Level Dependent Annuities: Defaults of Multiple Degrees

Mjøs, Aksel; Persson, Svein-Arne

doi:10.2139/ssrn.968130

Cited by 3 publications

(10 citation statements)

References 2 publications

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“…In terms of its position within the actuarial and finance literature, the RCLA is effectively a type of annuity option, and so this work is related to Ballotta and Haberman (2003), Deelstra, Vanmaele, and Vyncke (2010), as well as Hardy (2003) or Boyle and Hardy (2003) in which similar complete market techniques are relied upon. See Mjos and Persson (2010) for related work as well. In a subsequent paper we plan to describe the impact of incomplete markets and other frictions.…”

Section: Introductionmentioning

confidence: 99%

Valuation and Hedging of the Ruin‐Contingent Life Annuity (RCLA)

Huang

Milevsky

Salisbury

2013

J of Risk & Insurance

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VALUATION AND HEDGING OF THE RUIN-CONTINGENT LIFE ANNUITYThis paper analyzes a novel type of mortality contingent-claim called a ruin-contingent life annuity (RCLA). This product fuses together a path-dependent equity put option with a "personal longevity" call option. The annuitant's (i.e. long position) payoff from a generic RCLA is $1 of income per year for life, akin to a defined benefit pension, but deferred until a pre-specified financial diffusion process hits zero. We derive the PDE and relevant boundary conditions satisfied by the RCLA value (i.e. the hedging cost) assuming a complete market where No Arbitrage is possible. We then describe some efficient numerical techniques and provide estimates of a typical RCLA under a variety of realistic parameters.The motivation for studying the RCLA on a stand-alone basis is two-fold. First, it is implicitly embedded in approximately $1 trillion worth of U.S. variable annuity (VA) policies; which have recently attracted scrutiny from financial analysts and regulators. Second, the U.S. administration -both Treasury and Department of Labor -have been encouraging Defined Contribution (401k) plans to offer stand-alone longevity insurance to participants, and we believe the RCLA would be an ideal and cost effective candidate for that job.

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Section: Introductionmentioning

confidence: 99%

Valuation and Hedging of the Ruin‐Contingent Life Annuity (RCLA)

Huang

Milevsky

Salisbury

2013

J of Risk & Insurance

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“…The time 0 market value V A of the interest rate payments in the case where the starting value A 0 is above the barriers B n+1 , ..., B n+m+1 , is essentially the same as the one found in Expression (3) in Mjøs & Persson (2010), with the modification that c 1 r is multiplied by η. The factor η stems from the fact that B 0 = ∞ in our case.…”

Section: Proof Of Main Pricing Resultsmentioning

confidence: 96%

“…is given by Expression (12) and M ∞ T (A) is given by Expression (22) in Mjøs & Persson (2010) respectively. The formula for V B follows by direct calculations with c = 1 and c n+1 = 0.…”

Section: Proof Of Main Pricing Resultsmentioning

confidence: 99%

“…Market participants indicate that more than 50% of recently issued syndicated bank loans in Europe include such provisions. Based on standard no-arbitrage theory, using results from Mjøs & Persson (2010) and observed contractual specifications, we derive a closed-form valuation formula to price PSD contracts with a cash flow driven performance measure, and compare the theoretical market price of a PSD contract with the par value of the loan at the time of issue. We also study two important subclasses of PSD contracts; interest increasing and interest decreasing PSD contracts.…”

Section: Introductionmentioning

confidence: 99%

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On the Pricing of Performance Sensitive Debt

2011

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Performance sensitive debt (PSD) contracts link a loan's interest rate to the borrower's measure of credit relevant firm performance, e.g., if the borrower becomes less creditworthy, the interest rate increases according to a predetermined schedule. PSD provisions are included in approximately 35% of all U.S. and Canadian corporate loans (1994. Based on standard no-arbitrage theory and observed contractual specifications, we derive and empirically test a new pricing model for PSD contracts with a cash flow driven performance measure. Our sample consists of 270 PSD loans where the loan contractual terms are collected from Thomson Reuter's Dealscan database and the borrower information is collected from Compustat and CRSP. The theoretical market value of a PSD contract is on average 3.2% above par value at the time of issue. By considering the subsamples of only interest increasing and interest decreasing PSD contracts, respectively, we find that the former is overpriced by 7.7% on average, whereas the latter, on average, exhibits no significant mispricing. The empirically observed overpricing of interest increasing contracts is consistent with the signalling hypothesis of Manso, Strulovici & Tchistyi (2010) and the cost of moral hazard explanation of Asquith, Beatty & Weber (2005). The not significant mispricing of interest decreasing contracts is consistent with the idea that borrowers have increased bargaining power in the form of outside alternative financing options for these contracts.

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“…The paper is related to Brockman and Turtle (2003) as well as the associated models (Black and Cox, 1976;Ericsson and Reneby, 2005;Forte and Lovreta, 2012;Sokolinskiy, 2019). From a technical perspective, our work is related to Mjøs and Persson (2010) and 2 Negative capital requirements can arise when: (i) the bank capital is reported on an inappropriate accounting basis (e.g. historical cost accounting), even if the regulator imposes positive minimum capital requirements (Kane, 1989;Harding et al, 2013), and (ii) the regulator follows a capital forbearance policy (Ronn and Verma, 1986).…”

Section: Introductionmentioning

confidence: 99%