European and American options under proportional transaction costs

Research output: ThesisDoctoral Thesis

Abstract

This thesis is concerned with models of financial markets with proportional transaction costs on trading in shares, modelled as bid-ask spreads, and different interest rates for the borrowing and lending of cash. We establish the fundamental theorem of asset pricing by giving a necessary and sufficient condition for the absence of arbitrage, namely the making of risk-free profit without initial investment. We also study the pricing and hedging of derivative securities in such models. The fair price of a derivative security is defined as a market price for it that does not introduce arbitrage into the model, and a super-hedging strategy allows the seller and buyer to remain in a solvent position after respectively delivering and receiving the derivative security at the exercise date. We present efficient algorithms for the fair pricing of derivative securities of both European and American type, the first having a fixed exercise date and the latter having a predetermined interval of exercise dates. Our work unifies and extends all existing algorithms for the calculation of such prices. As a by-product, we also present a straightforward iterative method for determining the optimal super-hedging strategies for the buyers and sellers of such derivative securities, thus solving the hedging problem. We also extend existing theoretical results by giving new representations for the bid and ask prices of American and European options in terms of their expected payoffs.
Original languageEnglish
QualificationPhD
Awarding Institution
  • University of York
Award date22 Apr 2007
Publication statusPublished - 2006

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