“Normality” of Stock Prices Bo Shi Abstract. The Black-Scholes Model, often simply called Black-Scholes, models the varying price of financial instruments over time: stocks in particular. This model assumes that returns on the underlying stock are lognormally distributed, which can be reasonable for many assets that offer options. However, from a selection of 100 stock histories, I found that a...

Value-based IT portfolio management requires the consideration of intertemporal interdependencies that may exist among IT projects. Therefore, several papers suggest adopting the real options approach in order to include intertemporal interdependencies within the valuation of IT projects. However, this paper shows that the standard Black-Scholes model, which is often used for valuating real opt...

This is the first of two papers in which we consider a stock with price process defined by a stochastic differential equation driven by a process Y (·) different from Brownian motion. The adoption of such a colored noise input is motivated by an analysis of real market data. The process Y (·) is defined by a continuous-time AR(∞)-type equation and may have either short or long memory. We show t...

We propose a methodology of Genetic Programming to approximate the relationship between the option price, its contract terms and the properties of the underlying stock price. An important advantage of the Genetic Programming approach is that we can incorporate currently known formulas, such as the Black-Scholes model, in the search for the best approximation to the true pricing formula. Using M...

This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. The models are calibrated to intraday FTSE 100 option prices. We apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk oriented measures. When we analyze the t to observed prices, GAR...

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black–Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the tail asymptotics for these option types fall into four scenarios.

This paper aims to investigate the assumptions under which the binomial option pricing model converges to the Black-Scholes formula. The results are not original; the paper mostly follows the outline of Cox, Ross, and Rubenstein[1]. However, the convergence is treated in greater detail than I have found elsewhere in the literature. This exercise clarifies the assumptions behind the binomial mod...

Using the solitonic solution-generating technique we rederived the one-rotational five-dimensional black ring solution found by Emparan and Reall. The seed solution is not the Minkowski metric, which is the seed of S-rotating black ring. The obtained solution has more parameters than the Emparan and Reall’s S-rotating black ring. We found the conditions of parameters to reduce the solution to t...