We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at ha...

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time τ ≥ 0. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. After obtaining an effective one-dimensional market model, we achieve a closed expres...

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...

This study presents the methodology of sensitivity analysis and explores whether it can be an alternative evaluation criterion as well as a tool to “read” artificial neural networks’ knowledge. The simulation of the Black-Scholes formula is employed for this object. Since, in the Black-Scholes formula, the mapping relationship between the call price and five relevant variables is a mathematical...

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...

in this paper, installment options on the underlying assetwhich evolves according to black-scholes model and pays constant dividendto its owner will be considered. applying arbitrage pricing theory,the non-homogeneous parabolic partial differential equation governingthe value of installment option is derived. then, penalty method is usedto value the european continuous installment call option.

It has often been argued that there exists an underlying biological basis of utility functions. Taking this line of argument a step further in this paper, we have aimed to computationally demonstrate the biological basis of the Black-Scholes functional form as applied to classical option pricing and hedging theory. The evolutionary optimality of the classical Black-Scholes function has been com...

In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random{Time Binomial Model. We present the conditions to ensure weak{convergence to the Black{Scholes setup and convergence of the values for European and American put options. Di erently to the CRR{model the convergence beha...

In the Black-Scholes option price model Brownian motion and the underlying Normal distribution play a fundamental role. Empirical evidence however shows that the normal distribution is a very poor model to fit real-life data. In order to achieve a better fit we replace the Brownian motion by a special Lévy process: the Meixner process. We show that the underlying Meixner distribution allows an ...

The values of the parameters r, t, St, T , and K used to price a call option via the Black-Scholes formula can be easily obtained from market data. Estimating the volatility coefficient σ can be a more difficult task, and several estimation methods are considered in this section with some examples of how the Black-Scholes formula can be fitted to market data. We cover the historical, implied, a...