Financial derivatives play significant role in an investor's success. Financial option is one form of derivatives. Option pricing is one of the challenging and fundamental problems of computational finance. Due to highly volatile and dynamic market conditions, there are no closed form solutions available except for simple styles of options such as, European options. Due to the complex nature of the governing mathematics, several numerical approaches have been proposed in the past to price American style and other complex options approximately. Bio-inspired and nature-inspired algorithms have been considered for solving large, dynamic and complex scientific and engineering problems. These algorithms are inspired by techniques developed by the insect societies for their own survival. Nature-inspired algorithms, in particular, have gained prominence in real world optimization problems such as in mobile ad hoc networks. The option pricing problem fits very well into this category of problems due to the ad hoc nature of the market. Particle swarm optimization (PSO) is one of the novel global search algorithms based on a class of nature-inspired techniques known as swarm intelligence. In this research, we have designed a sequential PSO based option pricing algorithm using basic principles of PSO. The algorithm is applicable for both European and American options, and handles both constant and variable volatility. We show that our results for European options compare well with Black-Scholes-Merton formula. Since it is very important and critical to lock-in profit making opportunities in the real market, we have also designed and developed parallel algorithm to expedite the computing process. We evaluate the performance of our algorithm on a cluster of multicore machines that supports three different architectures: shared memory, distributed memory, and a hybrid architectures. We conclude that for a shared memory architecture or a hybrid architecture, one-to-one mapping of particles to processors is recommended for performance speedup. We get a speedup of 20 on a cluster of four nodes with 8 dual-core processors per node.

Financial derivatives play significant role in an investor's success. Financial option is one form of derivatives. Option pricing is one of the challenging and fundamental problems of computational finance. Due to highly volatile and dynamic market conditions, there are no closed form solutions available except for simple styles of options such as, European options. Due to the complex nature of the governing mathematics, several numerical approaches have been proposed in the past to price American style and other complex options approximately. Bio-inspired and nature-inspired algorithms have been considered for solving large, dynamic and complex scientific and engineering problems. These algorithms are inspired by techniques developed by the insect societies for their own survival. Nature-inspired algorithms, in particular, have gained prominence in real world optimization problems such as in mobile ad hoc networks. The option pricing problem fits very well into this category of problems due to the ad hoc nature of the market. Particle swarm optimization (PSO) is one of the novel global search algorithms based on a class of nature-inspired techniques known as swarm intelligence. In this research, we have designed a sequential PSO based option pricing algorithm using basic principles of PSO. The algorithm is applicable for both European and American options, and handles both constant and variable volatility. We show that our results for European options compare well with Black-Scholes-Merton formula. Since it is very important and critical to lock-in profit making opportunities in the real market, we have also designed and developed parallel algorithm to expedite the computing process. We evaluate the performance of our algorithm on a cluster of multicore machines that supports three different architectures: shared memory, distributed memory, and a hybrid architectures. We conclude that for a shared memory architecture or a hybrid architecture, one-to-one mapping of particles to processors is recommended for performance speedup. We get a speedup of 20 on a cluster of four nodes with 8 dual-core processors per node.

近來共享經濟商業模式崛起，對各國既有相關市場皆造成不少之衝擊，當中，優步公司用以計算車資之「訂價演算法」，於美國實務亦引起許多爭議。美國司法案例中其中一個重要爭議即為優步公司單方制定之「訂價演算法」與其採行之「高峰動態訂價法」究否構成價格聯合行為。於美國實務近來2起與價格聯合行為相關之案例，即包含Meyer v. Kalanick案與Chamber of Commerce & RASIER, LLC v. City of Seattle案（以下簡稱「City of Seattle案」）中，皆可見Uber企圖正當化其價格聯合行為，以免於競爭法審查下有違法之嫌。而美國對於價格聯合行為之規範，載明於休曼法第1條；依據休曼法第1條規定，若原告擬主張被告行為違反卡特爾行為，則應證明系爭卡特爾行為符合合意主體要件、具合意或共謀行為，與造成限制性之競爭效果等三項要件。由於上述二案皆仍於訴訟前階段，判決尚未出爐，因此，此議題值得吾等分析之。本文擬以美國實務判決為基準，彙整相關爭議，進而探討Uber所採訂價演算法是否構成價格聯合行為。 本文發現，雖然此等訂價演算法究否構成價格聯合行為尚未有定論，然由於訂價演算法中之高峰動態訂價法可提高駕駛於尖峰時段中提供載客服務之誘因，將有助於調節市場機制與促進競爭。此外，Uber亦可利用其訂價演算法與設置平台所奠立之優勢，使其得以潛在破壞市場秩序之形式，創造競爭優勢。據此，Uber除可克服既有行政管制下市場進入之劣勢外，亦得使相關市場交易效率大幅提升、市場更加競爭。因此，於探討Uber價格聯合行為合法與否時，亦應將此等因素納入考量。 / The rapid expansion of sharing economy enterprises around the world has led to many challenges. And among these enterprises, one of the most disruptive examples is Uber because of its algorithm. In the United States, the lawsuits regarding Uber's algorithm has also gained massive attention. One of the controversial issues of the complaints relies upon whether Uber's algorithm which set by Uber, and “surge pricing” model do constitute an illegal price-fixing in violation of Section 1 of the Sherman Act. In 2 recent high-profile cases, Meyer v. Kalanick & Chamber of Commerce & RASIER, LLC v. City of Seattle, Uber has tried to justify its price fixing to avoid antitrust scrutiny. There are three specific facts that the Plaintiff must prove to establish its antitrust claim in Section 1 of the Sherman Act: 2 or more entities entering into an agreement, conspiracy, and unreasonably restrains competition. Analysis regarding Uber's algorithm is significant because the trials are ongoing. Therefore, the thesis examines whether Uber's algorithm do constitute an illegal price-fixing in violation of Section 1 of the Sherman Act by exploring the potential problems with regard to the elements based on U.S. judicial decisions. The thesis believes that Uber's algorithm can enhance the efficiency of transaction and has pro-competitive effects, leading to the impact of Uber's surge pricing on providing the incentives for drivers during peak hours. Establishing platform and Uber's algorithm create Uber's strengths and advantages. By having disrupted the existing industry, Uber's algorithm serves pro-competitive purposes.