Abstract

In the first essay American call and put options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (CP, 2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of underpriced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads. The results are strongly supportive of mispricing and also strongly supportive of the CP bounds as screening mechanisms for mispriced options. The second essay introduces a result for call lower bound more powerful that the one applied in the first part of this thesis. The Proposition 5 call lower bound in Constantinides and Perrakis (2002) is shown to have a non-trivial limit as the time interval tends to zero. This establishes the bound as the first call lower bound known in the literature on derivative pricing in the presence of transaction costs with a non-trivial limit. The bound is shown to be tight even for a low number of time subdivisions. Novel numerical methods to derive recursive expectations under a Markovian but non-identically distributed stochastic process are presented. The third essay relaxes an assumption in the first part of this thesis on the optimal trading policy in the presence of transaction costs. We derive the boundaries of the region of no transaction when the risky asset follows a mixed jump-diffusion instead of a simple diffusion process. These boundaries are shown to differ from their diffusion counterparts in relation to the jump intensity for lognormally distributed jump size. A general numerical approach is presented for iid risky asset returns in discrete time. An error in an earlier published work on the region of no transaction for discretized diffusions is demonstrated and corrected results are presented. Comparative results with a recent study on the same topic are presented and it is shown that the numerical algorithm has equally attractive approximation properties to the unknown continuous time limit.