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Leland's approach to the hedging of derivatives under proportional transaction costs is based on an approximate replication of the European-type contingent claim VT using the classical Black Scholes formulae with a suitably enlarged volatility. The formal mathematical framework is a scheme of...
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We apply the Malliavin calculus to the stochastic string framework and obtain a Clark-Ocone-like formula. This result allows us to rewrite the hedging portfolio explicitly in terms of the Malliavin derivative of the discounted payoff. We illustrate this new result with two applications. Firstly,...
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This paper provides an introduction to derivative products and markets. It also reviews the basic conceptual framework for asset pricing. Derivative products and markets are defined and insight into asset pricing is provided. This is based on assumptions of no-arbitrage and frictionless markets....
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There are two major streams of literature on the modeling of financial bubbles: the strict local martingale framework … can exhibit strict local martingale behavior, we clarify the connection between these previously disconnected approaches …. While the original JLS model is never a strict local martingale, there are relaxations which can be strict local martingales …
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Taking a portfolio perspective on option pricing and hedging, we show that within the standard Black-Scholes-Merton framework large portfolios of options can be hedged without risk in discrete time. The nature of the hedge portfolio in the limit of large portfolio size is substantially different...
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