Approximate analytic solution for Asian options with stochastic volatility

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

“…Following Hull and White [1], Tsao, Chang, and Lin [14], and Lin and Chang [28], a European-style FSAO with stochastic volatility written on an asset with maturity date T was investigated.…”

“…The first three moments of V at µ = 0 can be derived as (Following the settings of Hull and White [19], Lin, and Chang [28], and to simplify the derivation of the analytic approximate solution for options, this paper only discusses the case in which µ = 0. However, the case in which µ 0 and the moments of V with nonzero µ can be derived without considerable effort; see Hull and White [19] for further details.…”

“…Motivated by these empirical results, the present study extended the research of Hull and White [19,20,25,28] to include a Taylor series expansion technique for deriving the approximate analytical solution of an FSAO in the context of stochastic volatility pricing.…”

“…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.…”