JMF  Vol.4 No.2 , February 2014
Pricing of Margrabe Options for Large Investors with Application to Asset-Liability Management in Life Insurance
Abstract: 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.
Cite this paper: E. Bølviken, F. Proske and M. Rubtsov, "Pricing of Margrabe Options for Large Investors with Application to Asset-Liability Management in Life Insurance," Journal of Mathematical Finance, Vol. 4 No. 2, 2014, pp. 113-122. doi: 10.4236/jmf.2014.42011.

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