Related papers: On the valuation of arithmetic-average Asian optio…
This paper derives integral representations for the Black-Scholes price of arithmetic-average Asian options. Their proof is by Laplace inverting the 1992 Laplace transform of Geman-Yor using complex analytic methods. The analysis ultimately…
Averaging problems are ubiquitous in Finance with the valuation of the so-called Asian options on arithmetic averages as their most conspicuous form. There is an abundance of numerical work on them, and their stochastic structure has been…
This paper will demonstrate some new techniques for developing the theory of Asian (arithmetic average) options pricing. We discuss the basic derivation of the diffusion equations, and how various techniques from potential theory can be…
The 1993 Laplace transform approach of Geman and Yor is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a financial perspective. In this paper, we discuss two observations regarding…
We derive a recursive formula for arithmetic Asian option prices with finite observation times in semimartingale models. The method is based on the relationship between the risk-neutral expectation of the quadratic variation of the return…
Laguerre polynomials are orthogonal polynomials defined on positive half line with respect to weight $e^{-x}$. They have wide applications in scientific and engineering computations. However, the exponential growth of Laguerre polynomials…
The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative L\'evy process \xi with unbounded variation.…
This paper is motivated by questions about averages of stochastic processes which originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with research of Yor's in 1992, these questions…
In this paper we establish different representations of the so-called Yor integral, which is one of the key ingredient in mathematical finance, in particular, to compute normalized prices of Asian options. We show, that the Yor integral is…
In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…
In this article we present new results for the pricing of arithmetic Asian options within a Black-Scholes context. To derive these results we make extensive use of the local scale invariance that exists in the theory of contingent claim…
The transformation of a Laguerre series $f (z) = \sum_{n=0}^{\infty} \lambda_{n}^{(\alpha)} L_{n}^{(\alpha)} (z)$ to a power series $f (z) = \sum_{n=0}^{\infty} \gamma_{n} z^{n}$ is discussed. Many nonanalytic functions can be expanded in…
We introduce two ordinary second-order linear differential equations of the Laguerre- and Jacobi-type. Solutions are written as infinite series of square integrable functions in terms of the Laguerre and Jacobi polynomials, respectively.…
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…
We consider partial theta series associated with periodic sequences of coefficients, of the form $\Theta(\tau) := \sum_{n>0} n^\nu f(n) e^{i\pi n^2\tau/M}$, with $\nu$ non-negative integer and an $M$-periodic function $f : \mathbb{Z}…
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
We derive a closed-form solution for the price of an average price as well as an average strike geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also…
To evaluate Riemann's zeta function is important for many investigations related to the area of number theory, and to have quickly converging series at hand in particular. We investigate a class of summation formulae and find, as a special…
We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average…