Pricing of geometric Asian options under Heston's stochastic volatility model

A Recursive Method for Discretely Monitored Geometric Asian Option Prices

“…But it is well-known that there is no analytic formula available for arithmetic Asian option prices even under the Black-Scholes model. On the contrary, continuous-time geometric Asian option prices are more tractable and can be expressed analytically or semi-analytically at least under more relaxed assumptions covering various models such as Black-Scholes, Heston, and Lévy model [2,3,4,7,11,12,13]. In this regard, geometric Asian option prices can be utilized as approximate values for the corresponding arithmetic Asian option prices.…”

“…Instead, we choose to focus on relatively more recent results for which analytic methods are employed. A more complete review can be found in Boyle and Potapchik [2], Tahani [12] and Kim and Wee [11]. Fusai and Meucci [7] provided analytic closed solutions for discretely monitored geometric Asian option prices and recursive formula for arithmetic Asian option prices under the framework of exponential Lévy model.…”

“…In Cai and Kou [3] they presented a closed form solution for the double-Laplace transform of Asian options under the hyper exponential jump diffusion model, and obtained continuous-time arithmetic Asian option by inverting numerically. In Kim and Wee [11], closed form of analytic formulas for geometric Asian options are derived, which involves explicit expression of generalized joint Fourier transform of the square-root process and its three different temporal integrals as multivariable complex-valued functions. Tahani [12] dealt with analogous problem and applied the results when underlying assets are stocks, foreign exchange rate, and interest rates.…”

Digital barrier options pricing: an improved Monte Carlo algorithm

“…In addition, Zhang et al [23], have presented the total least squares quasi-Monte Carlo approach for valuing American barrier options, and Jasra and Del Moral provided a review and development of sequential Monte Carlo (SMC) methods for option pricing [12], and in Kim et al [15], have considered Heston's stochastic volatility model and derive exact analytic expressions for the prices of fixed strike and floating-strike geometric Asian options with continuously sampled averages.…”

Jumps and stochastic volatility in crude oil prices and advances in average option pricing

“…Based on the same principles, Wong and Cheung (2004) and Fouque and Han (2004) provide price approximations for continuously monitored geometric average options for further use as control variates in generating price estimates for the more prevalent arithmetic options. Tahani (2013) and Kim and Wee (2014) derive exact expressions for continuous geometric options under the square root variance model with/out mean-reverting log-asset price dynamics, whereas Hubalek et al (2014) develop a pricing framework in a general affine stochastic volatility (ASV) model setup. Shiraya and Takahashi (2011) propose an approximation formula for pricing average options under the Heston and extended SABR stochastic volatility models.…”