In this paper we have derived the analytical kernels of the pricing formulae of the CEV knockout options with time-dependent parameters for a parametric class of moving barriers. By a series of similarity transformations and changing variables, we are able to reduce the pricing equation to one...

Since the pioneering paper of Black and Scholes was published in 1973, enormous research effort has been spent on finding a multi-asset variant of their closed-form option pricing formula. In this paper, we generalize the Kirk [Managing Energy Price Risk, 1995] approximate formula for pricing a...

Ever since Kirk proposed an approximate price formula for a European call spread option in 1995, Kirk's approximation has become the most widely used among the practitioners, especially in the energy markets. It is well known that Kirk's approximation extends from Margrabe's exchange option...

In this paper, by means of the Lie-Trotter operator splitting method, we have presented a new unified approach not only to rigorously derive Kirk's approximation but also to obtain a generalisation for multi-asset spread options in a straightforward manner. The derived price formula for the...

In this paper, based upon the Lie-Trotter operator splitting method proposed by Lo (2014), we present a simple closed-form approximation for pricing the (three-asset) dual spread options. Illustrative numerical examples show that the proposed approximation is not only extremely fast and robust,...

Time dependent barrier options have barrier periods covering a portion of option life. This feature makes them hybrids of barrier options and ordinary European options. There are two types of time dependent barrier options: 1. front end barrier options; 2. rear end barrier options. The options...