Academic papers mainly actuarial mathematics and insurance economics
Free Capital book biographical profiles of private investors
Loss Coverage why insurance works better with some adverse selection
Blog very occasional posts, mainly investment strategy (no stock tips!)
This paper considers the pricing of long-term options on assets such as housing, where either government intervention or the economic nature of the asset limits large falls in prices. The observed asset price is modelled by a geometric Brownian motion (“the notional price”) reflected at a lower barrier. The resulting observed price has standard dynamics but with localised intervention at the barrier, which allows arbitrage with interim losses; this is funded by the government’s unlimited powers of intervention, and its exploitation is subject to credit constraints. Despite the lack of an equivalent martingale measure for the observed price, options on this price can be expressed as compound options on the arbitrage-free notional price, to which standard risk-neutral arguments can be applied. Because option deltas tend to zero when the observed price approaches the barrier, hedging with the observed price gives the same results as hedging with the notional price and so exactly replicates option payoffs.
Hedging schemes are not unique, with the cheapest scheme for any derivative being the one which best exploits the interventions at the barrier. The price of a put is clear: direct replication has a lower initial cost than synthetic replication, and the replication portfolio always has positive value. The price of a call is ambiguous: synthetic replication has a lower initial cost than direct replication, but the replication portfolio may give interim losses. So the preferred replication strategy (and hence price) of a call depends on what margin payments need to be made on these losses.
full text Some R Code for Monte Carlo evaluation of the option and demonstration of the associated replication schemes.
When is utilitarian welfare higher under insurance risk pooling?
ABSTRACT: This paper considers the effect of bans on insurance risk classification on utilitarian social welfare. We consider two regimes: full risk classification, where insurers charge the actuarially fair premium for each risk, and pooling, where risk classification is banned and for institutional or regulatory reasons, insurers do not attempt to separate risk classes, but charge a common premium for all risks. For iso-elastic insurance demand, we derive sufficient conditions on higher and lower risks' demand elasticities which ensure that utilitarian social welfare is higher under pooling than under full risk classification. Using the concept of arc elasticity of demand, we extend the results to a form applicable to more general demand functions. Empirical evidence suggests that the required elasticity conditions for social welfare to be increased by a ban may be realistic for some insurance markets. full text
Will genetic test results be monetized in life insurance?
ABSTRACT: If life insurers are not permitted to use genetic test results in underwriting, they may face adverse selection. It is sometimes claimed that applicants will choose abnormally high sums insured as a form of financial gamble, possibly financed by life settlement companies (LSCs). The latter possibility is given some credence by the recent experience of "stranger-originated life insurance" (STOLI) in the United States. We examine these claims, and find them unconvincing for four reasons. First, apparently high mortality implies surprisingly high probabilities of surviving for decades, so the gamble faces long odds. Second, LSCs would have to adopt a different business model, involving much longer time horizons. Third, STOLI is being effectively dealt with by the U.S. courts. Fourth, the gamble would be predicated upon a deep understanding of the genetic epidemiology, which is evolving, subject to uncertain biases, and cannot predict the emergence of effective treatments. full text
Valuation of no-negative-equity guarantees with a lower reflecting barrier
ABSTRACT: If the general level of house prices falls a long way, policymakers may introduce new policies which seek to support prices. This paper considers the effect of such interventions on the valuation of no-negative-equity guarantees (NNEG) in equity release mortgages. I model interventions by a reflecting barrier expressed as a fraction of the current level of house prices. Reflection at the barrier is instantaneous, so the no-arbitrage property is preserved, and hence risk-neutral valuation of NNEG is possible. The reflecting barrier can alternatively be justified as a representation of the different economic nature of the underlying housing (and particularly freehold land) assets in NNEG valuations, compared with the underlying equity assets in many other option valuations. full text Some R Code for Monte Carlo evaluation of the option and demonstration of the associated replication schemes.
Whistleblowing and power: a network perspective
ABSTRACT: This article presents a network perspective on whistleblowing. It considers how whistleblowing affects, and is affected by, the preexisting distribution of power inside and outside an organization, where power is conceptualized as deriving from the network positions of the key actors. The article also highlights four characteristic features of whistleblowing: third-party detriment, local subversion, appeal to central or external power, and reasonable expectation of concern. The feature of local subversion succinctly explains why whistleblowing is difficult. The feature of appeal to central or external power highlights that contrary to the perception of a democratizing phenomenon, whistleblowing tends to redistribute discretion away from local power toward more central power. This suggests a need for caution about institutional measures to promote whistleblowing in contexts where governance is already highly centralized. full text
Why insurers are wrong about adverse selection
ABSTRACT: Insurers typically argue that regulatory limits on their ability to use genetic tests will induce 'adverse selection'; they say that this has disadvantages not just for insurers, but also for society as a whole. I argue that, even on its own terms, this argument is often flawed. From the viewpoint of society as a whole, not all adverse selection is adverse. Limits on genetic discrimination that induce the right amount of adverse selection (but not too much adverse selection) can increase 'loss coverage', and so make insurance work better for society as a whole. full text
Insurance loss coverage and social welfare
ABSTRACT: Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome, both for insurers and for society. However, a social benefit of modest adverse selection is that it can lead to an increase in 'loss coverage', defined as expected losses compensated by insurance for the whole population. We reconcile the concept of loss coverage to a utilitarian concept of social welfare commonly found in the economic literature on risk classification. For iso-elastic insurance demand, ranking risk classification schemes by (observable) loss coverage always give the same ordering as ranking by (unobservable) social welfare. full text
Insurance loss coverage and demand elasticities
ABSTRACT: Restrictions on insurance risk classification may induce adverse selection, which is usually perceived as a bad outcome. We suggest a counter-argument to this perception in circumstances where modest levels of adverse selection lead to an increase in 'loss coverage', defined as expected losses compensated by insurance for the whole population. This happens if the shift in coverage towards higher risks under adverse selection more than offsets the fall in number of individuals insured. The possibility of this outcome depends on insurance demand elasticities for higher and lower risks. We state elasticity conditions which ensure that for any downward-sloping insurance demand functions, loss coverage when all risks are pooled at a common price is higher than under fully risk-differentiated prices. Empirical evidence suggests that these conditions may be realistic for some insurance markets. full text
Insurance loss coverage under restricted risk classification: the case of iso-elastic demand
ABSTRACT: This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection; and 'loss coverage', defned as the expected population losses compensated by insurance. We find that equilibrium premium and adverse selection increase monotonically with demand elasticity, but loss coverage first increases and then decreases. We argue that loss coverage represents the efficacy of insurance for the whole population; and therefore, if demand elasticity is sufficiently low, adverse selection is not always a bad thing. pdf (29 pages)
Loss coverage in insurance markets: why adverse selection is not always a bad thing
ABSTRACT: This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection; and 'loss coverage', defned as the expected population losses compensated by insurance. We find that equilibrium premium and adverse selection increase monotonically with demand elasticity, but loss coverage first increases and then decreases. We argue that loss coverage represents the efficacy of insurance for the whole population; and therefore, if demand elasticity is sufficiently low, adverse selection is not always a bad thing. pdf (17 pages) This paper was awarded a prize In June 2015 by the International Actuarial Association!
Genetics and insurance in the United Kingdom 1995-2010: the rise and fall of "scientific" discrimination
ABSTRACT: Around the millennium there was extensive debate in the United Kingdom of the possible use of predictive genetic tests by insurance companies. Many insurance experts, geneticists and public policymakers appeared to believe that genetic test results would soon become widely used by the insurance industry. This expectation has not been borne out. This article outlines the history of exaggerated perceptions of the significance of genetic test results to insurance, with particular reference to the United Kingdom, suggesting reasons why they arose and also why they have declined. The article concludes with some speculation about how policy on genetics and insurance might develop in future. full text (20 pages)
Non-risk price discrimination in insurance: market outcomes and public policy
ABSTRACT: This paper considers price discrimination in insurance, defined as systematic price variations based on individual customer data but unrelated to those customers' expected losses or other marginal costs (sometimes characterised as 'price optimisation'). An analysis is given of one type of price discrimination, 'inertia pricing', where renewal prices are higher than prices for risk-equivalent new customers. The analysis suggests that the practice intensifies competition, leading to lower aggregate industry profits; customers in aggregate pay lower prices, but not all customers are better off; and the high level of switching between insurers is inefficient for society as a whole. Other forms of price discrimination may be more likely to increase aggregate industry profits. Some public policy issues relating to price discrimination in insurance are outlined, and possible policy responses by regulators are considered. It is suggested that competition will tend to lead to increased price discrimination over time, and that this may undermine public acceptance of traditional justifications for risk-related pricing. pdf (19 pages)
Demand elasticity, risk classification and loss coverage: when can community rating work?
ABSTRACT: This paper investigates the effects of high or low fair-premium demand elasticity in an insurance market where risk classification is restricted. High fair-premium demand elasticity leads to a collapse in loss coverage, with an equilibrium premium close to the risk of the higher risk population. Low fair-premium demand elasticity leads to an equilibrium premium close to the risk of the lower risk population, and high loss coverage - possibly higher than under more complete risk classification. The elasticity parameters which are required to generate a collapse in coverage in the model in this paper appear higher than the values for demand elasticity which have been estimated in several empirical studies of various insurance markets. This offers a possible explanation of why some insurance markets appear to operate reasonably well under community rating, without the collapse in coverage which insurance folklore suggests. pdf (25 pages)
Loss coverage as a public policy objective for risk classification schemes
This paper suggests that from a public policy perspective, some degree of adverse selection may be desirable in
some insurance markets. The paper suggests that a public policymaker should consider the criterion of 'loss coverage', and
that in some markets a policymaker may wish to regulate risk classification with a view to increasing loss coverage.
Either too much or too little risk classification may reduce loss coverage. The concept is explored by means of examples,
formulaic and graphical interpretations. An application to the UK life insurance market is considered.
pdf (22 pages)         Powerpoint (46 pages)
On the value of not taking advice
ABSTRACT: Conventional wisdom commonly exhorts non-experts to take expert advice when dealing with specialist fields. This works well in relation to the physical or biological world, because theories of these worlds are generally neutral: popular acceptance of a theory does not change the phenomena it describes. In contrast, theories of social phenomena such as finance are often reflexive: popular acceptance of a theory does change the phenomena it describes. Reflexive theories can be either self-fulfilling or self-negating. Advice based on self-negating theories is not likely to be useful. Expert advice is therefore less useful in fields such as investment, which are dominated by self-negating theories. pdf (9 pages)
Taxable and tax-advantaged portfolio management for UK personal investors
This paper makes some observations on the interaction of United Kingdom taxation and portfolio decisions by a
personal investor managing his own investments in quoted company shares. I consider five holding vehicles: three
types of tax-advantaged account (ISAs, SIPPs, and spread bets); and two types of taxable account (a company
controlled by the investor, and direct holdings in the investor's personal account). I note some ways in which portfolio
management for a taxable account differs from management of a tax-advantaged account. I use simple models to
illustrate the difficulty of producing post-tax out-performance from active management of a taxable account. I suggest
some heuristic guidelines for allocating different types of investments across the five types of accounts. I also provide
some guidance for decisions on switching between investments in a taxable account. I note several quirks in the CGT
legislation which are useful for the active personal investor to know. Readers who want to read just results should go
directly to sections 9 to 11 of the paper.
full version (46 pages) or published version (23 pages) (updated for April 2008 changes).
Some novel perspectives on risk classification
ABSTRACT: This paper considers a number of novel perspectives on risk classification, primarily in the context of life and critical illness insurance. I suggest that the terminology of "adverse selection" is often misleading, because from a public policy viewpoint adverse selection may not always be adverse. I suggest that public policymakers should consider the criterion of "loss coverage," and that in many markets a socially optimal level of adverse selection is that which maximises loss coverage. A review of empirical studies suggests that adverse selection is often difficult to observe in practice; this leads to the concept of propitious selection, and various psychological perspectives on risk classification. I suggest that competition between insurers in risk classification can sometimes be characterised as a malevolent invisible hand, and that public policy should direct competition towards areas which are more clearly beneficial to all insurance customers. I also consider the perspectives of risk classification as blame, the conflict between risk classification and human rights, and the fallacy of the one-shot gambler. pdf (28 pages)
An earlier version pdf (28 pages) presented at DIW Berlin in June 2005 included graphs of market prices.Accident compensation: compensation culture? No! Justice culture.
ABSTRACT: The Actuarial Profession in the UK has a policy (as explained on its website here) of campaigning against what it calls the "compensation culture." This involves the Profession in making various insinuations against accident victims - for example, that it is in some way blameworthy if accident victims receive compensation for negligence; or that the costs of such compensation are excessive, or rapidly increasing, or otherwise unjustifiable.
I believe that this campaign is inconsistent with the data on accident compensation in the UK, which show the costs of accident compensation to be lower than in almost all other industrialised countries.
Morris Review of the actuarial profession
ABSTRACT: My response to the Interim Report of the Morris Review, focusing on actuarial research. pdf (3pages)Pricing zero-dividend preference shares
ABSTRACT: Zero-dividend preference shares (zdps) are the simplest type of security issued by UK investment trusts (closed-end funds). Zdps have option-like properties, but there sometimes seems to be little awareness in the investment trust world of option pricing concepts. This three-page working note makes some rudimentary observations on the factors which should affect zdps prices. pdf (3 pages)Genetics and insurance: further notes to the Human Genetics Commission
ABSTRACT: An examination of actual premium rates suggests large variations for identical insurance covers, both between companies and over time. In this context, the impact on insurance markets of outlawing access to genetic tests is likely to be very small. pdf (7 pages)Genetics and insurance: an actuarial perspective with a difference
ABSTRACT: This is a response to a public consultation by the Human Genetics Commission (HGC) in Februry 2001; a revised version was given to the International Congress of Actuaries in Mexico in March 2002. Many individuals or organisations capable of commenting technically on insurance discrimination have a commercial interest in promoting such discrimination. Technical expertise is therefore directed to the promotion of discrimination for commercial ends, but little technical expertise is applied to counteract it. This paper attempts to redress the balance. Its central section comprises a point-by-point rebuttal of some of the myths and half-truths which are promulgated by those wishing to legitimise insurers' access to genetic test results.HGC version pdf (15 pages) or ICA version pdf (17 pages)A non-linear stochastic asset model for actuarial use ( with SP Whitten)
ABSTRACT: This paper reviews the stochastic asset model described in Wilkie (1995) and previous work on refining this model. The paper then considers the application of non-linear modelling to investment series, considering both ARCH techniques and threshold modelling. The paper suggests a threshold autoregressive (TAR) system as a useful progression from the Wilkie (1995) model. The authors are making available (by email, on request) a collection of spreadsheets, which they have used to simulate the stochastic asset models which are considered in this paper.pdf (33 pages) This paper was awarded a prize by the Institute of Actuaries!Positive theory and actuarial practice (with AD Smith)
ABSTRACT: Most of the extant theory which is used to justify actuarial practice is normative. This short paper proposes a positive approach to explaining actuarial practice, explains how this differs from a normative approach, and highlights the importance of the "market for excuses." pdf (5 pages)Actuarial values (with CD Sharp)
ABSTRACT: This paper seeks to identify the characteristic values implicit in contemporary actuarial thought and practice. 'Values' is used here to mean fundamental concepts which we use, largely intuitively, to guide our patterns of thought and behaviour. We consider to what extent these values are characteristic simply because actuarial work attracts individuals who already subscribe to them, and to what extent these values may be inculcated by actuarial training. We then consider whether the characteristic values we have identified are congruent with the changing values of wider society, and whether they are likely to be conducive to the continuing success of the profession in the 21st century. pdf (16 pages)The right to underwrite? An actuarial perspective with a difference (with TA Moultrie)
ABSTRACT: For a very long time, underwriting has formed part of the actuarial canon. With increasing frequency, challenges are being issued against the right of insurance companies to underwrite their applications for new business, arguing that certain aspects of the practice are undesirably discriminatory. This paper explores the role of the actuary in the underwriting process, and the challenges that are being set for the profession (as opposed to the life insurance industry) as a result of this role. pdf (12 pages)Indemnities for long term price risk in the UK housing market
ABSTRACT: Discusses the features which distinguish the market for residential property from the markets for other assets. Proposes that financial institutions should offer house buyers indemnity policies which pay out an amount related to any fall in the level of a general index of house prices, on the sale of the house at a loss at any time during the mortgage term. To facilitate hedging the risk of a portfolio of such policies (and therefore, the pricing of the policies), a market in 'perpetual futures' on indices of housing assets is proposed. Discuss possible users of these contracts, and outlines further research. pdf (17pages )loss coverage blog no negative equity guarantees. guy thomas, no negative equity guarantee