Arbitrage Pricing of Multi-person Game Contingent Claims

We introduce a class of financial contracts involving several parties by extending the notion of a two-person game option (see Kifer (2000)) to a contract in which an arbitrary number of parties is involved and each of them is allowed to make a wide array of decisions at any time, not restricted to simply `exercising the option'. The collection of decisions by all parties then determines the contract's settlement date as well as the terminal payoff for each party. We provide sufficient conditions under which a multi-person game option has a unique arbitrage price, which is additive with respect to any partition of the contract

New analytic approach to address Put - Call parity violation due to discrete dividends

The issue of developing simple Black-Scholes type approximations for pricing European options with large discrete dividends was popular since early 2000's with a few different approaches reported during the last 10 years. Moreover, it has been claimed that at least some of the resulting expressions represent high-quality approximations which closely match results obtained by the use of numerics. In this paper we review, on the one hand, these previously suggested Black-Scholes type approximations and, on the other hand, different versions of the corresponding Crank-Nicolson numerical schemes with a primary focus on their boundary condition variations. Unexpectedly we often observe substantial deviations between the analytical and numerical results which may be especially pronounced for European Puts. Moreover, our analysis demonstrates that any Black-Scholes type approximation which adjusts Put parameters identically to Call parameters has an inherent problem of failing to detect a little known Put-Call Parity violation phenomenon. To address this issue we derive a new analytic approximation which is in a better agreement with the corresponding numerical results in comparison with any of the previously known analytic approaches for European Calls and Puts with large discrete dividends