Abstract
An adjusted trinomial model for pricing both European and American arithmetic average-based Asian options is proposed. The Kamrad and Ritchken trinomial tree governs the underlying asset evolution. The algorithm selects a subset of the true averages realized at each node to serve as the representative averages. The option prices are then computed via backward induction and interpolation. The results show that the trinomial method produces more accurate prices especially in the case of European style Asian options.
Highlights
An Asian option is an exotic path dependent option
Vecer [6] came up with a method that overcomes the stability of problems encountered before but like all the methods mentioned above it cannot work for American Asian options
Dai [13] proposes a new trinomial lattice that models the American Journal of Applied Mathematics 2018; 6(2): 28-33 underlying price at every node to be a rational number of finite precision
Summary
An Asian option is an exotic path dependent option. Its value is pegged on the average underlying asset’s price over the option’s life. The averages that are considered are the arithmetic and geometric average The latter is straight forward as it results in a closed form expression for European options in line with the classical Black Scholes model [1]. This is because geometric average follows the same lognormal distribution as the underlying variable easing the mathematical tractability of the pricing problem. Vecer [6] came up with a method that overcomes the stability of problems encountered before but like all the methods mentioned above it cannot work for American Asian options It is this shortcoming that among others make lattice based models more suited for pricing arithmetic average-based Asian options. Dennis Odhiambo Ogot et al.: An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option
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