An analytic valuation method for multivariate contingent claims with regime-switching volatilities

The Pension Benefit Guaranty Corporation (PBGC) provides insurance coverage for single-employer and multiemployer pension plans in private sector. It has played an important role in protecting the retirement security for over 1.5 million people since it was established about half a decade ago. PBGC collects insurance premiums from employers that sponsor insured pension plans for its coverage and receives funds from pension plans that it takes over. To address the issue of underfunded plans that the PBGC has, this work studies how to evaluate risk-based premiums for the PBGC. Inspired by a couple of existing work in which the premature termination of pension fund and distress termination of sponsor assets are analyzed separately, our work examines the two types of terminations under one framework and considers the occurrence of each termination dynamically. Given that market regime might have a big impact on the dynamics of both pension fund and sponsor’s assets, we thus formulate our model using a continuous-time two-state Markov chain in which bull market and bear market are delineated. We thus formulate our model using a continuous-time two-state Markov Chain in which bull market and bear market are delineated. In other words, the pension fund and sponsor assets are market dependent in our work. Given that this additional uncertainty described by regime switching makes the market incomplete, we therefore utilize the Esscher transform to determine an equivalent martingale measure and apply the risk neutral pricing method to obtain the closed-form expressions for premium of PBGC. In addition, we carry out numerical analysis to demonstrate our results and observe that premium increases according to the retirement benefit irrespective of the type of terminations. In comparison to the case of early distress termination of sponsor assets, the premium goes up more quickly when premature termination of pension funds occurs first due to the fact that pension fund is the first venue of retirement security. Furthermore, we look at how the premium changes with respect to other key parameters as well and make some detailed observations in the section of numerical analysis.

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“…From Yoon et al [20], we can obtain the following lemma. Lemma 1.…”

Section: Premium Calculationsmentioning

confidence: 97%

Premium Valuation of the Pension Benefit Guaranty Corporation with Regime Switching

Wang

Xie

et al. 2021

Mathematical Problems in Engineering

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“…Furthermore, Cheang and Garces (2020) combined stochastic volatility with jump diffusions when pricing exchange options, while exchange options taking credit risks into consideration were studied by Wang (2016) and Xu et al (2019). In addition, varying economic condition is empirically shown to be a vital factor that affects stock prices (Hamilton, 1990; He & Chen, 2022; He & Lin, 2022; Siu & Elliott, 2022), which has also been taken into consideration when pricing exchange options (Yoon et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Analytically pricing exchange options with stochastic liquidity and regime switching

Lin

2023

Journal of Futures Markets

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We investigate the valuation of exchange options when the market is affected by changing economic conditions as well as liquidity risks. The volatility and expected returns of both stocks are assumed to be controlled by a continuous‐time Markov chain to reflect the effects of varying economic conditions, and a liquidity discounting factor is employed to capture the impact of market liquidity on stock prices. Once the model has been established, we construct a risk‐neutral measure with the use of regime‐switching Esscher transform, and the characteristic function is then derived in an analytical form, so that a closed‐form formula for exchange options can be presented. We further analyze the effects of the two considered factors on exchange option prices numerically.

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“…As far as we know, there are not so many papers focusing upon multivariate option pricing in a regime‐switching framework, especially not in a MMLP setting, and none of them considers synchronous jumps. Among others, we refer to Yoon et al, Chen et al, Fan and Wang, and Deelstra and Simon . In particular, Deelstra and Simon study the pricing of exchange and quanto options in a MMLP framework by using a fast Fourier transform method.…”

Section: Introductionmentioning

confidence: 99%

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

Deelstra

Kozpınar

Simon

2018

Appl Stoch Models Bus & Ind

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This paper considers the evaluation of spread and basket options when the underlying asset prices are driven by Markov-modulated Lévy processes with synchronous jumps. In particular, the asset prices may jump whenever there is a change of phase of the underlying Markov process. We further allow for dependence between the different price dynamics. In this general regime-switching framework, we provide lower and upper bounds to the exact option prices based upon ideas from the literature without regime switching. These bounds are obtained via univariate Fourier inversion under the assumption that the joint characteristic functions of the Markov-modulated Lévy processes are known. We study these obtained spread and basket option price approximations in different regime-switching models. Several numerical experiments are included and these show that, especially, the lower bounds have a very high precision.

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An analytic valuation method for multivariate contingent claims with regime-switching volatilities

Cited by 13 publications

References 31 publications

Premium Valuation of the Pension Benefit Guaranty Corporation with Regime Switching

Premium Valuation of the Pension Benefit Guaranty Corporation with Regime Switching

Analytically pricing exchange options with stochastic liquidity and regime switching

Spread and basket option pricing in a Markov‐modulated Lévy framework with synchronous jumps

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