Competitive Monte Carlo methods for the pricing of Asian options

Weak approximation of averaged diffusion processes

“…Coupling semi-analytical approximations and PDE is proposed in [Zha01]. Alternatively, evaluating (0.4) can be performed by Monte Carlo simulations [LT01]: in the case of the mean of exponentials, it is very efficient to use the geometric mean as a control variate, see [KV90]. In a more general framework (b and σ depending also on x), we notice the Markov projection techniques: the average has the same law as the marginal law of a SDE which coefficients can be approximated, for short time, by an explicit expression involving the different coefficients in the space A, see [ABOBF02].…”

Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing

“…When we apply the Euler-Maruyama scheme to this process (8), it may happen that the square volatility process (Y 2 ) (EM),n k becomes negative, and the algorithm then fails at the next step (as we will have to take its square root). On the other hand, equations (12) and (14) show that our new algorithm does not share this problem. There exists a way of avoiding this problem with the Euler-Maruyama scheme [4].…”

“…Many existing algorithms lack one or both of these properties. For example, in [14], they proposed the trapezoidal algorithm which accelerates Monte Carlo pricing of Asian option price. But this algorithm works only for the price of Asian option written on one dimensional diffusion.…”

Estimators of sensitivities of an Asian option: numerical analysis

“…An approach based on Taylor series approximations proposed by N.Ju [14]. For Monte Carlo simulation to price Asian options, we can name, for example, Kemna and Vorst (1990), or B.Lapeyre and E.Temam [4].…”