Longevity bond pricing under the threshold CIR model

Dong, Fangyuan; Wong, Hoi Ying

doi:10.1016/j.frl.2015.09.010

Cited by 3 publications

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“…In other words, the agent uses life insurance to hedge against the possibility of dying (unexpectedly) with positive or negative wealth, which would otherwise incur costs through forsaken consumption or penalties. The modeling framework in this article assumes that the representative agent 8 represents "a large number of identical agents", and as such life insurance contracts can be offered risk-less (on average) by life insurance companies. We assume that the market for life insurance contracts is competitive 9 , and hence free entry and exit will result in a expected zero profit condition, which in turn implies that the fair pricing of the insurance contract obliges/entitles the holder to a payment of…”

Section: The Modelmentioning

confidence: 99%

“…The two approaches, using either life insurance or actuarial notes are equivalent. In fact if no life insurance were available but an actuarial note paying a yield of r t + ν t the investor could use a portfolio of perpetual bonds and actuarial notes to create an interest income of X t ν t as in equation(8) and hence construct the payoff structure thatBlanchard (1985) uses. In this interpretation the extra term X t ν t is to be understood as an additional income from the insurance contract rather than the interest of a financial asset.…”

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On the effects of changing mortality patterns on investment, labour and consumption under uncertainty

Ewald

Zhang

2017

Insurance: Mathematics and Economics

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In this paper we extend the consumption-investment life cycle model for an uncertain-lived agent, proposed by Richard (1974), to allow for flexible labor supply. We further study the consumption, labor supply and portfolio decisions of an agent facing age-dependent mortality risk, as presented by UK actuarial life tables spanning the time period from 1951-2060 (including mortality forecasts). We find that historical changes in mortality produces significant changes in portfolio investment (more risk taking), labour (decrease of hours) and consumption level (shift to higher level) contributing up to 5% to GDP growth during the period from 1980 until 2010.

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On the effects of changing mortality patterns on investment, labour and consumption under uncertainty

Ewald

Zhang

2017

Insurance: Mathematics and Economics

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Variance swaps under the threshold Ornstein–Uhlenbeck model

Dong

Wong

2017

Appl Stoch Models Bus & Ind

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Variance swap is a typical financial tool for managing volatility risk. In this paper, we evaluate different types of variance swaps under a threshold Ornstein-Uhlenbeck model, which exhibits both mean reversion and regime switching features in the underlying asset price. We derive the analytical solution for the joint moment generating function of log-asset prices at two distinct time points. This enables us to price various types of variance swaps analytically.regime-switching is originated by Hamilton ([10]). Although there are many possible models for regime-switching, the self-exciting threshold autoregressive (SETAR) model proposed by Tong ([11]) admits a tractable likelihood function for parameter estimation and is a popular regime-switching model alternative to the one used in Kim et al. ([3]). Tsay ([12]) points out that the SETAR model can capture jump phenomena observed in practice because of discontinuity at the threshold. Therefore, it can be efficiently estimated and empirically tested with real data. We offer empirical evidence for the SETAR model with historical crude-oil spot price.By considering the diffusion limit of the SETAR model, we propose a threshold Ornstein-Uhlenbeck (TOU) process {X t } t≥0 and derive the corresponding analytical formulas for various variance swaps. To this end, we have to examine the joint distribution of X T 1 and X T 2 at two fixed time points. To characterize the distributional property, we derive the joint moment-generating function (MGF) [e 1 X T 1 + 2 X T 2 |X t = x] in two steps. We find the closed-form expression for[e X T |X t = x] in the first step and apply it to the joint MGF in the second step. A PDE framework similar to Wong and Zhao ([13]) is applied to obtain the solution. Consequently, the analytical solution of the MGF brings us the pricing formulas of variance swaps in terms of Laplace inversion. We implement the solution using numerical methods proposed by Abate and Valkó ([14], [15]).The remainder of the paper is organized as follows. Section 2 introduces TOU model with empirical support. Section 3 states the two-step method for deriving the analytical solution of the joint MGF. Section 4 is the application of the joint MGF in variance swaps pricing. Section 5 numerically examines the accuracy of the closed-form solution of MGF and variance swaps price derived under TOU model. Section 6 concludes. The preliminaryTo formulate our problem in a PDE framework under a n-regime TOU model, we introduce Lemma 2.1 in the succeeding text, which is useful in many circumstances in this paper.With the conditions in (27) and (28) and the derivative property of Kummer's function M (a, b, z) and U(a, b, z), we deduce a linear equation system (17) for solving the coefficients c 21 and c 22 .

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Approximate maximum likelihood estimation of a threshold diffusion process

Tsai

Rachinger

2020

Computational Statistics & Data Analysis

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Longevity bond pricing under the threshold CIR model

Cited by 3 publications

References 19 publications

On the effects of changing mortality patterns on investment, labour and consumption under uncertainty

On the effects of changing mortality patterns on investment, labour and consumption under uncertainty

Variance swaps under the threshold Ornstein–Uhlenbeck model

Approximate maximum likelihood estimation of a threshold diffusion process

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