Project CEMAPRE internal
| Title | Modelling short term memory effects in financial derivatives |
| Participants | João Guerra, João Janela (Principal Investigator), Gilson Silva |
| Summary | The pricing of financial derivatives has been a central topic in modern finance for many years, since it was initially introduced by Merton, Black and Scholes back in 1973, and the famous Black-Scholes formula was first proposed. Black-Scholes formula relies on a number of assumptions that are not satisfied in many situations of practical interest. Successful generalizations of the Black-Scholes equation require a balance between two usually conflicting aspects: On one hand, a sufficiently elaborated stochastic differential equation to simulate the value of the underlying assets; on the other hand a stochastic equation that provides the desired mathematical properties to carry out a proper analysis of the problem. This project concerns with a generalization of the Jump telegraph drift diffusion model, where the jumps can have stochastic amplitude. The selection of this model is motivated by the fact that it can be reformulated as a system of PDEs, coupled by the reaction terms, that exhibits memory effects in both the price and the volatility. This new model will be compared with existing ones and we will address model calibration with real market data, as well as a full consistency and convergence analysis of the numerical schemes. |