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The Effect of Correlation and Transaction Costs on the Pricing of Basket Options

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  • C. Atkinson
  • P. Ingpochai

Abstract

In this article, we examine the problem of evaluating the option price of a European call option written on N underlying assets when there are proportional transaction costs in the market. Since the portfolio under consideration consists of multiple risky assets, which makes numerical methods formidable, we use perturbation analyses. The article extends the model for option pricing on uncorrelated assets, which was proposed by Atkinson and Alexandropoulos (2006; Pricing a European basket option in the presence of proportional transaction cost, Applied Mathematical Finance , 13(3), pp. 191--214). We determine optimal hedging strategies as well as option prices on both correlated and uncorrelated assets. The option valuation problem is obtained by comparing the maximized utility of wealth with and without option liability. The two stochastic control problems, which arise from the transaction costs, are transformed to free boundary and partial differential equation problems. Once the problems have been formulated, we establish optimal trading strategies for each of the portfolios. In addition, the optimal hedging strategies can be found by comparing the trading strategies of the two portfolios. We provide a general procedure for solving N risky assets, which shows that for ‘small’ correlations the N asset problem can be replaced by N ( N − 1)/2 two-dimensional problems and give numerical examples for the two risky assets portfolios.

Suggested Citation

  • C. Atkinson & P. Ingpochai, 2012. "The Effect of Correlation and Transaction Costs on the Pricing of Basket Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(2), pages 131-179, June.
  • Handle: RePEc:taf:apmtfi:v:19:y:2012:i:2:p:131-179 DOI: 10.1080/1350486X.2011.601919
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    References listed on IDEAS

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    1. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    2. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
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    5. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Erik Schlögl, 2001. "Arbitrage-Free Interpolation in Models of Market Observable Interest Rates," Research Paper Series 71, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Alexander van Haastrecht & Antoon Pelsser, 2011. "Generic pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility," Quantitative Finance, Taylor & Francis Journals, pages 665-691.
    9. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    10. Grzelak, Lech & Oosterlee, Kees, 2009. "On The Heston Model with Stochastic Interest Rates," MPRA Paper 20620, University Library of Munich, Germany, revised 18 Jan 2010.
    11. Grzelak, Lech & Oosterlee, Kees, 2010. "An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile," MPRA Paper 20574, University Library of Munich, Germany.
    12. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
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    1. repec:mje:mjejnl:v:12:y:2017:i:3:p:7-18 is not listed on IDEAS
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