Mimicking the one-dimensional marginal distributions of stochastic diffusions

In the large maturity limit, we compute explicitly the Local Volatility surface for Heston, through Dupire’s formula, with Fourier pricing of the respective derivatives of the call price. Than we verify that the prices of European call options produced by the Heston model, concide with those given by the local volatility model where the Local Volatility is computed as said above.

Observations and modeling of the Marginal Ice Zone

Global climate change in recent decades has strongly influenced the Arctic generating pronounced warming accompanied by significant reduction of sea ice in seasonally ice-covered seas and a dramatic increase of open water regions exposed to wind [Stephenson et al., 2011]. By strongly scattering the wave energy, thick multiyear ice prevents swell from penetrating deeply into the Arctic pack ice. However, with the recent changes affecting Arctic sea ice, waves gain more energy from the extended fetch and can therefore penetrate further into the pack ice. Arctic sea ice also appears weaker during melt season, extending the transition zone between thick multi-year ice and the open ocean. This region is called the Marginal Ice Zone (MIZ). In the Arctic, the MIZ is mainly encountered in the marginal seas, such as the Nordic Seas, the Barents Sea, the Beaufort Sea and the Labrador Sea. Formed by numerous blocks of sea ice of various diameters (floes) the MIZ, under certain conditions, allows maritime transportation stimulating dreams of industrial and touristic exploitation of these regions and possibly allowing, in the next future, a maritime connection between the Atlantic and the Pacific. With the increasing human presence in the Arctic, waves pose security and safety issues. As marginal seas are targeted for oil and gas exploitation, understanding and predicting ocean waves and their effects on sea ice become crucial for structure design and for real time safety of operations. The juxtaposition of waves and sea ice represents a risk for personnel and equipment deployed on ice, and may complicate critical operations such as platform evacuations. The risk is difficult to evaluate because there are no long-term observations of waves in ice, swell events are difficult to predict from local conditions, ice breakup can occur on very short time-scales and wave-ice interactions are beyond the scope of current forecasting models [Liu and Mollo-Christensen, 1988,Marko, 2003]. In this thesis, a newly developed Waves in Ice Model (WIM) [Williams et al., 2013a,Williams et al., 2013b] and its related Ocean and Sea Ice model (OSIM) will be used to study the MIZ and the improvements of wave modeling in ice infested waters. The following work has been conducted in collaboration with the Nansen Environmental and Remote Sensing Center and within the SWARP project which aims to extend operational services supporting human activity in the Arctic by including forecast of waves in ice-covered seas, forecast of sea-ice in the presence of waves and remote sensing of both waves and sea ice conditions. The WIM will be included in the downstream forecasting services provided by Copernicus marine environment monitoring service.