Valuation of equity-indexed annuities under correlated jump–diffusion processes

Sharma, Nitu; Pasricha, Puneet; Selvamuthu, Dharmaraja

doi:10.1016/j.cam.2021.113575

Cited by 6 publications

(6 citation statements)

References 17 publications

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“…Some of the recent literature in VA pricing using variants of GBM model includes articles by Ballotta et al, 3 Gerber et al, 4 Ko and Bae, 5 Escobar et al, 6 Yu et al, 7 Sharma et al, 8 and Sharma et al. 9 Gerber et al 4 valued the GMDB rider using a JDBM model. Ko and Bae 5 priced a GMDB rider with a roll-up and fixed-guarantee features under Black-Scholes framework.…”

Section: Introductionmentioning

confidence: 99%

“…The correlated jump-diffusion model is used for modeling investment risk in an equity-indexed annuities (EIAs) contract by Sharma et al. 9 EIAs are insurance contracts similar to VAs. Under EIA, the rate of return is linked to the returns of the underlying index.…”

Section: Introductionmentioning

confidence: 99%

“…Some of the popular variations of the GBM model involve consideration of jumps (denoted by jump‐diffusion Brownian motion (JDBM) models), stochastic volatility, stochastic interest rate, and correlated jump‐diffusion processes. Some of the recent literature in VA pricing using variants of GBM model includes articles by Ballotta et al, 3 Gerber et al, 4 Ko and Bae, 5 Escobar et al, 6 Yu et al, 7 Sharma et al, 8 and Sharma et al 9 . Gerber et al 4 valued the GMDB rider using a JDBM model.…”

Section: Introductionmentioning

confidence: 99%

“…Sharma et al 8 priced a GLWB rider using a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. The correlated jump‐diffusion model is used for modeling investment risk in an equity‐indexed annuities (EIAs) contract by Sharma et al 9 . EIAs are insurance contracts similar to VAs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

Sharma

Selvamuthu

Natarajan

2022

Appl Stoch Models Bus & Ind

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Pricing a variable annuity (VA) is traditionally based on models with standard Brownian motion (BM). The assumption of independent increments in the BM is not always realistic as the price process of the risky assets exhibit a long-range dependency. To model such assets, a fractional Brownian motion (FBM) with Hurst parameter)is an appropriate model. However, due to arbitrage in an FBM model and jumps in stock returns, we consider in this work a mixed FBM (MFBM) model with jumps and evaluate variable annuities with different riders. We analyze the proposed model numerically to see the impact of mortality risk. We perform a comparison between eight stochastic models to obtain the best-suited mortality model, for a dataset of the US male population. Finally, we obtain the price of VA guarantees using the forecasted values from the fitted mortality model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

Sharma

Selvamuthu

Natarajan

2022

Appl Stoch Models Bus & Ind

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“…Pasricha and Goel 15 addressed the problem of pricing power exchange options in a Hawkes jump‐diffusion model. Recently, Nitu et al 16 considered Hawkes jump‐diffusion model for the pricing of equity indexed annuities.…”

Section: Introductionmentioning

confidence: 99%

Hedging and utility valuation of a defaultable claim driven by Hawkes processes

Pasricha

Selvamuthu

Tardelli

2021

Appl Stoch Models Bus & Ind

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This article studies the problem of hedging a defaultable claim via the maximization of the mean value of exponential utility, over a set of admissible strategies. The dynamics of the underlying asset is assumed to be governed by mutually exciting Hawkes processes, which captures the jumps clustering phenomenon observed in the market. The resulting market is incomplete and does not allow perfect replication. Hence, a dynamic programming approach is adopted to characterize the value function as the largest solution to a suitable backward stochastic differential equation (BSDE) with a non‐Lipschitz generator. The value function of the optimal investment problem and of the indifference prices are represented in terms of limits of the sequence of value functions of suitable Lipschitz BSDEs and, further, a result of uniqueness is achieved. Finally, numerical experiments are performed to demonstrate the applicability of the proposed framework and to understand the impact of the jump‐clustering on the values of the claims.

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Structural credit risk models with stochastic default barriers and jump clustering using Hawkes jump-diffusion processes

Pasricha,

Selvamuthu,

Tardelli

2024

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This paper derives a closed-form expression for the default probability and the default correlation of firms under a structural model of credit risk. Specifically, the underlying firms are assumed to have the value process driven by a Hawkes jump-diffusion model with the continuous parts of the trajectories being driven by correlated Brownian motions, while the jumps being driven by Hawkes processes having general structure of the exciting functions. The proposed framework takes into account the numerically observed facts about the default, i.e., clustering and unexpectedness. Furthermore, the default barriers are assumed to be stochastic in nature and modeled as stochastic processes, affected by common factors reflecting the systematic risk. A sensitivity analysis of default probability and correlation is conducted to investigate the impact of jump risk, clustering, and stochastic default barriers. These numerical studies demonstrate that jump clustering increases the default probability but reduces the correlation of defaults.

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Valuation of equity-indexed annuities under correlated jump–diffusion processes

Cited by 6 publications

References 17 publications

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

Variable annuities valuation under a mixed fractional Brownian motion environment with jumps considering mortality risk

Hedging and utility valuation of a defaultable claim driven by Hawkes processes

Structural credit risk models with stochastic default barriers and jump clustering using Hawkes jump-diffusion processes

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