This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined Black-Scholes closed form solution modified (MBS) partial differential equation using Crank-Nicolson finite difference method. These equations were approximated to obtain Call Put prices. The explicit price both options found accordingly. solutions c...

The object of this study was to investigate some implications of the tenets of behavioral finance on the pricing of financial derivatives. In particular, based on the work by Wolff et al (2009) we have investigated how prospect theory (Kahneman and Tversky, 1979) can be intregrated into the Black and Scholes (1973) option pricing framework. We have then used the resulting " behavioral version "...

The maximality principle [6] is shown to be valid in some examples of discounted optimal stopping problems for the maximum process. In each of these examples explicit formulas for the value functions are derived and the optimal stopping times are displayed. In particular, in the framework of the Black-Scholes model, the fair prices of two lookback options with infinite horizon are calculated. T...

Using the symmetry group that was found in [1] and further studied in [2], in this work we study the partial differential equation of the Black-Scholes model [3] and relate such symmetries with the Mellin transform to find the price of an european like investment option. We also consider the Black-Schoes-Merton equation in the non-linear case that models investments in which volatility is a fun...

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...

We consider the infinite horizon optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model. For a general class of utility functions, we provide the value function in explicit form, and we derive closed-form ...

Keywords: Black–Scholes equation Completely monotonic function Finite difference scheme Laplace Transform M-Matrix Positivity-preserving Post–Widder formula a b s t r a c t In this paper we explore discrete monitored barrier options in the Black–Scholes framework. The discontinuity arising at each monitoring data requires a careful numerical method to avoid spurious oscillations when low volati...

We consider the infinite horizon optimal consumption-investment problem under the drawdown constraint, i.e. the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the constant coefficients Black and Scholes model. For a general class of utility functions, we provide the value function in explicit form, and we derive closed-form ...

Under the assumptions of the market of Black and Scholes, options are redundant since, through the classic Black-Scholes delta hedging argument, they can be replaced by an equivalent combination the risky asset underlying the option and a risk free asset. We show that options are not redundant when small proportional transaction costs of size ε are added to the model, which provides mathematica...