Narrow Results

The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large Platonic markets, which allow infinitely many assets and incorporate a restricted information setting. The discussion is divided into information delays and order execution delays. The former enables modeling of markets, where the observed information is delayed, while the latter provides the opportunity to defer the indexed time of a received asset price. Both delays may be designed randomly and inhomogeneously over time. We show that delayed markets are equipped with a fundamental theorem of asset pricing and our main result is inheritance of the no asymptotic Lp-free lunch condition under both delay types. Eventually, we suggest an approach to verify absence of Lp-free lunch on markets with multiple brokers endowed with deviating trading speeds.

Based upon Ritchken (1985), Levy (1985), Lo (1987), Zhang (1994), Jackwerth and Rubinstein (1996), and others, this chapter discusses the alternative method to determine option bound in terms of the first two moments of distribution. This approach includes stochastic dominance method and linear programming method, then we discuss semi-parametric method and non-parametric method for option-bound determination. Finally, we incorporate both skewness and kurtosis explicitly through extending Zhang (1994) to provide bounds for the prices of the expected payoffs for options, given the first two moments and skewness and kurtosis.

For valuing derivatives and other assets in securities and commodities markets, arbitrage pricing theory has been a major approach for decades. This paper derives fundamental arbitrage pricing results in finite dimensions in a simple unified framework using Tucker's theorem of the alternative. Frictionless results, that is perfect market results, plus imperfect market results such as those with dividends, periodic interest payments, transaction costs, different interest rates for lending and borrowing, shorting costs and constrained short selling are presented. While the results are mostly known and appear in various places, our contribution is to present them in a coherent and comprehensive fashion with very simple proofs. The analysis yields a simple procedure to prove new results and some arc presented for cases with imperfect market frictions.

Based upon Ritchken (1985), Levy (1985), Lo (1987), Zhang (1994), Jackwerth and Rubinstein (1996), and others, this chapter discusses the alternative method to determine option bound in terms of the first two moments of distribution. This approach includes stochastic dominance method and linear programming method, then we discuss semi-parametric method and non-parametric method for option-bound determination. Finally, we incorporate both skewness and kurtosis explicitly through extending Zhang (1994) to provide bounds for the prices of the expected payoffs for options, given the first two moments and skewness and kurtosis.