Pricing American options under discrete and continuous time setting

---

Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, İktisadi ve İdari Bilimler Fakültesi, İşletme Bölümü, Türkiye

Tezin Onay Tarihi: 2013

Öğrenci: SİNEM KOZPINAR

Danışman: ZEHRA NURAY GÜNER

Özet:

In this thesis, pricing of American options are analyzed in discrete and continuous time markets. We first discuss the discrete-time valuation of American options assuming that the underlying asset pays no dividend during the life of the option. In this setting, we uniquely price American options by introducing the Snell envelope and optimal stopping time problem. We prove the main results studied in Lamberton and Lapeyre (1996) in details. In addition, we show that the price of an American call option with no dividend is equal to the price of its European counterpart. Then, we extend this results to the continuous-time for both dividend and no dividend case. Following Black-Scholes model, we present two different techniques to price American options: martingale pricing technique and variational inequalities. Under martingale pricing approach, we take the expectation of discounted payoff process and determine the stopping time that maximizes this expected value. Then, we derive a pricing formula for both dividend and no dividend case. We also show that an early exercise is not optimal for American call options without dividend. We observed that this rule is not valid for American call options on a dividend paying underlying asset. Then, we introduce the variational inequalities that an American option satisfies and investigate the regular solutions of this inequalities. However, these approaches generally do not admit a closed-form solution for the price of American options. Therefore, we give a brief introduction to the finite difference and PSOR methods and adapt these methods for American options. Finally, a numerical application is done by comparing the e fficiencies of these methods. Moreover, the impact of Black-Scholes parameters strike price, volatility and dividend yield on the price of American options are also investigated. The thesis ends with a conclusion and an outlook to future studies.