Abstract
This paper studies the European option pricing on the zero-coupon bond in which the Skew Vasicek model uses to predict the interest rate amount. To do this, we apply the skew Brownian motion as the random part of the model and show that results of the model predictions are better than other types of the model. Besides, we obtain an analytical formula for pricing the zero-coupon bond and find the European option price by constructing a portfolio that contains the option and a share of the bond. Since the skew Brownian motion is not a martingale, thus we add transaction costs to the portfolio, where the time between trades follows the exponential distribution. Finally, some numerical results are presented to show the efficiency of the proposed model.
Highlights
Classical models are popular financial models to forecast interest rate, where Brownian motion is used to display the random part of these models [2,4,5]
Even if we know that the interest rate will increase or decrease in the future, there is no parameter in the models so that we can adapt the model with the future data. erefore, in such cases, the skew financial models are a better choice [6, 7]
If δ > 0, the mathematical expectation of the process is an ascending function. erefore, the process is a suitable noise for financial models, when interest rate amounts increase
Summary
We present a skew version of the Vasicek model and calibrate parameters of the model based on the real data market. E skew Vasicek model can be obtained by using the skew process instead of the standard Brownian motion in equation (3): dRt κ θ − Rtdt + σ dXt,. We calibrate the mentioned model’s parameter by the Newton–Raphson method. Calibration the Skew Vasicek Model’s Parameters by Newton–Raphson Method. E first column of Table 2 shows the value of Ireland’s interest rate forecast in 12/2012 according to different versions of the model and obtains parameters of the first column of Table 1. E other columns of Table 1 show the calibrate amounts of model’s parameters according to Ireland’s interest rate data from 12/2011 to 12/ 2012 (the second column), from 12/2012 to 12/2013 (the third column), and from 12/2013 to 12/2014 (the fourth column), respectively.
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