Maximum likelihood estimation for sub-fractional Vasicek model

We investigate the asymptotic properties of maximum likelihood estimators of the drift parameters for the fractional Vasicek model driven by a sub-fractional Brownian motion.

Bond and Option Prices under Skew Vasicek Model with Transaction Cost

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.

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

Interest rate paths experience discontinuities in the presence of certain factors. Much of the work on interest rate modelling has no consideration for effects of such unexpected occurrences in real life. A good risk manager needs to have a better model that considers possibility of unexpected occurrences. In this paper, we discuss step by step extension of Vasicek model to both jump model and jumpdiffusion model using Itô’s formula as the major tool. We also derive the greeks ‘delta’ and ‘vega’ that measure sensitivity of the interest rate with respect to both changes in its initial interest rate and volatility in an interbank rate.

Bid and Ask spreads for the cap and floor contracts under the Liouville fractional Vasicek model

This paper presents bid and ask formulas for cap and floor contracts prices byusing Wang transform under a Liouville fractional Vasicek (LfVasicek) interest rate model. To do this, the parameters of the model are calibrated by using the Newton-Raphson (NR) method. Then the standard and Liouville fractional versions of the Vasicek model are compared by the Bayes information criterion (BIC). Finally, we obtain the bid-ask boundaries for interest rate amount and cap and foor prices.