Pricing Annuity Guarantees Under a Regime-Switching Model

Abstract

We consider the pricing problem of equity-linked annuities and variable annuities under a regimeswitching model when the dynamic of the market value of a reference asset is driven by a generalized geometric Brownian motion model with regime switching. In particular, we assume that regime switching over time according to a continuous-time Markov chain with a finite number state space representing economy states. We use the Esscher transform to determine an equivalent martingale measure for fair valuation in the incomplete market setting. The paper is complemented with some numerical examples to highlight the implications of our model on pricing these guarantees.     

Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting

A general class of fair valuations which are both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evolutions) was introduced in Dhaene et al. [Insurance: Mathematics & Economics, 76, 14–27 (2017)] in a single period framework. In particular, the authors considered mean-variance hedge-based (MVHB) valuations where fair valuations of insurance liabilities are expressed in terms of mean-variance hedges and actuarial valuations. In this paper, we generalize this MVHB approach to a multi-period dynamic investment setting. We show that the classes of fair valuations and MVHB valuations are equivalent in this generalized setting. We derive tractable formulas for the fair valuation of equity-linked contracts and show how the actuarial part of their MVHB valuation decomposes into a diversifiable and a non-diversifiable component.     

Fair Terms and Fair Pricing for Multiple Warrant Issues

Abstract

Some firms utilize one or more tranches of warrant issues to supplement their capital base. Unlike exchange-traded options, the exercise of warrants requires the issuance of stock by the company, resulting in a form of dilution. Some previous studies of warrant valuation relied on “the value of the firm,” which is nonobservable, making it difficult to apply the corresponding valuation formula. This paper derives closed-form formulas to value single and multiple tranches of warrants based on the underlying stock price, its volatility, and other known parameter values. The paper first establishes the equivalence of the Black-Scholes formula for both call options and warrants in the case of a single tranche. Thereafter, it considers the impact on the value of previously issued warrants that results when a new tranche of warrants is subsequently issued, showing in each case that fair treatment of the first-issued warrant holders requires an adjustment (due to dilution) in the terms of those warrants and a corresponding modification in the warrants’ value once a second tranche of warrants is issued. To promote such fair treatment, terms of a warrant indenture would specify the nature of the adjustment required when future warrants are issued or exercised, analogous to the antidilution terms related, for example, to stock dividends. Unlike multiple issues of traded options, which are valued independently of one another, multiple warrant issues will be shown to have prices dependent on other warrants outstanding. Also examined is the sensitivity of the fair-value adjustment to changes in the underlying variables, and the theoretical fair-value prices are compared with Black-Scholes prices and with market prices of warrants in the case of two publicly traded companies, each with two warrant issues outstanding. As warrant issues modify the equity structure of a firm, the methodology of valuing warrants presented here will be useful to investment actuaries in situations in which a comprehensive market value for all of a firm’s securities is called for. In addition, risk management practices may sometimes include the use of warrant transactions to hedge stock positions similar to the way that call options are used for that purpose. This may include hedging the risk in equity-linked insurance contracts when the equity position includes stock in companies that have one or more warrant issues that are traded. The methods developed here are also applicable to multiple issues of executive stock options (ESOs) or to combinations of warrant issues and ESOs.     

Managerial shareholding policies and retention of vested equity incentives

Previous literature documents that executives tend to cash out equity incentives when equity-linked compensation vests. Such a behavior destroys long-term incentives and hence is costly to outside shareholders. It is recommended that the unloading of incentives can be limited when the firm adopts a minimum executive shareholding policy. We provide the first evidence of the effectiveness of such policies in that respect. Using data for UK FTSE 350 companies we show that executives whose ownership is below the minimum set by the policy retain more newly vesting equity and the incentives to retain shares weaken when the holdings are above the minimum. We also document economic implications of compliance with the policy and we find higher firm valuations when actual ownership increases relative to the minimum holdings required. Our results have implications for the debate on executive remuneration regulations and practices.     

Incentivizing managers to build innovative firms

We investigate whether the equity-linked components of top executive pay have an effect on patenting activity within a firm. We find a positive relationship between firm patenting activity and managerial alignment incentives created by stock and stock option grants. Prior work has shown that the market value of a firm reflects the value of its patents. Thus, our finding suggests innovation is one such channel through which equity alignment incentives positively impact firm value. On the other hand, we find that the risk-taking incentive from stock options does not increase patenting.     

Hedging Equity-Linked Life Insurance Contracts

Abstract

This paper examines a portfolio of equity-linked life insurance contracts and determines risk-minimizing hedging strategies within a discrete-time setup. As a principal example, I consider the Cox-Ross-Rubinstein model and an equity-linked pure endowment contract under which the policyholder receives max(S_T , K) at time T if he or she is then alive, where S_T is the value of a stock index at the term T of the contract and K is a guarantee stipulated by the contract. In contrast to most of the existing literature, I view the contracts as contingent claims in an incomplete model and discuss the problem of choosing an optimality criterion for hedging strategies. The subsequent analysis leads to a comparison of the risk (measured by the variance of the insurer’s loss) inherent in equity-linked contracts in the two situations where the insurer applies the risk-minimizing strategy and the insurer does not hedge. The paper includes numerical results that can be used to quantify the effect of hedging and describe how this effect varies with the size of the insurance portfolio and assumptions concerning the mortality.     

Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models

Abstract

In this paper we develop a valuation method for equity-linked insurance products. We assume that the premium information of term life insurances, pure endowment insurances, and endowment insurances at all maturities is obtainable within a company or from the insurance market. Using a method similar to that of Jarrow and Turnbull (1995), we derive three martingale probability measures associated with these basic insurance products. These measures are agedependent, include an adjustment for the mortality risk, and reproduce the premiums of the respective insurance products. We then extend the martingale measures to include the financial market information using copulas and use them to evaluate equity-linked insurance contracts and equity-indexed annuities in particular. This is different from the traditional approach under which diversification of mortality risk is assumed. A detailed numerical analysis is performed for various existing equity-indexed annuities in the North American market.     

The Iterated Cte

Abstract

In this paper we present a method for defining a dynamic risk measure from a static risk measure, by backwards iteration. We apply the method to the conditional tail expectation (CTE) risk measure to construct a new, dynamic risk measure, the iterated CTE (ICTE). We show that the ICTE is coherent, consistent, and relevant according to the definitions of Riedel (2003), and we derive formulae for the ICTE for the case where the loss process is lognormal. Finally, we demonstrate the practical implementation of the ICTE to an equity-linked insurance contract with maturity and death benefit guarantees.     

Insider Ownership,Subsidiary Cash Holdings,and Economic Consequences: Evidence from Listed Chinese Companies

ABSTRACT

Using a large sample of listed Chinese companies, we investigate how the equity ownership of business group insiders affects subsidiary cash holdings. We find that ownership by the largest shareholders and senior managers in the listed parent firm is negatively related to its subsidiaries’ cash holdings, whereas there is a positive relationship with minority equity in subsidiaries. We also find that the market places a more significant value discount on listed firms whose cash holdings are more located in the affiliated subsidiaries. Our evidence demonstrates how cash policy inside business groups is influenced by insider ownership, and it reveals to what extent cash allocated in subsidiaries may suffer from losses in efficiency.     

An Approach to Fair Valuation of Insurance Liabilities Using the Firm’s Cost of Capital

Abstract

There are two competing and seemingly different methodologies for calculating fair values—the direct and indirect methods. The direct approach has the advantage of providing a more reliable assessment of the risk of financial leverage. The indirect method can be structured to adjust for financial leverage, however, the methodology becomes excessively complex. The advantage of the indirect method is that it can be more easily related to exit prices. Intuitively, an exit price should reflect both the creditworthiness of the firm and the cost of capital of the firm. How are these two concepts related? This paper attempts to advance the fair valuation methodology by addressing these questions and presenting a methodology for deriving the firm or own credit risk assumption (to be used with the direct method) that is consistent with the cost of capital assumption used with the indirect method.     

Financial reporting and corporate political connections: An analytical model of interactions

We analyze the interactions between accounting institutions and corporate political connections (CPCs). We present a model where a costly policy depends on the perceived economic condition of a firm. This policy and the valuation of the firm by capital market participants create incentives for the firm to manipulate its financial reports. A politician has some discretion over the policy and can use it to favor a connected firm. Our analysis reveals that the firm’s financial reporting is determined by the interplay of an accounting standard, enforcement strictness, and the salience of the policy for the firm. The possibility to manipulate the financial reports imposes an upper boundary on the value of political connectedness which does not exist if only truthful reporting is possible. The reason is that a low credibility of reported figures leads only to a weak revision of the policy. In general, the value of CPCs is highest when the financial reporting regime evenly splits between firms in good and bad economic condition. Our analysis further suggests that while connected firms generally report being in good condition more often than non-connected firms do, the effect of CPCs on absolute reporting manipulation depends on policy salience. If policy salience is low, connected firms exhibit a higher absolute degree of manipulation than non-connected firms do; the opposite holds if policy salience is high.     

Production and hedging implications of executive compensation schemes

This paper connects executive compensation with hedging and analyzes a crucial shareholders and managers agency source that evolves from the pricing of the hedging device. The shareholders are risk-neutral, while the risk-averse manager hedges the price risk of the manufactured quantity, and his compensation package includes equity-linked compensation-stock grants. Only when the hedging instrument's pricing includes a risk premium, hedging is costly to the shareholders, while it is costless to the manager. Then from the owners' point of view, we observe managerial over-hedging, increasing in the equity-linked compensation level. This result leads to a violation of the classical production and hedging separation theorem. We conclude that, in the case where the hedging device's pricing bears a risk premium, shareholders can regulate the corporate value diversion to managers through diminishing the managerial equity-linked compensation scheme or by putting restrictions on the extent of hedging activities of executives.     

The Value Relevance of Equity Method Fair Value Disclosures

We assess the valuation implications of the fair value disclosures made for publicly traded securities accounted for under the equity method. We test the association between investors' stock price metrics and fair value disclosures while controlling for book values on a sample of 172 investor firm-years during 1993–1997. Our results indicate that the information in the fair value disclosures is incremental to the information provided by both an investment's equity method book value and equity method reported income. This suggests that there is nothing unique about investments in publicly traded common stock that involve significant influence that makes the fair value disclosures irrelevant for firm valuation.     

The pricing of equity-linked life insurance policies with an asset value guarantee

This paper considers the equilibrium pricing of equity-linked life insurance policies with an asset value guarantee; such policies provide for benefits which depend upon the performance of a reference portfolio subject to a minimum guaranteed benefit. The benefit is decomposed into a sure amount and an immediately exercisable call option on the reference portfolio. A numerical procedure for determining the value of the call option is presented and the risk minimizing investment strategy to be followed by the issuer of the policy is derived.     

An Out-of-Sample Analysis of Investment Guarantees for Equity-Linked Products

Abstract

In this paper we analyze the risk underlying investment guarantees using 78 different econometric models: GARCH, regime-switching, mixtures, and combinations of these approaches. This extensive set of models is compared with returns observed during the financial crisis in an out-of-sample analysis, bringing a new perspective to the study of equity-linked insurance. We find that despite the very good fit of recent models, too few of them are capable of consistently generating low returns over long periods, which were in fact observed empirically during the financial crisis. Moreover, tail risk measures vary significantly across models, and this emphasizes the importance of model risk. Most insurance companies are now focusing on dynamically hedging their investment guarantees, and so we also investigate the robustness of the Black-Scholes delta hedging strategy. We find that hedging errors can be very large among the top fitting models, implying that model risk must be taken into consideration when hedging investment guarantees.     

A bivariate model for evaluating equity-linked policies with surrender option

This article proposes a bivariate lattice model for evaluating equity-linked policies embedding a surrender option when the underlying equity dynamics is described by a geometric Brownian motion with stochastic interest rate. The main advantage of the model stays in that the original processes for the reference fund and the interest rate are directly discretized by means of lattice approximations, without resorting to any additional transformation. Then, the arising lattices are combined in order to establish a bivariate tree where equity-linked policy premiums are computed by discounting the policy payoff over the lattice branches, and allowing early exercise at each premium payment date to model the surrender decision.     

On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Bühlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.     

Economic Determinants and Information Environment Effects of Earnouts: New Insights from SFAS 141(R)

Contingent considerations (earnouts) in acquisition agreements provide sellers with future payments conditional on meeting certain conditions. Prior research provides evidence that acquiring firms use earnouts to minimize agency costs associated with acquisitions. Using earnout fair value information, recently mandated by SFAS 141(R), we provide new insights into the economic determinants to include earnout provisions in acquisition agreements, including motivations to resolve moral hazard and adverse selection problems, bridge valuation gaps, and retain target firm managers. We document variations in initial earnout fair value estimates and earnout fair value adjustments that correspond with these underlying motivations. We also provide evidence that target managers stay longer with the firm after the acquisition when earnouts are included primarily to retain target managers. Finally, we demonstrate that earnout fair value adjustments required by SFAS 141(R) provide valuable information to market participants and are negatively associated with the likelihood of contemporaneous and future goodwill impairments.     

How should firms selectively hedge? Resolving the selective hedging puzzle

We provide a model of intertemporal hedging consistent with selective hedging, a widespread practice corroborated by recent empirical studies. We argue that the optimal hedge is a value hedge involving total current value of future earnings. More importantly, the hedging decision is independent of risk preferences of the firm or agent. Our closed-form solutions imply several implications for the risk management policy in a firm. In order to lock in profits a hedge increase is recommended in favorable states of nature, while in bad states the firm should decrease the hedge and wait. Our main new empirical implication is that selective hedging should be more prevalent in industries where managers are exposed to convex cash flow structures and are more likely to “value hedge” their exposures.     

Fair Value Accounting and Managers' Hedging Decisions

We conduct two experiments with experienced accountants to investigate how fair value accounting affects managers’ real economic decisions. In experiment 1, we find that participants are more likely to make suboptimal decisions (e.g., forgo economically sound hedging opportunities) when both the economic and fair value accounting impact information is presented than when only the economic impact information is presented, or when both the economic and historical cost accounting impact information is presented. This adverse effect of fair value accounting is more likely when the price volatility of the hedged asset is higher, which is a situation where, paradoxically, hedging is more beneficial. We find that the effect is mediated by participants’ relative considerations of economic factors versus accounting factors (e.g., earnings volatility). Experiment 2 shows that enhancing salience of economic information or separately presenting net income not from fair value remeasurements reduces the adverse effect of fair value accounting. Our findings are informative to standard setters in their debate on the efficacy of fair value accounting.