Analytical Valuation of American-Style Asian Options

Abstract

This article derives the first analytical pricing formulas for American-style Asian options of the so-called floating strike type. Geometric as well as arithmetic averaging is considered. The setup is a standard Black-Scholes framework where the price of the underlying security evolves according to a geometric Brownian motion. A decomposition result that splits up the value of the floating strike American option into the price of an otherwise equivalent European option and an early exercise premium is first presented. This decomposition result is then manipulated further for the two separate types of averaging. With geometric averaging we derive an exact pricing formula, whereas with arithmetic averaging we develop an analytical approximation formula that proves to be very precise. Numerical examples are provided.asian options, american options, analytical valuation formulas, numerical work, change of numeraire

Fair valuation of participating policies with surrender options and regime switching

“…By considering the surrender options as the early exercise privilege of an American-style option (see Grosen and Jørgensen, 2000), the fair valuation of the policy can be formulated as an optimal stopping problem from which the value of the policy and the optimal surrender strategy can be determined. We reduce the dimension of the optimal stopping problem for the policy by adopting the method of changing probability measures in Hansen and Jørgensen (2000). We also provide a decomposition for the value of the policy into the value of an identical policy without surrender options and the premium for surrender options.…”

“…There is a relatively little work on the fair valuation of participating American contract under the regime switching models for the asset price dynamics. Here, we provide a valuation method of some particular participating American-style contracts under the Markov-Modulated GBM by modifying the method employed in Hansen and Jørgensen (2000). In the sequel, we introduce the set up of our model.…”

Lognormal Approximation of Complex Path-Dependent Pension Scheme Payoffs

“…Prices are lognormal when the typical Black and Scholes (1973) assumptions are made. 7 In parts of their study on American-style Asian options Hansen and Jørgensen (2000) pursue a similar idea.…”

Free boundary and optimal stopping problems for American Asian options

“…[14]) and were introduced to avoid the well-known problem related to European options that can be subject to price manipulations of the underlying asset near the maturity. In case of arithmetic average (2.3), by usual no-arbitrage arguments we obtain the pricing…”

“…While there are several papers on the valuation of Asian options with early exercise (for instance, Barraquand and Pudet [2], Barles [1], Hansen and Jorgensen [14], Meyer [27], Wu, You and Kwok [33], Fu and Wu [13], Jiang and Dai [20], Ben-Ameur, Breton and L'Ecuyer [4], Marcozzi [26], Dai and Kwok [8], Huang and Thulasiram [17]), most of these are devoted to numerical issues (the development of numerical techniques for pricing and determining the exercise boundary) by some means assuming as established the existence and regularity of the solution to the free boundary or optimal stopping problem. To a certain extent, using the weak notion of viscosity solution, it is possible to obtain general existence results.…”