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In this paper, we employ correlated skew Brownian motions to describe the dynamics of the two assets underlying the spread option. In the pricing model, the two underlying assets are exposed to exogenous risks captured by the same Brownian motion, and their endogenous risks are also assumed to be correlated with each other. We obtain an approximate pricing formula of spread options and calibrate model parameters to real data. In addition, we compare the results obtained from the approximate formula with those derived from the exact closed-form formula and from the Monte Carlo method. Finally, we analyze the impact of the skewness parameter on option prices after checking the accuracy of the approximations numerically. [ABSTRACT FROM AUTHOR]

In this paper, we study the joint Laplace transform of the sticky Brownian motion on an interval, its occupation time at zero and its integrated process. The perturbation approach of Li and Zhou [The joint Laplace transforms for diffusion occupation times, Adv. Appl. Probab.45 (2013) 1049–1067] is adopted to convert the problem into the computation of three Laplace transforms, which is essentially equivalent to solving the associated differential equations with boundary conditions. We obtain the explicit expression for the joint Laplace transform in terms of the modified Bessel function and Airy functions. [ABSTRACT FROM AUTHOR]

This study presents a pricing model for power exchange options, in which the possibility of default by the risky counterparty as well as the arrival of important business information are taken into consideration. The idiosyncratic and common jump components induced by the arrival of business information are subsumed into all asset price processes whose dynamics are correlated with each other. Employing the measure-change technique, we obtain a pricing formula for the values of power exchange options with counterparty risk. At last, based on the derived formula, we numerically analyze the impacts of counterparty risk and jump risk on option prices. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:499-521, 2017 [ABSTRACT FROM AUTHOR]

Motivated by the close connection between the skew Brownian motion and the random particle motion in heterogeneous media, we investigate the reflected skew Brownian motion and try to find out its relationship with the corresponding dispersion problem when there exists a reflecting boundary. Through the use of the knowledge of stochastic analysis, we provide some basic properties of reflected skew Brownian motions, including the transition density, the Laplace transform of the first passage time, and some related results. A simple method to generate the sample path is also proposed. At the end of this paper, we reveal the strong relationship between the reflected skew Brownian motion and the solute dispersion in the presence of a sharp interface and a reflecting boundary. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some properties of the doubly skewed CIR process which is an extension of skew Brownian motion. The weak existence and pathwise uniqueness of this process is considered in the beginning. Then we present the explicit formulae for the stationary density function and show that the process is positive Harris recurrent and geometrically ergodic. We also provide the explicit Laplace transforms of the first hitting times by using the basic theory of linear diffusions. As a natural corollary, the expectations of the first hitting times are given in the end. [ABSTRACT FROM AUTHOR]