An empirical study on using Hurst exponent estimation methods for pricing Call options by fractional Black–Scholes model

2018 ◽  
Vol 7 (1-2) ◽  
pp. 51-62
Author(s):  
Soňa Kilianová ◽  
Boris Letko
Keyword(s):  
Empirical Study ◽  
Hurst Exponent ◽  
Estimation Methods ◽  
Call Options ◽  
Black Scholes Model ◽  
Black Scholes

A NUMERICAL ANALYSIS OF THE EXTENDED BLACK–SCHOLES MODEL

2006 ◽  
Vol 09 (01) ◽  
pp. 69-89 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
ALEX POPOVICI ◽  
VICTORIA STEBLOVSKAYA
Keyword(s):  
Implied Volatility ◽  
Historical Data ◽  
Numerical Results ◽  
Estimation Methods ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Stochastic Volatilities ◽  
Parameter Estimation Methods ◽  
Implied Volatility Surfaces ◽  
Two Parameter

In this article some numerical results regarding the multidimensional extension of the Black–Scholes model introduced by Albeverio and Steblovskaya [1] (a multidimensional model with stochastic volatilities and correlations) are presented. The focus lies on aspects concerning the use of this model for the practice of financial derivatives. Two parameter estimation methods for the model using historical data from the market and an analysis of the corresponding numerical results are given. Practical advantages of pricing derivatives using this model compared to the original multidimensional Black–Scholes model are pointed out. In particular the prices of vanilla options and of implied volatility surfaces computed in the model are close to those observed on the market.

scholarly journals An Asymptotic Solution for Call Options on Zero-Coupon Bonds

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1940
Author(s):  
Michael J. Tomas Tomas III ◽  
Jun Yu
Keyword(s):  
Stochastic Process ◽  
Asymptotic Solution ◽  
Interest Rates ◽  
Perturbation Approach ◽  
Return Volatility ◽  
Leading Order ◽  
Bond Price ◽  
Call Options ◽  
Black Scholes Model ◽  
Black Scholes

We present an asymptotic solution for call options on zero-coupon bonds, assuming a stochastic process for the price of the bond, rather than for interest rates in general. The stochastic process for the bond price incorporates dampening of the price return volatility based on the maturity of the bond. We derive the PDE in a similar way to Black and Scholes. Using a perturbation approach, we derive an asymptotic solution for the value of a call option. The result is interesting, as the leading order terms are equivalent to the Black–Scholes model and the additional next order terms provide an adjustment to Black–Scholes that results from the stochastic process for the price of the bond. In addition, based on the asymptotic solution, we derive delta, gamma, vega and theta solutions. We present some comparison values for the solution and the Greeks.

Analysis of Options Pricing Methods: the Black-Scholes Model and the Monte-Carlo Method

2020 ◽  
Vol 9 (3) ◽  
pp. 39-42
Author(s):  
Leysen Yunusova
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Investment Decisions ◽  
Estimation Methods ◽  
Options Pricing ◽  
Financial Instruments ◽  
Strategic Investment ◽  
Black Scholes Model ◽  
The Monte Carlo Method ◽  
Black Scholes

Currently, the market of financial instruments is quite developed. Traditional financial instruments prevail on the Russian market, while derivatives of these financial instruments (options, futures, forwards, bills, etc.) are faintly developed. The reason for this situation is that few participants in the financial market can correctly evaluate financial products. Scientific researchers and large companies use different methods of estimating the value of financial instruments in making strategic investment decisions, since incorrect calculations can be irreparable. Therefore, it is important to apply the appropriate pricing methodology to various derivative financial instruments. The topic of derivative financial instruments in terms of scientific and theoretical aspects has been worked out in sufficient volume, but as for the pricing of these instruments, there are some gaps. There is still no method for pricing derivatives that would allow you to accurately assess the value of financial instruments for subsequent effective investment decisions. In this article considers the methodology of pricing of derivative financial instruments using the Black-Scholes model and the Monte Carlo method. The presented estimation methods allow us to calculate the range of price values that allows us to provide the most accurate expected results.

scholarly journals Black-Scholes Model in Determining European Option Prices on Netflix,Inc.

d'CARTESIAN ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 80
Author(s):  
Desty A. Tambingon ◽  
Jullia Titaley ◽  
Tohap Manurung
Keyword(s):  
Share Price ◽  
Option Prices ◽  
European Option ◽  
Put Options ◽  
Call Options ◽  
Price Data ◽  
Black Scholes Model ◽  
Black Scholes

Research has been conducted to compare the prices of European option on the Yahoo Finance website with prices obtained from the Black-Scholes model (theoretical price). Data was taken on January 31, 2019 which included the daily share price of Netflix, Inc. (NFLX) on February 14, 2018 - January 31, 2019 to obtain volatility, and NFLX options data due on January 17, 2020. Options with prices lower than theoretical prices are said to be underpriced, so the decision taken is to buy the options. Whereas options with prices higher than theoretical prices are said to be overpriced, so it has to be reconsidered. The proportion of the underpriced call options for the total number of call options is 77.7778%, while the proportion of the underpriced put options for the total number of put options is 38.5714%.

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