This thesis examines the improvement in the pricing of the Swedish OMXS30 index options with deterministic volatility models and stochastic volatility models, by using Excel VBA. To answer our problem statement - Do option pricing models which incorporate the volatility smile perform better than BS (Black-Scholes) empirically using option prices from OMXS30? we compare empirical performances of five alternative option pricing models: (1) The classic Black-Scholes using the volatility of index returns for the last 30 trading days and fitted volatility, (2) Practitioner Black-Scholes that fits the implied volatility surface, (3) Gram-Charlier which incorporate skewness and kurtosis, (4) Heston’s continuous-time stochastic volatility model and (5) Heston and Nandi’s GARCH model. The alternative option pricing models are compared to the Black-Scholes models as benchmark. We find that none of the models can fully approximate the market, but they can however improve the pricing errors significantly. Both Practitioner Black-Scholes and Heston outperform the benchmarks and other models in terms of effectiveness for in-sample and out-of-sample pricing as they are better to fit and forecast the volatility smile. The pricing errors show a pattern of being highest for out-of-the-money options and decreases as we move to in-the-money options for all models. For delta hedging, only Practitioner Black-Scholes are able to outperform Black-Scholes, but the difference in performance is marginal. The thesis concludes that models that are able to incorporate the volatility smile and mitigate the maturity bias improve the ability of pricing the options. As for hedging, these model parameters are of minor importance as Practitioner Black-Scholes barely outperforms Black-Scholes.
|Educations||MSc in Applied Economics and Finance, (Graduate Programme) Final Thesis|
|Number of pages||107|