Structured Products Modelled as Stochastic Processes

Abstract: In this thesis, the value of the two composed financial products (structured products), sprinters and auto-calls, are studied and compared to the European call option. The study is preformed using both analytical and numerical solutions, where the underlying is either said to follow a GBM-process (Geometric Brownian Motion) or a GARCH-process (Generalized Autoregressive Conditional Heteroskedasticity). One of the main results is that the GARCHdt-model is optimistic to a larger extent than the GBM-model. This is shown by a generally higher price of derivatives. Many times this is an effect of the individually high payoffs resulting from the simulations. This effect is clearest seen in the simulations of option, where the GARCHdt-simulations reach payoffs ten times higher than the highest GBM pay off. With the introduction of structured products and several underlies, this effect is somewhat damped, but still substantial. Although the GARCHdt-model gave unreasonable high payoffs occasionally, it many times out-performed the GBM-model. When compared to structured products with real data as underlies, the GARCHdt- simulations showed a higher number of similarities than the GBM-simulations.