Motor Insurance Loss Rate Options and Swaps

In an attempt to manage the risk of mismatch between the actual claims and the anticipated claim amounts in motor insurance pool, we introduce a few new concepts of motor loss ratelinked securities such as motor loss rate options and motor loss rate swaps. These hybrid derivatives can transfer the motor insurance loss rate risks to the capital markets. For the valuation of the motor loss rate-linked securities, we assume that motor insurance aggregate claims follow a compound Poisson distribution. An Esscher transform is chosen for a risk adjusted measure change. Using the Fourier transform of the risk neutral distribution of increment of loss process and its inversion, we derive integral expressions of the price of a ratchet option and a fixed-for-floating plain vanilla swap on the motor loss rate. As illustrations, some numerical examples are given under a few specified assumptions on the distribution of the discounted losses and the parameters.