Essays on financial derivatives: Essay One. Predicting future volatility in currency options market. Essay Two. Calibration of Heston's model in currency options market. Essay Three. Pricing European options and calibration in equity -linked derivatives market.

摘要

This paper examines the relation between New Zealand dollar (NZD) - US dollar (USD) exchange rate volatility implied in option prices and realized volatility. To the best of our knowledge, this is the first paper which uses Garman-Klass estimator of realized volatility to predict future volatility in currency options. Using Generalized Method of Moments estimation (GMM) consistent with observations evidence suggest that implied volatilities give better forecasts of future volatility than the GARCH model and historical models. However, using Garman-Klass estimator increases the efficiency of the realized volatility and provides some additional information to implied volatility.;My second essay investigates the calibration technique applied to Heston's stochastic volatility model in currency options markets. I use closed form solution to price European vanilla call and put options and calibrate the Heston's model to market data. My study differs from the previous studies since I didn't use a penalty function on parameters when I calibrated the Heston's model to market volatility smile. Another difference from the previous studies is that instead of using spot market prices, I'm using the derivative prices and I calibrate the model to derivative prices. I find that calibrating Heston's model to market data, under no penalization, gives good fitting for the maturities between one month to two years.;My third essay investigates the European vanilla option pricing and calibration procedure in equity options market with using Heston's stochastic volatility model. I consider Euro Stoxx 50 market volatilities for vanilla call and put options. To the best of our knowledge, wide range of call and put deltas for Risk reversals and Butterflies were firstly used in the literature in my paper. Even though there were some small fitting problems in very short maturity, the calibration method produced very good results for short, medium and long term option maturities. Important distinction of my study is, I didn't use a penalty function on calibration parameters.