قیمت گذاری گزینه های واحد پول با رگرسیون بردار پشتیبان و مدل نوسانات تصادفی با جهش
|کد مقاله||سال انتشار||تعداد صفحات مقاله انگلیسی||ترجمه فارسی|
|1845||2011||7 صفحه PDF||سفارش دهید|
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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Expert Systems with Applications, Volume 38, Issue 1, January 2011, Pages 1–7
This paper presents an efficient currency option pricing model based on support vector regression (SVR). This model focuses on selection of input variables of SVR. We apply stochastic volatility model with jumps to SVR in order to account for sudden big changes in exchange rate volatility. We use forward exchange rate as the input variable of SVR, since forward exchange rate takes interest rates of a basket of currencies into account. Therefore, the inputs of SVR will include moneyness (spot rate/strike price), forward exchange rate, volatility of the spot rate, domestic risk-free simple interest rate, and the time to maturity. Extensive experimental studies demonstrate the ability of new model to improve forecast accuracy.
The foreign exchange market is the deepest, largest and most liquid financial market in the world. There has been a thriving over-the-counter market for currency options, which reflects the growing need to manage exchange rate risk in the integrated global economy. And appropriate and accurate option pricing is crucial for proper use of currency options. Option pricing was revolutionized by Black–Scholes in 1973. However, a lot of evidence indicates that option pricing models premised upon Black–Scholes model exhibiting severe error when fitted to market data. In 1983 Garman and Kohlhagen extended the Black–Scholes model to cope with the presence of two interest rates. Many methodologies for the currency options pricing have been proposed by using the modification of Garman–Kohlhagen (GK) model, such as Amin and Jarrow, 1991, Heston, 1993, Ekvall et al., 1997 and Rosenberg, 1998 and Bollen and Rasiel (2003). In those parametric models it is quite difficult to justify selection of one parametric specification over the other. This leads to serious problem of misspecification. Market participants change their option pricing attitudes from time to time, a stationary nonlinear relationship between theoretical option prices and many variables described by parametric models may fail to adjust to such rapidly changing market behavior. In recent years, many scholars have also turned to nonparametric methods. Artificial neural network (ANN) is introduced into option pricing by Hutchison in 1994. Neural networks confirm their usefulness in modeling option pricing due to their data-driven and nonparametric weak properties. Then a lot of machine learning techniques are used for calculating the options value. Support vector machine proposed by Vapnik (1995) is another hot topic in machine learning following neural network. Support vector machine is developed on the basis of statistical learning theory. It is approximate implementation of structural risk minimization (SRM) induction principle that aims at minimizing a bound on the generalization error of a model, rather than minimizing only the mean square error over the data set. Support vector machines are used for classification and regression (SVR) (Vapnik, Golowich, & Smola, 1997). SVR is a powerful machine learning method that is useful for constructing data-driven nonlinear empirical process models. It shares many features with neural networks but possesses some additional desirable characteristics. SVR overcomes one of important weaknesses of neural networks that they cannot avoid to get trapped in local minima (Gunn, Brown, & Bossley, 1997). SVR is gaining widespread acceptance in data-driven nonlinear modeling applications (Cao, 2003 and Fan and Palaniswami, 2000). In recent years, some scholars have also turned to SVR method for option pricing (Kim, 2003 and Xun et al., 2009). Xun (2009) focus on capturing error residuals. Instead of researching into complicated option market directly, SVR is implemented based on results of three well known and successful traditional methods in Xun model (2009). Most authors focus on architectures incorporating nonparametric methods for option pricing. However the selection of reasonable input variables is also important. According to Garman–Kohlhagen formula, following notations are used: underlying asset price, option’s exercise price, asset price volatility, domestic current risk-free interest rate, foreign current risk-free interest rate, and expiration time. This study has two goals for selection of input variables based on the existing literatures. The first goal is to use forward exchange rate as the input variable of SVR to develop a new currency options pricing model. The behaviors of the spot exchange rate and two economic interest rates must be linked in order to prevent arbitrage chances. And forward exchange rate reflects the expectation of future spot rate. Using the forward exchange rate as the input variable of SVR can take interest rates of the pair of currencies into account. The second goal is to estimate exchange rate volatility with stochastic volatility model with jumps (SVJ). The Other inputs can be obtained directly from market data except for currency volatility. SV models are used to model the volatility of foreign exchange rates (Harvey et al., 1994 and Mahieu and Schotman, 1998). Asset returns are leptokurtic, and reflect volatility clustering (Chernov, Gallant, Ghysels, & Tauchen, 1999). As economic environments change, so do the data generating processes of related financial variables. Empirical results in the studies of Eraker, Johannes, and Polson (2003) and Bakshi, Cao, and Chen (1997) among others show that it is necessary to include jumps in the stochastic volatility in order to account for sudden changes in volatility. Bates (1996) and Scott (1997) combine stochastic volatility models with jumps in returns. Duffie, Pan, and Singleton (2000) and Raggi (2006) propose that SVJ models can well describe foreign exchange market volatility. The inputs of SVR will include moneyness (spot rate/strike price), forward rate, domestic risk-free simple interest rate, time to maturity, and volatility of spot rate. The new model reduces forecasting errors of the parametric methods and performs better than ANN model. The remaining part of this paper is as follows. In next section, the basic ideas and arithmetic of SVJ model and SVR are discussed. In Section 3, the new European currency options pricing model is proposed. In Section 4, the empirical study is performed, i.e., the new model is applied to China currency options market. And relative performance of new model is then analyzed by comparing its results with that of artificial network on the same data sets. Finally, some important conclusions and further study are stated in Section 5.
نتیجه گیری انگلیسی
The paper construct a new nonparametric model SSJF to estimate currency option prices. The new model has several notable advantages over traditional parametric models. Firstly, we employ SVR in currency option pricing, and combine SVJ model with SVR to provide the functional flexibility to capture the nonlinearities in financial data. Secondly, we add foreign exchange rate as input variable, as foreign exchange rate takes stochastic interest rates of the pair of currencies into account. Thirdly, the volatility of the foreign exchange market is described by SVJ model. Volatility often plays a crucial role in evaluating currency option price. It is necessary to include jumps in the stochastic volatility to account for sudden changes in volatility. And SVJ model can well capture volatility of the foreign exchange market and incorporate uncertainty regarding market sudden changes. Finally, it is intuitive and easy to use. Different estimating currency options approaches, GK model, ANN approach and new model SSJF, are applied to estimate currency option prices, the potential of SSJF for currency options pricing problems is demonstrated by induction from empirical data. SSJF model enhances the practicality and adaptability in currency option pricing. It is flexible in modeling real-world phenomena for which observations are generally available. We are trying to apply the simple SVR and SVJ model to currency option, and in future investigations we will pay more attention to kernel function in SVR other than those that are used in this study, and adopt estimating volatility approach in foreign exchange market