APPLYING THE GENETIC-BASED NEURAL NETWORKS TO VOLATILITY TRADING

2005 ◽  
Vol 01 (02) ◽  
pp. 285-293
Author(s):  
SHINN-WEN WANG
Keyword(s):  
Theoretical Model ◽  
Implied Volatility ◽  
Options Pricing ◽  
Pricing Model ◽  
Options Markets ◽  
Volatility Smile ◽  
Two Phase ◽  
Enterprise Value ◽  
Black Scholes ◽  
Value Estimation

The Black-Scholes options pricing model is widely applied in various options contracts, including contract design, trading, assets evaluation, and enterprise value estimation, etc. Unfortunately, this theoretical model limited by the influences of many unexpected real world phenomena due to six unreasonable assumptions. If we were to soundly take these phenomena into account, the opportunity to gain an excess return would be created. This research therefore combines both the remarkable effects caused by the implied volatility smile (or skew) and the tick-jump discrepancy between the underlying and derivative prices to establish a two-phase options arbitrage model using a genetic-based neural network (GNN). Using evidence from the warrant market in Taiwan, it is shown that the GNN model with arbitrage operations is superior in terms of performance to the original Black-Scholes-based arbitrage model. The GNN model is found to be suitable for application to various options markets as the valuation factors are modified. This paper helps to integrate the theoretical model with important practical considerations.

scholarly journals A mean bound financial model and options pricing

2017 ◽  
Vol 04 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Yu Li
Keyword(s):  
Implied Volatility ◽  
Heavy Tails ◽  
Asset Returns ◽  
Mathematical Explanation ◽  
Options Pricing ◽  
Fat Tails ◽  
Volatility Smile ◽  
Financial Model ◽  
Black Scholes Model ◽  
Black Scholes

Most of financial models, including the famous Black–Scholes–Merton options pricing model, rely upon the assumption that asset returns follow a normal distribution. However, this assumption is not justified by empirical data. To be more concrete, the empirical observations exhibit fat tails or heavy tails and implied volatilities against the strike prices demonstrate U-shaped curve resembling a smile, which is the famous volatility smile. In this paper we present a mean bound financial model and show that asset returns per time unit are Pareto distributed and assets are log Gamma distributed under this model. Based on this we study the sensitivity of the options prices to a change in underlying parameters, which are commonly called the Greeks, and derive options pricing formulas. Finally, we reveal the relation between correct volatility and implied volatility in Black–Scholes model and provide a mathematical explanation of volatility smile.

Cooperative Governance of Inter-provincial air pollution based on a Black–Scholes Options Pricing Model

2020 ◽  
Vol 277 ◽  
pp. 124031
Author(s):  
Jian Xue ◽  
Shengnan Zhao ◽  
Laijun Zhao ◽  
Di Zhu ◽  
Shuxin Mao
Keyword(s):  
Air Pollution ◽  
Options Pricing ◽  
Pricing Model ◽  
Black Scholes ◽  
Cooperative Governance

UNCERTAINTY IN PRICING TRADABLE OPTIONS

2003 ◽  
Vol 06 (02) ◽  
pp. 103-117 ◽  
Author(s):  
JORGE R. SOBEHART ◽  
SEAN C. KEENAN
Keyword(s):  
Interest Rates ◽  
Market Equilibrium ◽  
Expected Value ◽  
Options Pricing ◽  
Options Market ◽  
Pricing Model ◽  
Random Delays ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Random Fluctuations

In this paper we introduce an options pricing model consistent with the level of uncertainty observed in the options market. By assuming that the price at which an option can be traded is intrinsically uncertain, either because of the inability to hedge continuously or because of errors in the estimation of the security's volatility and interest rates, random delays in the execution of orders or information deficiencies, we show that the Black-Scholes model produces a biased estimate of the expected value of tradable options. Information deficiencies lead to a call-put relationship that reduces to the standard call-put expression on average but shows random fluctuations consistent with the concept of market equilibrium. The same information deficiencies can contribute to the volatility skew that affects the Black-Scholes model.

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.

A PARADOX OF INTUITION: HEDGING THE LIMIT OR HEDGING IN THE LIMIT?

2002 ◽  
Vol 05 (07) ◽  
pp. 729-736
Author(s):  
J. R. SOBEHART ◽  
S. C. KEENAN
Keyword(s):  
Stochastic Processes ◽  
Differential Calculus ◽  
Options Pricing ◽  
Pricing Model ◽  
No Arbitrage ◽  
Itô Calculus ◽  
Black Scholes

Here we review the notion of covergence in Itô calculus and its application to the Black-Scholes options pricing model and its extensions. The concept of covergence is fundamental to the development of the differential calculus of stochastic processes. It is also the key to understanding the validity of the no arbitrage condition imposed by Black and Scholes (1973) that leads to their options pricing equation.

scholarly journals Patterns of 50 ETF Options Implied Volatility in China: On Implied Volatility Functions

2021 ◽  
Vol 24 (1) ◽  
pp. 135-145
Author(s):  
Pengshi Li ◽  
Yan Lin ◽  
Yuting Zhong
Keyword(s):  
Implied Volatility ◽  
Stock Exchange ◽  
Empirical Work ◽  
Ordinary Least Squares ◽  
Options Pricing ◽  
Options Market ◽  
European Options ◽  
Volatility Smile ◽  
Volatility Function ◽  
Better Than

The aim of this study is to examine the volatility smile based on the European options on Shanghai stock exchange 50 ETF. The data gives evidence of the existence of a well-known U-shaped implied volatility smile for the SSE 50 ETF options market in China. For those near-month options, the implied volatility smirk is also observed. And the implied volatility remains high for the short maturity and decreases as the maturity increases. The patterns of the implied volatility of SSE 50 ETF options indicate that in-the-money options and out-of-the-money options are more expensive relative to at-the-money options. This makes the use of at-the-money implied volatility for pricing out-of- or in-the-money options questionable. In order to investigate the implied volatility, the regression-based implied volatility functions model is considered employed to study the implied volatility in this study as this method is simple and easy to apply in practice. Several classical implied volatility functions are investigated in this paper to find whether some kind of implied volatility functions could lead to more accurate options pricing values. The potential determinants of implied volatility are the degree of moneyness and days left to expiration. The empirical work has been expressed by means of simple ordinary least squares framework. As the study shows, when valuing options, the results of using volatility functions are mixed. For far-month options, using at-the-money implied volatility performs better than other volatility functions in option valuation. For near-month options, the use of volatility functions can improve the valuation accuracy for deep in-the-money options or deep out-of-the-money options. However, no particular implied volatility function performs very well for options of all moneyness level and time to maturity.

scholarly journals Implied volatility estimation of bitcoin options and the stylized facts of option pricing

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Noshaba Zulfiqar ◽  
Saqib Gulzar
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Volatility Smile ◽  
Stylized Facts ◽  
Approximation Techniques ◽  
Risk Hedging ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Newton Raphson ◽  
Futures And Options

AbstractThe recently developed Bitcoin futures and options contracts in cryptocurrency derivatives exchanges mark the beginning of a new era in Bitcoin price risk hedging. The need for these tools dates back to the market crash of 1987, when investors needed better ways to protect their portfolios through option insurance. These tools provide greater flexibility to trade and hedge volatile swings in Bitcoin prices effectively. The violation of constant volatility and the log-normality assumption of the Black–Scholes option pricing model led to the discovery of the volatility smile, smirk, or skew in options markets. These stylized facts; that is, the volatility smile and implied volatilities implied by the option prices, are well documented in the option literature for almost all financial markets. These are expected to be true for Bitcoin options as well. The data sets for the study are based on short-dated Bitcoin options (14-day maturity) of two time periods traded on Deribit Bitcoin Futures and Options Exchange, a Netherlands-based cryptocurrency derivative exchange. The estimated results are compared with benchmark Black–Scholes implied volatility values for accuracy and efficiency analysis. This study has two aims: (1) to provide insights into the volatility smile in Bitcoin options and (2) to estimate the implied volatility of Bitcoin options through numerical approximation techniques, specifically the Newton Raphson and Bisection methods. The experimental results show that Bitcoin options belong to the commodity class of assets based on the presence of a volatility forward skew in Bitcoin option data. Moreover, the Newton Raphson and Bisection methods are effective in estimating the implied volatility of Bitcoin options. However, the Newton Raphson forecasting technique converges faster than does the Bisection method.

An Empirical Test of the Black-Scholes Option Pricing Model and the Implied Variance: A Confidence Interval Approach

1987 ◽  
Vol 2 (4) ◽  
pp. 355-369 ◽  
Author(s):  
Haim Levy ◽  
Young Hoon Byun
Keyword(s):  
Confidence Interval ◽  
Option Pricing ◽  
Implied Volatility ◽  
Empirical Test ◽  
Market Price ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
S Model ◽  
Over Time

The empirical studies on the Black-Scholes (B-S) option pricing model have reported that the model tends to exhibit systematic biases with respect to the exercise price, time to expiration, and the stock's volatility. This paper attempts to test the B-S model with a new approach: derive the confidence interval of the model call option value based on the confidence interval of the. estimated variance. The test reports that even when the variance's confidence interval is considered, a systematic deviation between the theoretical “range” of the option price values and the observed market price still exist. If the stock variance is constant over time, the interpretation of the results is that the B-S model is wrong. However, if stock variance changes over time, the interpretation of the results is that the implied volatility in options market prices had a tendency to be significantly higher than the estimate that could have been obtained from historical data.

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