Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated with an underlying asset reduces to computing an expectation w.r.t. a diffusion process. In general, these expectations cannot be calculated analytically, and one way to approximate these quantities is via the Monte Carlo (MC) method; MC methods have been used to price options since at least the 1970s. It has been seen in Del Moral P, Shevchenko PV. [Valuation of barrier options using sequential Monte Carlo. 2014. arXiv preprint] and Jasra A, Del Moral P. [Sequential Monte Carlo methods for option pricing. Stoch Anal Appl. 2011;29:292–316] that Sequential Monte Carlo (SMC) methods are a natural tool to apply in this context and can vastly improve over standard MC. In this article, in a similar spirit to Del Moral and Shevchenko (2014) and Jasra and Del Moral (2011), we show that one can achieve significant gains by using SMC methods by constructing a sequence of artificial target densities over time. In particular, we approximate the optimal importance sampling distribution in the SMC algorithm by using a sequence of weighting functions. This is demonstrated on two examples, barrier options and target accrual redemption notes (TARNs). We also provide a proof of unbiasedness of our SMC estimate.