Abstract
This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price arithmetic Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in CEV process.
Highlights
Asian options are the popular financial tool in the over-the-counter market, whose payoffs depend on some form of averaging of the underlying stock price during some specific period
This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV) process
We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process
Summary
Asian options are the popular financial tool in the over-the-counter market, whose payoffs depend on some form of averaging of the underlying stock price during some specific period. Arithmetic Asian options have become increasingly prevalent in the over-the-counter market. Most of the published investigations on arithmetic Asian options assume that the underlying stock follows lognormal distribution process. When the Black-Scholes model is used to price stock options, certain biases, such as the strike price bias (volatility smile), persist because there lies in the negative correlation between stock price changes and volatility changes (Macbeth & Merville, 1980). The CEV option-pricing model, originally developed by Cox (1975), incorporates this negative correlation. It is instructive to apply the CEV process to arithmetic Asian options
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