Fractional Brownian motion (fBm) can be introduced by a moving average representation driven by standard Brownian motion, which is an affine Markov process. Motivated by this we aim at results analogous to those achieved in recent years for affine models. Using a simple prediction formula for the conditional expectation of a fBm and its Gaussianity, we calculate the conditional characteristic f...

Alternatives to the Black-Scholes-Vasicek deflator introduced in [25] are proposed. They are based on the multivariate Wang variance-gamma process considered in [66]. As an application, closed form analytical multiple integral formulas for pricing the European geometric basket option with a deflated multivariate exponential Wang variance-gamma asset pricing model are derived. Mathematics Subjec...

The valuation for an American continuous-installment put option on zero-coupon bond is considered by Kim’s equations under a single factor model of the short-term interest rate, which follows the famous Vasicek model. In term of the price of this option, integral representations of both the optimal stopping and exercise boundaries are derived. A numerical method is used to approximate the optim...

There is a massive amount of study deals with the stochastic modelling of the interest rates. The first approach to specify the interest rate movements as continuoustime Ito process was introduced by Merton in 1973. But his approach had many shortcomings including possibility of negative interest rates. In his seminal work in 1977, Vasicek developed Merton’s model by introducing mean-reverting ...

In this work, we analyze two important and simple models of short rates, namely Vasicek and CIR models. The models are described and then the sensitivity of the models with respect to changes in the parameters are studied. Finally, we give the results for the estimation of the model parameters by using two different ways.

Assuming that the underlying stock follows Fractional Brownian motion and that stochastic interest rate meets the Vasicek model of interest rates, this paper establishes pricing model of Warrant Bonds and deduces the pricing formula of Warrant Bonds by utilizing risk-neutral valuation theory. Finally, this paper analyzes influence of concerned parameters of pricing model on the value of Warrant...

Black’s (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, all term rates are strictly positive. A similar model was independently discussed by Rogers (1995)....