TY: THES
T1 - Lévy processes in exotic options pricing
A1 - Enes, Diana Catarina Gonçalves
N2 - Prices fluctuations in markets, both liquid and illiquid, exhibit discontinuous behaviour. Levy processes are a natural generalization for stochastic processes with jumps, since they comprehend simultaneously a deterministic component as well as continuous and discontinuous stochastic com¬ponents. As it is possible to model asset prices as exponential of Levy processes, in this work we set the model using two pure jump processes: variance gamma and generalized hyperbolic. While using this class of processes, some important economic characteristics change in relation to the usual Black-Scholes model. The market is no longer complete for a more general Levy model, with several sources of randomness. We start by introducing some important results about Levy processes and follow with a brief exposition on possible equivalent martingale measures. After this introduction, we estimate the parameters of the distributions, by using market data and the Fourier transform to calculate vanilla option prices, and then minimizing the error be¬tween the market and the model prices. With the models calibrated to market data, we use Monte Carlo simulation to price an exotic option on the underlying, with double barriers. The results are compared with the Black-Scholes model and the market prices, requested over the counter to some of the main liquidity providers for that kind of structures.
UR - http://www.repository.utl.pt/handle/10400.5/4324
Y1 - 2011
PB - Instituto Superior de Economia e Gestão