Abstract
Conic finance is a new and exciting development in quantitative finance, which is widely applied to several topics in finance. The theory of conic finance extends the law of one price to the law of two prices, which yields closed forms for bid-ask prices of European options. In this paper, within the framework of conic finance, we derive effective, explicit, approximate formulas to estimate the bid-ask prices for the European discrete geometric average and arithmetic average Asian options. Finally, we give two examples to demonstrate and validate that the approximate closed-form solutions are efficient and accurate.
Highlights
In the OTC markets, the Asian option is one of the most popular exotic options
Asian options are options whose payoffs depend on some average price of the underlying asset over some prescribed period; Asian options are called average price options. ere are two main advantages of Asian options: one for reducing the risk of market manipulation of the underlying instrument at maturity and the other one for reducing the volatility inherent in the option
In the Black–Scholes–Merton framework, many scholars have sufficient research on exotic options. ey develop many methods such as chaos theory, fractal Brownian motion, time-changed Brownian, stochastic volatility, and models based on Levy processes to incorporate two empirical features: the asymmetric leptokurtic features and the volatility smile [2, 3]
Summary
In the OTC markets, the Asian option is one of the most popular exotic options. Asian options are options whose payoffs depend on some average price of the underlying asset over some prescribed period; Asian options are called average price options. ere are two main advantages of Asian options: one for reducing the risk of market manipulation of the underlying instrument at maturity and the other one for reducing the volatility inherent in the option. In [7], Madan and Cherny established the conic finance theory by using the acceptability indices’ theory and the nonlinear expectation theory and derived the general closed-form formulas for bid and ask prices for European options. 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. In this paper, motivated by the conic finance theory, we derive an effective, explicit, approximate formula to calculate the bid and ask prices for the discrete Asian options including discrete geometric average and arithmetic average Asian options.
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