Estimation of Ask and Bid Prices for Geometric Asian Options

Abstract

Traditional derivative pricing theories usually focus on the risk-neutral price or the equilibrium price. However, in highly competitive financial markets, we observed two prices which are called bid and ask prices; then the unique risk-neutral price fails to hold. In this paper, within the framework of conic finance, we provide a useful approach to evaluate the ask and bid prices of geometric Asian options and obtain the explicit formulas for the ask and bid prices. Finally, numerical examples show that the higher the market liquidity parameter , the wider the spread and hence the less the liquidity.

Estimation of the Bid-Ask Prices for the European Discrete Geometric Average and Arithmetic Average Asian Options

“…At the same time, many research topics including conic CVA and DVA, conic portfolio theory, conic hedging of financial and insurance risks, and conic trading are presented in the recently published book by Madan and Schoutens [16]. Recently, the researchers derived the explicit formulas for the bid and ask prices of European vanilla options [15,16], interest rate options [17], and continuous geometric average Asian options [18], respectively, by using the conic finance theory. To the best of our knowledge, there is no literature research to estimate the bid-ask prices of the discrete Asian options.…”

“…Substituting n ⟶ ∞ and h ⟶ 0, (n − 1)h ⟶ τ, into T sa n− j and T sa μ,n− j yields T sa n− j ⟶ τ/2 and T sa μ,n− j ⟶ τ/3. Furthermore, substituting these two limiting values into (25) and (27), we obtain the bid-ask prices of a continuous geometric average Asian option in [18]. On the contrary, substituting these two limiting values into (42) and (43), we can also derive the bidask prices of a continuous arithmetic average Asian option.…”