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Dissertations&thesesDissertations & Theses - Gradworks

Pricing options on trading strategies

by Zhu, Guo Dong . Ph. D. NEW YORK UNIVERSITY . 2007, 164 pages; 3283361

Option pricing and dynamic trading strategies are two fundamental topics in financial mathematics. This thesis investigates the interrelation between these two topics. To insure against adverse outcomes from dynamic strategies, new derivatives have arisen or are needed, whose payoff depends on the profit and loss of the strategies. We choose to study the pricing of options on the PL obtained following two classes of trading strategies: (1) options on optimal strategies and (2) options on leverage strategies. We consider that both classes of strategies are invested in a risky asset whose price follows a geometric Brownian motion with stochastic volatility. Our pricing scheme assumes that the volatility evolves independently of the trading asset, but requires no other modelling of the volatility dynamics. As a result, this scheme has minimal modelling risks associated with volatility.

In Chapter 2, we study strategy options. These are call options on the nal PL obtained following an optimal strategy, optimizing over a class of trading strategies whose position in the risky asset is subject to constraints. After identifying the optimal strategy, we then price the strategy options relative to co-terminal European calls on the trading asset. Strategy options are a generalization of passport options. This study builds on prior work about passport options, along with work about lookback options.

In Chapter 3, we introduce and study options on CPPI. These are options on the PL obtained using leverage strategies originating from Constant Proportion Portfolio Insurance (CPPI). The options considered vary in their payoff and in the structure of the leverage. Except for one case, we price these options relative to the co-terminal European claims on the trading asset. For the remaining case, we compute the price as an explicit function of the asset price.

In the Appendix, we revisit two problems concerning CPPI. First, we prove that CPPI is an optimal strategy for maximizing a HARA utility function. Second, we study the optimal execution of CPPI in the presence of transaction costs.

Dissertations & Theses - Gradworks

Dynamic Trading Strategies in the Presence of Market Frictions

by Saglam, Mehmet . Ph. D. COLUMBIA UNIVERSITY . 2012, 156 pages; 3541497

This thesis studies the impact of various fundamental frictions in the microstructure of financial markets. Specific market frictions we consider are latency in high-frequency trading, transaction costs arising from price impact or commissions, unhedgeable inventory risks due to stochastic volatility and time-varying liquidity costs. We explore the implications of each of these frictions in rigorous theoretical models from an investor's point of view and derive analytical expressions or efficient computational procedures for dynamic strategies. Specific methodologies in computing these policies include stochastic control theory, dynamic programming and tools from applied probability and stochastic processes.

In the first chapter, we describe a theoretical model for the quantitative valuation of latency and its impact on the optimal dynamic trading strategy. Our model measures the trading frictions created by the presence of latency, by considering the optimal execution problem of a representative investor. Via a dynamic programming analysis, our model provides a closed-form expression for the cost of latency in terms of well-known parameters of the underlying asset. We implement our model by estimating the latency cost incurred by trading on a human time scale. Examining NYSE common stocks from 1995 to 2005 shows that median latency cost across our sample more than tripled during this time period.

In the second chapter, we provide a highly tractable dynamic trading policy for portfolio choice problems with return predictability and transaction costs. Our rebalancing rule is a linear function of the return predicting factors and can be utilized in a wide spectrum of portfolio choice models with minimal assumptions. Linear rebalancing rules enable to compute exact and efficient formulations of portfolio choice models with linear constraints, proportional and nonlinear transaction costs, and quadratic utility function on the terminal wealth. We illustrate the implementation of the best linear rebalancing rule in the context of portfolio execution with positivity constraints in the presence of short-term predictability. We show that there exists a considerable performance gain in using linear rebalancing rules compared to static policies with shrinking horizon or a dynamic policy implied by the solution of the dynamic program without the constraints.

Finally, in the last chapter, we propose a factor-based model that incorporates common factor shocks for the security returns. Under these realistic factor dynamics, we solve for the dynamic trading policy in the class of linear policies analytically. Our model can accommodate stochastic volatility and liquidity costs as a function of factor exposures. Calibrating our model with empirical data, we show that our trading policy achieves superior performance in the presence of common factor shocks.