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Option Pricing of Twin Assets

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  • Marcelo J. Villena
  • Axel A. Araneda
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    Abstract

    How to price and hedge claims on nontraded assets are becoming increasingly important matters in option pricing theory today. The most common practice to deal with these issues is to use another similar or "closely related" asset or index which is traded, for hedging purposes. Implicitly, traders assume here that the higher the correlation between the traded and nontraded assets, the better the hedge is expected to perform. This raises the question as to how \textquoteleft{}closely related\textquoteright{} the assets really are. In this paper, the concept of twin assets is introduced, focusing the discussion precisely in what does it mean for two assets to be similar. Our findings point to the fact that, in order to have very similar assets, for example identical twins, high correlation measures are not enough. Specifically, two basic criteria of similarity are pointed out: i) the coefficient of variation of the assets and ii) the correlation between assets. From here, a method to measure the level of similarity between assets is proposed, and secondly, an option pricing model of twin assets is developed. The proposed model allows us to price an option of one nontraded asset using its twin asset, but this time knowing explicitly what levels of errors we are facing. Finally, some numerical illustrations show how twin assets behave depending upon their levels of similarities, and how their potential differences will traduce in MAPE (mean absolute percentage error) for the proposed option pricing model.

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    File URL: http://arxiv.org/pdf/1401.6735
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1401.6735.

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    Date of creation: Jan 2014
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    Handle: RePEc:arx:papers:1401.6735

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    Web page: http://arxiv.org/

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    1. Adam-Müller, Axel F.A. & Nolte, Ingmar, 2011. "Cross hedging under multiplicative basis risk," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2956-2964, November.
    2. Chang, Eric C. & Wong, Kit Pong, 2003. "Cross-Hedging with Currency Options and Futures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(03), pages 555-574, September.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    4. Fei Chen & Charles Sutcliffe, 2012. "Better cross hedges with composite hedging? Hedging equity portfolios using financial and commodity futures," The European Journal of Finance, Taylor & Francis Journals, vol. 18(6), pages 575-595, August.
    5. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 351-373.
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