Stock Price ◽  
Standard Form ◽  
Small Time ◽  
Market Model ◽  
Short Term ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Elapsed Time ◽  
Black Scholes Model ◽  
Black Scholes

The Black-Scholes model is derived under the assumption that heding is done instantaneously. In practice, there is a “small” time that elapses between buying or selling the option and hedging using the underlying asset. Under the following assumptions used in the standard Black-Scholes analysis, the value of the option will depend only on the price of the underlying asset S, time t and on other Variables assumed constants. These assumptions or “ideal conditions” as expressed by Black-Scholes are the following. The option us European, The short term interest rate is known, The underlying asset follows a random walk with a variance rate proportional to the stock price. It pays no dividends or other distributions. There is no transaction costs and short selling is allowed, i.e. an investment can sell a security that he does not own. Trading takes place continuously and the standard form of the capital market model holds at each instant. The last assumption can be modified because in practice, trading does not take place in-stantaneouly and simultaneously in the option and the underlying asset when implementing the hedging strategy. We will modify this assumption to account for the “lag”. The lag corresponds to the elapsed time between buying or selling the option and buying or selling - delta units of the underlying assets. The main attractions of the Black-Scholes model are that their formula is a function of “observable” variables and that the model can be extended to the pricing of any type of option. All the assumptions are conserved except the last one.

Sign in / Sign up

Export Citation Format

Share Document