Universal option valuation using quadrature methods

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

“…We define the order of convergence as b where the absolute error is ϵ n = an −b ; thus, the log-absolute error ln ϵ n is linear in ln n and has slope −b. In all cases we find that the slope coefficient isb = 2 and the coefficient of determination is R 2 = 1.0 implying order 2 convergence, in consistency with the error analyses of Andricopoulos et al (2003), Lord et al (2008) andČerný andKyriakou (2011) for the case of one-dimensional pricing problems under Lévy log-returns and continuous value functions. We exploit the order 2 convergence to achieve very high precision faster by extrapolation via a simple Richardson-type procedure; in Table 5 we report results with accuracy of seven decimals achieved in 30s.…”

Chapter 8 Discrete Barrier and Lookback Options

“…See Ait-Sahalia and Lai (1997Lai ( , 1998, Sullivan (2000), Tse et al (2001), Andricopoulos et al (2003), and Fusai and Recchioni (2003).…”

Pricing early-exercise and discrete barrier options by fourier-cosine series expansions

“…according to (3). To study the impact of x on ǫ 1 , we use the property f (y|x) = f (y − x), which holds for Lévy processes.…”

“…Recently, transform methods have been generalized to solving somewhat more complicated option contracts, like Bermudan, American or barrier options, see, for example, [33,21,3,4,30,42,17,41]. These exotic options, still with basic features, are used in the financial industry as building blocks for more complicated products.…”