Browsing by Author "Marques, Hugo Miguel Fernandes"
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- The Heston model under stochastic interest ratesPublication . Marques, Hugo Miguel Fernandes; Nunes, João Pedro VidalIn this dissertation the Heston (1993) model is considered, but using, instead of a constant interest rate, stochastic interest rates according to Vasicek (1977) and to Cox, Ingersoll and Ross (1985) models. Under this framework, a closed-form solution is determined for the price of European standard calls, which, by using a manipulation implemented by Attari (2004), only require the evaluation of one characteristic function. For forward-start European calls, starting from the result for standard calls and using analytic characteristic functions, it is determined a closed-form solution that only requires one numerical integration. In the end, the results of these closedform solutions are compared with the results presented by Monte Carlo simulations for the considered models.