Universal Journal of Accounting and Finance Vol. 4(5), pp. 137 - 156
DOI: 10.13189/ujaf.2016.040501
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Currency Option Pricing under Stochastic Interest Rates and Extended Normal Distribution


Yu-hong Liu 1, Yu-Chen Lin 2,*, Ya-hsin Hung 1
1 Graduate Institute of Finance, National Cheng Kung University, Taiwan
2 Department of Accountancy, National Cheng Kung University, Taiwan

ABSTRACT

In this paper, we have constructed a model to price currency option. It contributes to releasing some assumptions the Black-Scholes' (1973) model makes. One of them is that the log price of asset doesn't follow a normal distribution any more. The other one is the interest rates in the domestic and foreign countries become stochastic. This general formula is first proposed by Amin and Jarrow (1991). Based on this model, we build extended normal distribution model [developed by Ki, Choi, Chang and Lee (2005)] under the assumption of stochastic interest rate economy. In numerical examples, our proposed model would be compared with Amin and Jarrow (1991) under CIR [Cox, Ingersoll and Ross (1985)] interest rate term structure. Furthermore, Monte Carlo simulation is used to provide another outcome to be another comparative example. Finally, we think that the proposed model provides more correct currency option prices when taking account of stochastic interests and extended normal distribution. The drawback of the Black-Scholes' formula which fails to catch the volatility smile effect is resolved by using the proposed model. The market participants can use the actual market data to calibrate the parameters of the proposed model and use the proposed model to price the currency options and derivatives accurately.

KEYWORDS
Currency Option, Stochastic Interest Rate, Kurtosis, Skewness, Extended Normal Distribution

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Yu-hong Liu , Yu-Chen Lin , Ya-hsin Hung , "Currency Option Pricing under Stochastic Interest Rates and Extended Normal Distribution," Universal Journal of Accounting and Finance, Vol. 4, No. 5, pp. 137 - 156, 2016. DOI: 10.13189/ujaf.2016.040501.

(b). APA Format:
Yu-hong Liu , Yu-Chen Lin , Ya-hsin Hung (2016). Currency Option Pricing under Stochastic Interest Rates and Extended Normal Distribution. Universal Journal of Accounting and Finance, 4(5), 137 - 156. DOI: 10.13189/ujaf.2016.040501.