Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation

Randomization and the Valuation of Guaranteed Minimum Death Benefits

“…Our results have strong links to derivative valuation in Finance with deterministic payment dates (e.g. Cai, Song, & Kou, 2015, Hieber, 2018, Deelstra et al, 2020, Kirkby, 2023. We adapt these results to popular insurance payoffs where lookback-type payoffs are more common components of (for example) dynamic withdrawal benefits, than digital and barrier-like products covered in articles with a stronger focus on financial derivatives (e.g.…”

Analyzing The Interest Rate Risk of Equity-Indexed Annuities Via Scenario Matrices

“…First, it is straightforward to use a different stochastic interest rate model, for example a two-factor Hull-White model. Second, the scenarios might incorporate not only interest rate risk but also a stochastic volatility (see also Cui et al, 2017;Kirkby, 2023). Instead of conditioning on 𝑟 (𝑘) and 𝑟 (𝑗) , the scenario matrix conditions on pairs (𝑟 (𝑘) , 𝜎 (𝑘) ) and (𝑟 (𝑗) , 𝜎 (𝑗) ) for an appropriately chosen volatility grid 𝜎 (𝑘) , 𝑘 = 1, 2, … , 𝐾.…”

“…This idea is applied by Cui et al (2017) to a cliquet option where the underlying can incorporate stochastic volatility models with jumps that are approximated by Markov chain processes. Kirkby (2023) uses the same technique for stochastic interest rate models.…”