To illustrate and test the proposed approximations in case of index-linked instruments, we conduct simulation analyses and additionally derive the price of an ILW using secondary market cat bond prices and compare the resulting price with the available real-world ILW prices, finding a high degree of consistency with both robustness tests, which support our suggested approximations for replicating portfolios. Moreover, as a further application, we approximate prices of cat bonds using empirical data and compare them with real secondary market data in order to examine whether the market prices consistently.
To ensure this consistency, the prices of these other instruments should be equal to the expectations under the same risk-neutral measure or, equivalently, should be equal to the prices of replicating portfolios consisting of tradable derivatives, for instance.
Thus, one main contribution of the article is to propose an approach to overcome the crucial point of tradability of the underlying loss processes in case of index-linked catastrophe loss instruments through suitable approximations and by deriving explicit replicating portfolios or close approximations using traded derivatives providing explicit pricing formulas.
First, the models under consideration are calibrated to the observed cross-sectional vanilla option prices and the resulting models are used to set up replicating portfolios for other options at the same time.
By looking at barrier options, these studies address the essence of model risk in options but are limited in their focus on static hedging where the replicating portfolios are not rebalanced until the maturity of the target option once they have been constructed.
To avoid this problem, ATM options with a fixed maturity are used when constructing the replicating portfolios at any rebalance time.
We use the replicating portfolios to illustrate properties of bonds outstanding in the US credit market.
More generally, the replicating portfolios for the most average neighboring bonds.
The errors are obtained using (32) for both replicating portfolios based on 100,000 index trajectories.
On the other hand, fewer trading dates may lead to less expensive replicating portfolios when including transaction costs.
To hedge an option, or any risky security, one needs to construct a replicating portfolio of other securities, one in which the payoffs of the portfolio exactly match the payoffs of the option.
As for the one-period model, the example for a two-period model assumes a replicating portfolio for a call option on a stock currently valued at $100 with a strike price of $100 and which expires in a year.