Pricing of Margrabe Options for Large Investors with Application to Asset-Liability Management in Life Insurance

摘要

This paper investigates a problem arising in asset-liability management in life insurance. As shown by other authors, an insurance company can guarantee its solvency by purchasing a Margrabe option enabling it to exchange its assets for a certain portfolio replicating its insurance liabilities. The objective of the 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. This setting contradicts the assumptions underlying traditional financial models and requires alternative pricing techniques. One existing approach to dealing with such problems relies on the use of forward-backward stochastic differential equations (FBSDEs). We use this framework to formulate a pricing equation and solve the latter numerically to obtain the price of the option.