Two essays in modeling and analysis of exchange rate dynamics

Abstract

This thesis has two main chapters that are focusing on the di erent aspects of foreign exchange modeling. In the rst chapter, a dynamic programming approach is used to model the problem that; an investor has to decide on the foreign currency levels at the beginning of each period in order to meet an uncertain demand. The investor tries to minimize his cost with the constraint of meeting the uncertain demand. The problem is formulated with dynamic programming approach and solved, the structure of the optimal decision is given. In the second part of the thesis, the problem of pricing FX options is tackled. FX options market is getting very popular among emerging market economies. Since traders in emerging markets are more prone to FX risk instead of interest-rate, FX derivatives market has been developing faster than Interest- Rate derivatives market. The importance of FX options market and the its unique conventions are described rstly in the second part of the thesis. FX options market has its own market conventions, and it is necessary to understand those conventions before going deep in modeling. After the FX conventions are described, the problem of options pricing is handled through stochastic modeling. The model used is commonly known as Heston's stochastic volatility model. Theoretical background of the model and the interpretation of the parameters are discussed and the relation between implieddistribution and option smile are discussed. The calibration procedure is described and practical use of the Heston's model is given. Heston's model is commonly used as a tool to price exotic options through Monte Carlo simulation or nite di erence method. In this thesis, the model will be used for creating trading signals in the market.