On an Alternative Approach to Pricing General Barrier Options

In this paper, an alternative approach to pricing barrier options is presented that relies on the use of the first hitting time density to the barrier. The lateral Chapman-Kolmogorov relation is used as a major tool in order to determine option prices. It turns out that this approach allows for pricing barrier options with more general payoffs and with general continuous Markovian stochastic processes as underlying (at least numerically). As an illustrative example, a simple down-and-in call option is considered and its well-known closed form pricing formula is obtained.Barrier options, first passage time density, first hitting time density, lateral Chapman-Kolmogorov relation

Default Risk, Bankruptcy Procedures and the Market Value of Life Insurance Liabilities

The topic of insolvency risk in connection with life insurance companies has recently attracted a great deal of attention. In this paper, the question is investigated of how the value of the equity and of the liability of a life insurance company are affected by the default risk and the choice of the relevant bankruptcy procedure. As an example, the U.S. Bankruptcy Code with Chapter 7 and Chapter 11 bankruptcy procedures is used. Grosen and Jørgensen's (2002) contingent claim model, implying only a Chapter 7 bankruptcy procedure, is extended to allow for more general bankruptcy procedures such as Chapter 11. Thus, more realistically, default and liquidation are modelled as distinguishable events. This is realized by using so-called standard and cumulative Parisian barrier option frameworks. It is shown that these options have appealing interpretations in terms of the bankruptcy mechanism. Furthermore, a number of representative numerical analyses and comparative statics are performed in order to investigate the effects of different parameter changes on the values of the insurance company's equity and liability, and hence on the value of the life insurance contract. To complete the analysis, the shortfall probabilities of the insurance company implied by the proposed models are computed and compared.Equity--Linked Life Insurance, Default Risk, Liquidation Risk, Contingent Claims Pricing, Parisian Options, Bankruptcy Procedures

Produktdesign und Semi-Statische Absicherung von Turbo-Zertifikaten

Turbo-Certificates are one of the most popular structured equity products for private investors in Germany. They can be regarded as special forms of barrier options. The relation between the barrier level and the strike price is especially important for the design of these products. By using a certain choice of these parameters, the issuer is able to obtain an almost static (super-) hedge in standard option contracts. If the barrier level is equal to the strike, the upper price bound of a Turbo-Long-Certificate coincides with the value of a forward contract. Therefore, in the case of a Turbo-Short-Certificate, the forward implies only a lower price bound. It is shown that in general, the issuer can neither hedge a single certificate nor a portfolio of certificates without using standard options.Turbo-Zertifikate, Put-Call-Symmetrie, Static Hedging, Barrier-Optionen, Produktdesign