Pricing of Geometric Average Asian Options in Risk-Averse Markets

Considering that real financial markets are usually incomplete and exhibit risk aversion, this paper investigates the pricing of geometric-average fixed-strike Asian options in risk-averse markets. Assuming that the price of the underlying asset follows geometric Brownian motion, we adopt two risk measures, namely Value-at-Risk (VaR) and standard deviation (STD), and derive the pricing formulas for geometric-average fixed-strike Asian options via the terminal-value discounting method. Numerical analysis explores the effects of key parameters on option prices, including the underlying asset price S, strike price K, risk-free rate r, volatility σ, drift rate μ, and risk-aversion coefficient λ. Monte Carlo simulations confirm the validity of the obtained results. The proposed pricing formulas are derived under fewer explicitly imposed assumptions than those of the classical Black–Scholes framework. In a risk-neutral market, where λ=0 and μ=r, the derived expressions reduce to the classical risk-neutral formulas for geometric-average fixed-strike Asian options.