Contingent claim valuation with penalty costs on short selling positions. / Um modelo estocástico para o apreçamento de derivativos com penalidades em vendas a descoberto.
AUTOR(ES)
Edivar Vilela de Queiroz Filho
DATA DE PUBLICAÇÃO
2006
RESUMO
In this work we present a financial theory with penalty costs on short selling positions. Penalty costs differ from transaction costs for they do not depend on changes on trading positions (strategies). In the case of short selling in stocks, the investor borrows and then sells the position; in this case, the penalty costs are associated with the borrowing rate. For the risk free asset the penalty costs are associated with the spread between the credit and deposit rates. The work is developed in a discrete and finite framework; the mathematics involved is the same found in traditional financial literature; roughly, it runs through concepts of linear algebra, linear programming and discrete stochastic calculus. This framework is aligned with the objectives of this work which consist of developing a new theory without losing its financial intuition or the computational feasibility to implement solutions; in other words, the ability to apply the theory in practical applications. We begin by studding the Single-Period case and then extend the results to the Multi-Period case. In particular we present the necessary and sufficient conditions for the non existence of arbitrage, these conditions become the same as in the traditional model if the penalty costs are zero. Also, we show that the necessary and sufficient conditions for the model to be complete are the same in both cases. The introduction of penalty costs induces a difference in the costs of replicating the contingent claims -X and X; the replicating prices will be denominated bid and ask prices, respectively. To finish, we show that under certain conditions we can build an algorithm to calculate the maximal replicating strategy in a consistent manner, that is, we can calculate the bid and ask prices free of arbitrage.
ASSUNTO(S)
penalty cost preços de compra e venda prising apreçamento de títulos contingentes contingent claim custos de penalidade
