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.

Abstract
1. Introduction
2. Brownian Motion
    2.1. Definition
    2.2. The impact of random waves and floating rate inbending
    2.3. Problem Definition
3. Monte Carlo Simulation
4. Antithetic Variables
5. Multi-level Monte Carlo
6. Stochastic Volatility Model
    6.1. One-Factor Volatility Model
    6.2. Two-Factor Volatility Model
7. Numerical Results
    7.1. Example 1
    7.2. Example 2
8. Conclusion
References

• Behrouz FATHI-VAJARGAH(Department of Statistics, University of Guilan) Corresponding Author
• Ayoob SALIMIPOUR(Department of Applied Mathematics, University of Guilan)