A More General Valuation and Arbitrage Theory for Itô Processes

A New Logistic-Type Model for Pricing European Options

“…In general do not impose conditions on the eigenvalues of the volatility of the price process. The main results in this paper are complementary to results in Londoño (2008) since it gives us concrete examples beyond standard models of financial markets.…”

“…From the above arguments, one of the possible one-dimensional stochastic extensions derived from the deterministic logistic equation under Londoño (2008) framework is:…”

“…The family of models studied in this paper is an example of models where a pricing theory can be obtained using the results of Londoño (2008Londoño ( , 2004. In general, the theory developed in Londoño (2008) does not impose conditions on the eigenvalues of the volatility matrix.…”

“…In general, the theory developed in Londoño (2008) does not impose conditions on the eigenvalues of the volatility matrix. Traditional models usually require that the eigenvalues of the volatility matrix remain away from 0 (see Karatzas and Shreve 1998).…”

“…In Londoño (2008), we developed a general theoretical framework for valuation and arbitrage. However, in order to provide models beyond the standard literature models, we needed to give conditions to guarantee the market completeness and the existence of non-explosive solutions for the stochastic differential equations than define the models.…”