Unbiased Monte Carlo valuation of lookback, swing and barrier options with continuous monitoring under variance gamma models

Modeling and measuring intraday overreaction of stock prices

“…The left graph shows the results under adequate reaction to news (i 0 = i 0,p = i 0,n = 1), while the right graph was produced using (7), with adequate reactions to news originating from the continuous information flow modeled by Brownian motion (i 0 = 1), intraday underreaction to good news (i 0,p = 0.75) modeled by positive jumps in fundamental prices, and intraday overreaction to bad news (i 0,n = 1.75) modeled by negative jumps in fundamental prices; all reactions have a half-life of s 0.5 = 0.2. 5 Simulation with exact algorithm (adaptive difference-of-gammas bridge sampling) described in Becker (2010b). 6 Simulation with 390-step discretization of subordinated Brownian motion (with inverse Gaussian subordinator) using the exact simulation for IG random variates described in Devroye (1986, p. 149 adequate (i 0 = 1), markets underreact to good news (i 0,p = 0.75) and overreact to bad news (i 0,n = 1.75).…”

Simulation of Tempered Stable Lévy Bridges and Its Applications

“…Although such a direct extension of DGBS does not yield any relative advantages, bridge sampling is ideally suited to adaptive versions of DGBS that can lead to large savings in simulation costs. Becker (2010) has developed such an adaptive algorithm for VG processes, and we now extend the algorithm to CGMY processes. The key idea of adaptive sampling is to exclude the intervals from a given partition of the time dimension that neither contribute to the minimum nor to the maximum of a sample path.…”

“…• It allows adaptive sampling for pricing path-dependent options under finite variation tempered stable processes (e.g., CGMY processes). Such an adaptive technique extended from Becker (2010) results in remarkable savings in simulation costs.…”

Simulation of Lévy processes and option pricing

“…Note that for variance gamma processes the condition (2.6) is not satisfied. The fair price given by Becker (2010) is V (S + ) = 9.3982. In Table 5.1, we compare V (S + ) and V (S + ).…”