Pricing Jump-Diffusion Currency Options with Support Vector Regression
Huang Yun-cheng · Industrial Engineering and Engineering Management · 2011
The currency option market has the highest degree of liquidity in comparison with other markets.It is important to use a reasonable option pricing approach in order to use the currency option properly.Existing literature has adopted parametric and nonparametric option pricing approaches to help improve the return of currency option investment.A new model based on the merits of both parametric and nonparametric methods in currency option pricing practices is constructed to provide insight on foreign currency option pricing.The first part reviews the Jump-Diffusion model,a parametric method.Sudden changes to the financial market can lead to the volatility of currency exchange rates and disrupt the continuity of the geometric diffusion process.A few jump-diffusion models are discussed.We decide to adopt Hanson and Westman's Log-Uniform Model because the model enables us to modify infinite domain and the tails of exponent.Obtaining a closed option pricing formula is unviable because of the complexity of the UMP diffusion models.A quasi maximum likelihood is used to estimate the parameters of the log-uniform model.The Monte Carlo algorithm is used to compute European option prices.The second part introduces the Support Vector Machine(SVM) Theory.SVM is developed on the basis of the statistical learning theory.SVM is used for classification(SVC) and regression(SVR).SVR overcomes the weakness of neural networks that get trapped when local minima are unavoidable.The third party proposes a new currency option pricing model.The model-reference architecture is a commonly-used framework in neutral network applications.We further extend the pricing framework in the model-reference architecture to the analysis of forecasting activities.SVR are employed to capture the nonlinear residuals between the actual option prices and the predicted prices given by parametric models.The forecast system is supported by the conventional methods coded in the MATLAB.The exchange rate volatility is significant for predicting currency option prices and determining the expected market return.The stochastic volatility(SV) model can help explain foreign exchange market volatility and improve the predictive ability of currency options pricing model.WINBUGS are used to estimate SV model's parameters of spot rates.The last part enters the actual financial time series data into the model.The analyzed data are transactional data of the GBP /EUR currency option,which come from the Societe Generale database.Our proposed model can achieve better performance in option pricing than other popular currency option models,including the GK model,log-uniform model and neural networks model.