An efficient convergent lattice algorithm for European Asian options

Pricing Asian option by the FFT with higher-order error convergence rate under Lévy processes

“…The x-axis and the y-axis denote ln h and the natural logarithm of the absolute pricing error, respectively. In panel (a) we use the closed-form pricing formula given by [12] to evaluate the exact value needed for calculating the pricing errors. The value 2:36828545183 obtained by the extrapolation method proposed by [21] is used as a proxy for the true option value in panel (b).…”

“…If the stock price follows LGNO and the strike price K ¼ 0, the Asian call option can be priced analytically [12]. In this case we can calculate exact pricing errors and compare the error convergence rate between the Benhamou algorithm and our Oðh 4 Þ and Oðh 6 Þ algorithms in panel (a) of Fig.…”

Partial differential equations for Asian option prices

“…We take S 0 = 100, T = 1 with interest rates r = 0.02, 0.09, 0.15, volatilities σ = 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 and strikes K = 90, 95, 100, 105, 110; we use n = 400, m = 200. Benchmark values (BM) were calculated using the method given in Dai et al (2005); in that paper, the authors gave convincing evidence that their method is accurate. The cases considered here allow for a range of high and low values for the volatility and interest rate parameters.…”

An efficient and accurate lattice for pricing derivatives under a jump-diffusion process

“…Developing efficient lattice algorithms for complex derivatives has been widely studied [5][6][7][8][9][10][11][12][13]. Although a lattice can be efficient for simple derivatives, evaluating complex derivatives can be computationally intractable as some problems are socalled #P-hard [14].…”