Applications of stochastic modeling to quantitative finance and operations management.

摘要

This thesis consists of four essays on applications of stochastic modeling to problems in the areas of quantitative finance and operations management.;In Chapter 2, we propose and develop a new stochastic process model to solve a specific problem for hedge funds: quantifying the premium from extended hedge-fund lockups. A lockup period for a hedge fund is a time period after making the investment during which the investor cannot freely redeem his investment. Recently, lockup periods have been increasing from one year to multiple years. Then, for an investor in hedge funds, it is important to calculate the premium in compensation deserved for the restricted investment opportunities imposed by an extended lockup restriction. We model returns from an investment in hedge funds with a discrete-time Markov chain (DTMC). We use this model to calculate the premium from an extended lockup period. One key modeling feature is the statistical persistence in the quality of relative returns of hedge funds, that is, the tendency for a fund that generates relatively high (or low) returns in a period to continue generating relatively high (or low) returns again in the next period. By solving systems of equations, we fit the Markov chain transition probabilities to three directly observable hedge fund performance measures from the limited data: the persistence of return, the variance of return and the hedge-fund death rate. This so-called "calibration" of a model is a common and time-tested strategy in the practical use of contingent claim models. We also quantify how the lockup premium depends on the model parameters and the lockup period.;In Chapter 3, we extend the model just described: a stochastic-difference-equation is introduced to directly model the relative returns of a hedge fund. An important feature of the model is that for the relative returns of a hedge fund, the limiting distribution is easily analyzed. Just as in Chapter 2, we incorporate the persistence of returns in our modeling. Specifically, for the relative return Xn of a hedge fund in year n, we propose a stochastic-difference-equation of the form Xn = AnXn-1+Bn where An represents persistence and B n represents noise. This model is appealing because it involves relatively few parameters, can be analyzed, and can be fit to the limited and less reliable data reasonably well. We show that a simple model framework where An is constant and Bn is normal random variable provides a good fit for hedge funds with light return tails. We also show that the model within the same general framework can also be fit to the heavy-tail case successfully.;The second part contains two essays on operations management, presented in Chapter 4 and 5. These essays employ stochastic modeling to better understand operational decisions and behavior of firms in the business of procurement and supply chain management. In operations management, stochastic models are popular in modeling uncertainties in the demand of a customer or cost of a product. We study a procurement problem in operations management that interfaces with economics in Chapter 4 and a supply chain problem that interfaces with accounting in Chapter 5.;The first part contains two essays on quantitative finance, presented in Chapter 2 and 3. The essays develop stochastic process models designed to better understand the performance of hedge funds. Recently, the number of hedge funds and the amount of assets they manage have been increasing rapidly. However, hedge funds reveal relatively little about their performance, and, since hedge funds report their returns voluntarily, their performance data is limited and not clearly reliable. Thus, models of hedge fund performance that can be easily analyzed and fit to limited data are valuable.;In Chapter 4, we consider a procurement system where a buyer wants to procure a product from sellers who have random production costs. We especially study a procurement that combines both auctions and bargaining, a combination that has become increasingly popular recently. Although both auction and bargaining in procurement have been studied extensively in the both economics and operations management literature recently, research that combines auctions and bargaining is limited. We model and analyze a combined auction and bargaining procurement system where an auction is followed by bargaining between the buyer and the winning seller in the auction. For this auction-bargaining model, we find a symmetric equilibrium bidding strategy for the sellers in a closed form. We also show that the buyer's expected profit in the combined procurement is higher than the profit in auction or bargaining only procurement.;In Chapter 5, we study the impact of a transfer pricing scheme for tax purposes for intra-firm transactions in the supply chain of a multinational firm. Although the impact of transfer pricing has been studied in the cost accounting literature, a detailed impact of the transfer pricing method on operational decisions and divisional profits in a supply chain has not yet been explicitly studied in both the cost accounting and operations management literature. In this chapter, we consider a supply chain where a retailer sub-division of a multinational firm orders a product from a manufacturing sub-division of the firm through an intra-firm transaction and sells it to customers under random demands. Our analysis shows that the problem can be analyzed as a variant of well known price-setting newsvendor framework in operations management. We also study the efficiency of a supply chain under the two popular transfer pricing schemes for tax reporting and show how transfer pricing methods affect operational decisions and profits of a firm and its sub-divisions.