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Perfect Hedging of Index Derivatives Under a Locally Arbitrage Free Minimal Market Model

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Abstract

The paper presents a financial market model that generates stochastic volatility using a minimal set of factors. These factors, formed from transformations of square root processes, model the dynamics of different denominations of a benchmark portfolio. Benchmarked prices are assumed to be local martingales. Numerical results for the pricing and hedging of basic derivatives on indices are described. This includes cases where the standard risk neutral pricing methodology fails. However, payoffs can be perfectly hedged using self-financing strategies and a form of arbitrage still exists. This is illustrated by hedge simulations. The term structure of implied volatilities is documented.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp61.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 61.

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Date of creation: 01 Jun 2001
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Handle: RePEc:uts:rpaper:61

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Keywords: derivative pricing; arbitrage; minimal market model;

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  1. Eckhard Platen, 2001. "A Benchmark Model for Financial Markets," Research Paper Series 59, Quantitative Finance Research Centre, University of Technology, Sydney.
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