A unified approach to Bermudan and barrier options under stochastic volatility models with jumps

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“…According to Ravindran [1998], barrier options can be also valued using multivariate integrals, binomial method, and Monte Carlo method. In recent years, numerous papers presenting alternative approaches to barrier options pricing have been published (see for example Chiarella et al [2012], Hong et al [2015], Rashidi Ranjbar and Seifi [2015], Kirkby et al [2017], or Nouri and Abbasi [2017]). The majority of the papers focus on double-barrier options pricing.…”

Full‐fledged SABR Through Markov Chains

“…Note that l is fixed by definition for each l , and each of the processes defined by l share the same state space,  X . That is, conditioned on a variance state l , the dynamics (transition probabilities) of X (N) t are determined by Equation (8). Meanwhile, (t) will make transitions between states in accordance with Equation (5).…”

“…While the FDM and CTMC are able to compute the option prices across the given strike spectrum, the exact integral method of Antonov et al (2013) fails for the ATM case as their integral diverges. All six strikes are computed by CTMC in about 3 s. 8 Given that the primary cost is the matrix exponential, increasing the number of strikes by 500 only adds about 1 s, roughly 0.002 s per additional strike. For European options, the CPU cost for CTMC is greater than the expansion methods and that of Antonov et al (2013).…”

“…Numerical experiments confirm the accuracy and efficiency of the proposed method, which is suitable for practical use.1 Our framework is applicable to general SLV models; refer to Cui et al (2018b) for full details. It also covers the stochastic volatility models with linear local volatility components, as discussed in Kirkby et al (2017). Source code is available at https://github.com/jkirkby3.…”

Static hedging and pricing of exotic options with payoff frames

“…Utilizing the theory of frame projection, the methodology developed in Kirkby () obtains orthogonal projections of risk‐neutral return densities for processes with known characteristic functions, enabling the efficient pricing of any finitely valued claim. Extensions to exotic option pricing are considered in Kirkby (, ), Cui, Kirkby, and Nguyen (, ), and Kirkby, Nguyen, and Cui ().…”