Some comments on the paper “What is fair? Proxy discrimination vs. demographic disparities in insurance pricing”

This blog first makes a brief comment on an interesting recent paper by Mathias Lindholm, Ronald Richman, Andreas Tsanakas and Mario Wüthrich. I then expand on two points tangential to their paper: non-risk price discrimination, which they touched on in their concluding comments by referencing a previous discussion note from me; and loss coverage, which … Read more

Option prices, margin requirements and Schelling points

My paper Long-term option pricing with a lower reflecting barrier has just been published by Annals of Actuarial Science. This post gives background context, and touches on some points not covered in the paper. Motivation The intended application is pricing of options over “actuarial” timescales – at least one decade, and typically two or three. … Read more

Valuation of no-negative-equity guarantees with a lower reflecting barrier

This draft paper develops some of the thoughts in my earliest blog post on NNEG valuation.  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 … Read more

Fractional shares and dodgy pie charts

TLDR: When fractional shares (revenue by product, market shares by company, or similar quantities) are ranked and grouped in buckets, any ratio of successive bucket means >0.5 is suspect. ————– Listening to this interview with John Hempton reminded me of his forensic scepticism about the following pie chart, taken from an investor presentation about the pharma company Valeant. John wrote (in 2014, when … Read more

NNEG: Rental yields versus imputed yields

My Kent colleague Radu Tunaru’s recent report for the Institute and Faculty of Actuaries (IFoA) on valuation of no negative equity guarantees was discussed at a meeting at Staple Inn last Thursday.  A controversial element was the adjusted rental yield calculation of 0.2 x 5% = 1%, where 5% is the observed gross yield on rented properties and 0.2 … Read more

Black-Scholes: my “Buffett mistakes”

A confession: I am the actuary who disagreed with this post by Dean Buckner, a former PRA official, which asserts that the Black-Scholes formula gives a good valuation of an option under the assumption of mean reversion in prices. In a follow-up post he said my critique was “ingenious” but “wrong” and that it was similar to … Read more

Black-Scholes: a navigational analogy

My previous post presumed some understanding not just of the Black-Scholes formula, but also of its derivation; in particular, of the hedging argument whereby the drift in the underlying asset can be ignored. My likely readers at this blog probably do understand this, but some other commentators may not. How to explain?  Here, with some trepidation, is … Read more

No-negative-equity guarantees: Black-Scholes and its discontents

The Prudential Regulation Authority (PRA) has issued a consultation paper CP13-18 on valuation of the no-negative-equity guarantee (NNEG) in equity release mortgages.  I think the use of the Black-Scholes formula in this context is flawed, in ways which are more fundamental than suggested by the PRA’s rather bland observation that “some of the assumptions that allow the mathematical … Read more