A Quasi‐Analytical Pricing Model for Arithmetic Asian Options

Abstract

We develop a quasi‐analytical pricing method for discretely sampled arithmetic Asian options. We derive an asymptotic approximation of the arithmetic average with the geometric average of lognormal variables. Numerical experiments show that the asymptotic approximation is accurate and the absolute error converges very quickly as the number of observations increases. The absolute error is of the order of 10−5 to 10−6 for daily average. We then derive quasi‐analytical formulas for arithmetic Asian options under the Black–Scholes framework, in which the probability density of the geometric average is used. Extensive experiments are conducted to compare the proposed method with the various existing semianalytical methods. The overall accuracy of the proposed method is better than any other methods tested. The proposed method performs much better than the second best one for at‐the‐money Asian options under high volatility. The mean pricing error of the proposed method for a daily average Asian option is 37.5% less than the second best one. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:1143–1166, 2013

Geometric Asian Options Pricing under the Double Heston Stochastic Volatility Model with Stochastic Interest Rate

“…substituting (14) into (12) and applying the Markov property of {V : 0 ≤ ≤ }, = 1, 2, lead to (5), which completes the proof.…”

“…Since the best-known closed-form pricing formula for the European vanilla option derived by Black and Scholes [2]), many researchers have devoted themselves to developing the Asian options pricing based on the Black-Scholes assumptions; see, e.g., Kemna and Vorst (1990), Turnbull and Wakeman [3], Ritchken et al [4], Geman and Yor [5], Rogers and Shi [6], Boyle et al [7], Angus [8], Linetsky [9], Cui et al [10], and the references therein. For a recent review, one can refer to Fusai and Roncoroni [11] and Sun et al [12].…”

Valuation and applications of compound basket options

“…3 According to Li and Pearson (2007), Kim (2009), Jackwerth andRubinstein (2012), and Fan, Taylor, and Sandri (2018), the ad hoc Black-Scholes formula from a geometric Brownian motion outperforms other sophisticated models such as Merton (1976) and Heston (1993). In line with this, a geometric Brownian motion is still widely used for option pricing (Andersen, Lake, & Offengenden, 2016;Escobar, Mahlstedt, Panz, & Zagst, 2017;Miao, Lee, & Chao, 2014;Shevchenko & Del Moral, 2017;Sun, Chen, & Li, 2013;Wang, Wang, Ko, & Hung, 2016). 4 We allow wi to being negative.…”

Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading

“…In the second approach, the unknown distribution of the Asian option is approximated to obtain an approximate analytical option price formula. Well-known examples of researchers who have adopted this approach are [19][20][21][22][23][24][25][26][27][28]. Generally, the method involves applying Edgeworth expansion or a Taylor series approach to a log-normal reference distribution to approximate the distribution of the arithmetic average of the underlying price or strike price.…”