scholarly journals Implied Volatility in Black-scholes Model with Garch Volatility

2014 ◽  
Vol 8 ◽  
pp. 658-663 ◽  
Author(s):  
Muhammad Sheraz ◽  
Vasile Preda
Keyword(s):  
Implied Volatility ◽  
Black Scholes Model ◽  
Black Scholes

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.

A Simple Model for Option Pricing with Jumping Stochastic Volatility

1998 ◽  
Vol 01 (04) ◽  
pp. 487-505 ◽  
Author(s):  
Stefano Herzel
Keyword(s):  
Implied Volatility ◽  
Market Price ◽  
Volatility Risk ◽  
Simple Modification ◽  
Closed Form Solutions ◽  
Black Scholes Model ◽  
A Value ◽  
Black Scholes ◽  
Delta Hedging ◽  
Actual Price

This paper proposes a simple modification of the Black–Scholes model by assuming that the volatility of the stock may jump at a random time τ from a value σa to a value σb. It shows that, if the market price of volatility risk is unknown, but constant, all contingent claims can be valued from the actual price C0, of some arbitrarily chosen "basis" option. Closed form solutions for the prices of European options as well as explicit formulas for vega and delta hedging are given. All such solutions only depend on σa, σb and C0. The prices generated by the model produce a "smile"-shaped curve of the implied volatility.

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.

scholarly journals Solving Black-Schole Equation Using Standard Fractional Brownian Motion

2019 ◽  
Vol 11 (2) ◽  
pp. 142
Author(s):  
Didier Alain Njamen Njomen ◽  
Eric Djeutcha
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Financial Market ◽  
Implied Volatility ◽  
Classical Model ◽  
Hurst Index ◽  
European Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
The Cost

In this paper, we emphasize the Black-Scholes equation using standard fractional Brownian motion BHwith the hurst index H ∈ [0,1]. N. Ciprian (Necula, C. (2002)) and Bright and Angela (Bright, O., Angela, I., & Chukwunezu (2014)) get the same formula for the evaluation of a Call and Put of a fractional European with the different approaches. We propose a formula by adapting the non-fractional Black-Scholes model using a λHfactor to evaluate the european option. The price of the option at time t ∈]0,T[ depends on λH(T − t), and the cost of the action St, but not only from t − T as in the classical model. At the end, we propose the formula giving the implied volatility of sensitivities of the option and indicators of the financial market.

Option Pricing using Black Scholes Model (Case-Tata Motors and Reliance)

2015 ◽  
Vol 9 (1and2) ◽  
Author(s):  
Ms. Mamta Shah
Keyword(s):  
Stock Price ◽  
Implied Volatility ◽  
Safety Net ◽  
Volatility Smile ◽  
Model Case ◽  
Underlying Asset ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Strategies ◽  
Additional Income

The power of options lies in their versatility. It enables the investors to adjust position according to any situation that arises. Options can be speculative or conservative. This means investor can do everything from protecting a position from a decline to outright betting on the movement of a market or index. Options can enable the investor to buy a stock at a lower price, sell a stock at a higher price, or create additional income against a long or short stock position. One can also uses option strategies to profit from a movement in the price of the underlying asset regardless of market direction. the responsible act and safe thing to do. Options provide the same kind of safety net for trades and investments already committed, which is known as hedging. The research paper is based on Black Scholes Model. The study includes the Implied Volatility Test and Volatility Smile Test. This study also includes the solver available in MS Excel. This study is based on stock price of Reliance and Tata Motors.

scholarly journals ESTIMASI NILAI IMPLIED VOLATILITY MENGGUNAKAN SIMULASI MONTE CARLO

2018 ◽  
Vol 7 (3) ◽  
pp. 239
Author(s):  
MAKBUL MUFLIHUNALLAH ◽  
KOMANG DHARMAWAN ◽  
NI MADE ASIH
Keyword(s):  
Monte Carlo ◽  
Capital Market ◽  
Implied Volatility ◽  
Option Price ◽  
European Options ◽  
Price Variation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Alternative Investment ◽  
The Capital Market

Investing among investors is an exciting activity to gain profit in the financial world. The development of investment in the financial world affects the number of alternative investment instruments that can be offered to investors in the capital market. The management of instruments in finance depends on the accuracy of forecasting of variables for example volatility. Volatility is a statistic of the degree of price variation in one period to the next which is expressed by ?. Volatility values can be estimated using Implied Volatility. Implied Volatility is the volatility used in determining the price of European options obtained by equalizing the price of the theoretical options, the price obtained from the Black-Scholes model, with the option price in the market. In this research will discuss how to estimate Implied Volatility value using the option obtained from simulation with Monte Carlo.

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.

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