JMFJournal of Mathematical Finance2162-2434Scientific Research Publishing10.4236/jmf.2014.42011JMF-43336ArticlesBusiness&Economics Physics&Mathematics Pricing of Margrabe Options for Large Investors with Application to Asset-Liability Management in Life Insurance rikBølviken1*FrankProske1*MarkRubtsov1*Centre of Mathematics for Applications, University of Oslo, Oslo, Norway* E-mail:erikb@math.uio.no(RB);proske@math.uio.no(FP);mark.rubtsov@gmail.com(MR);140220140402113122September 30, 2013November 25, 2013 December 19, 2013© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

We study a problem related to asset-liability management in life insurance. As shown by Wüthrich, Bühlmann and Furrer in [1], an insurance company can guarantee solvency by purchasing a Margrabe option enabling it to exchange its asset portfolio for a valuation portfolio. The latter can be viewed as a replicating portfolio for the insurance liabilities in terms of financial instruments. Our objective in this paper is to investigate numerically a valuation technique for such an option in a situation when the insurance company is a “large” investor, implying that its trading decisions can affect asset prices. We view this situation through the framework employed in the Cvitanic and Ma’s 1996 paper [2] and use the method of finite differences to solve the resulting non-linear PDE. Our results show reliability of this numerical method. Also we find, similarly to other authors, that the option price for the large investor is higher than that for a Black-Scholes trader. This makes it particularly compelling for a large insurance company to purchase a Margrabe option at the Black-Scholes price.

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