The Laplace transform approach of [GY] is a celebrated advance in valuing Asian options. Its insights are fundamental from both a mathematical and a nancial perspective. In this paper, we discuss two observations regarding the nancial relevance of its results. First, we show that the [GY] Laplace transform is not that of an Asian option price, as reported in [GY] and other papers. We nonetheles...

HRUŠKA JURAJ. 2015. Delta-gamma-theta Hedging of Crude Oil Asian Options. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 63(6): 1897–1903. Since Black-Scholes formula was derived, many methods have been suggested for vanilla as well as exotic options pricing. More of investing and hedging strategies have been developed based on these pricing models. Goal of this paper i...

We derive a series expansion by Hermite polynomials for the price of an arithmetic Asian option. This requires computation moments and correlators underlying asset which polynomial jump–diffusion process are given analytically; hence, no numerical simulation is required to evaluate series. allows analytical expressions option Greeks. The weight function defining Gaussian density with scale b. f...

A general framework is developed to analyze the optimal stopping (exercise) regions of American path dependent options with either Asian feature or lookback feature. We examine the monotonicity properties of the option values and stopping regions with respect to the interest rate, dividend yield and time. From the ordering properties of the values of American lookback options and American Asian...

Han, Chuan-Hsiang. Singular Perturbations on Non-Smooth Boundary Problems in Finance. (Under the direction of Jean-Pierre Fouque.) In this work we apply asymptotic analysis on compound options, American options, Asian options, and variance (or volatility) contracts in the context of stochastic volatility models. Singular perturbation techniques are primarily used. A singular-regular perturbatio...

This thesis investigates computational methods for pricing complex path-dependent derivative securities, especially geometricand arithmetic-moving-average-lookback options. The latter security was rst issued by Polaris Securities in 1999. Our methodology can be easily modi ed to price similarly structured options issued by other securities rms. The moving-average-lookback option is a call optio...