Wind waves are important due to their high energy and impact on marine activities. This phenomenon is affects directly or indirectly the construction of coastal infrastructure, shipping and recreational activities. Due to the issues presented, marine parameters are very important. In this study, we try to pay attention to wave as one of the most important marine parameters. As the movements of waves have high uncertainty, financial models can be used to simulate the wave's paths. We use the Monte Carlo method for this purpose. The Monte Carlo simulation is a flexible and simple tool that is widely used in the evaluation of random paths. To compute a random path, we require an integral discretization. In this paper, we study the valuation of European options using Monte Carlo simulation and then compare this result with multi-level Monte Carlo approach and other antithetic variables. Then, we use the multi-level Monte Carlo approach proposed by (M. B. Giles 2008) for pricing under the two-factor stochastic volatility model. We show that the multi-level Monte Carlo method reduces the computational complexity and also cost of the two-factor stochastic volatility model when compared with the standard Monte Carlo method. Also, we compare the multi-level Monte Carlo method and standard Monte Carlo method using an Euler discretization scheme and then, analyze the numerical results.

Cryptography is a science to maintain the security of the message by changing data or information into a different form, so the message cannot be recognized. Today, many algorithms have been proposed for image encryption, but the chaotic encryption methods have a good combination of speed and high security. In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. The chaos-based encryption schemes are composed of two steps: chaotic confusion and pixel diffusion. In the chaotic confusion stage, a combination of the chaotic maps is used to realize the confusion of all pixels. In this paper, we first give a brief introduction into chaotic image encryption and then we investigate some important properties and behaviour of the logistic map. The logistic map, aperiodic trajectory, or random-like fluctuation, could not be obtained with some choice of initial condition. Therefore, a noisy logistic map with an additive system noise is introduced. The proposed scheme is based on the extended map of the Clifford strange attractor, where each dimension has a specific role in the encryption process. Two dimensions are used for pixel permutation and the third dimension is used for pixel diffusion. In order to optimize the Clifford encryption system we increase the space key by using the noisy logistic map and a novel encryption scheme based on the Clifford attractor and the noisy logistic map for secure transfer images is proposed. This algorithm consists of two parts: the noisy logistic map shuffle of the pixel position and the pixel value. We use times for shuffling the pixel position and value then we generate the new pixel position and value by the Clifford system. To illustrate the efficiency of the proposed scheme, various types of security analysis are tested. It can be concluded that the proposed image encryption system is a suitable choice for practical applications.