The Random Walk is considered to be a tool trying to explain the characteristic of movement of prices in the financial markets. It can also be seen in the form of a trial to demonstrate the non-predictability of future changes in the financial markets through reliance on the characteristics identified based on past price changes. In this paper used is the variance-ratio test initiated by Lo and MacKinlay to test the Random Walk Hypothesis for a more recent data of eleven Stock Indexes, seen as main indexes of the current market.

For practitioners of equity markets, option pricing is a major challenge during high volatility periods and Black-Scholes formula for option pricing is not the proper tool for very deep out-of-the-money options. The Black-Scholes pricing errors are larger in the deeper out-of-the money options relative to the near the-money options, and it's mispricing worsens with increased volatility. Experts opinion is that the Black-Scholes model is not the proper pricing tool in high volatility situations especially for very deep out-of-the-money options. They also argue that prior to the 1987 crash, volatilities were symmetric around zero moneyness, with inthe-money and out-of-the money having higher implied volatilities than at-the-money options. However, after the crash, the call option implied volatilities were decreasing monotonically as the call went deeper into out-of-the-money, while the put option implied volatilities were decreasing monotonically as the put went deeper into in-the-money. Since these findings cannot be explained by the Black-Scholes model and its variations, researchers searched for improved option pricing models. Feedforward networks provide more accurate pricing estimates for the deeper out-of-the money options and handles pricing during high volatility with considerably lower errors for out-of-the-money call and put options. This could be invaluable information for practitioners as option pricing is a major challenge during high volatility periods. In this article a nonparametric method for estimating S&P 100 index option prices using artificial neural networks is presented. To show the value of artificial neural network pricing formulas, Black-Scholes option prices are compared with the network prices against market prices. To illustrate the practical relevance of the network pricing approach, it is applied to the pricing of S&P 100 index options from

No abstract

In every parametric formula of pricing a financial instrument, factors used in the calculation generally include the volatility estimate. Volatility measures the likely changes of the price for a specific period of time. The accuracy of estimated price strongly relies on the accuracy of provided expected changes in the market volatility for the period of interest. As opposed to other variables, which are assigned values to financial instrument, volatility is the only estimated one. For that reason, big focus of researchers was and still is on improving the volatility estimate. Initiated are different estimation approaches through last few decades. This paper explains few ARCH models, symmetric and asymmetric, and compares their estimates of daily volatility for the Standard and Poor's Indexes.

Currently the most popular method of estimating volatility is the implied volatility. It is calculated using the Black-Scholes option price formula, and is considered by traders to be a significant factor in signaling price movements in the underlying market. A trader is able to establish the proper strategic position in anticipation of changes in market trends if she/he could accurately forecast future volatility. There is an abundance of ways to compute the volatility. For two decades neural networks has been developed to forecast future volatility, using past volatilities and other options market factors. In this article a network is created for this purpose whose performance demonstrates the value of neural networks as a predictive tool in volatility analysis.