Guy Thomas has an interesting post (‘No-negative-equity guarantees: Black-Scholes and its discontents’, guythomas.org.uk, Thursday 06 September 2018), arguing that the use of the Black-Scholes formula in the context of valuing the no-negative-equity guarantee (NNEG) in equity release mortgages, is flawed in ways that are more fundamental than the PRA blandly suggests.
You can read his article for yourself, but his key points are (1) that the Black-Scholes argument depends crucially on the idea of dynamic hedging and arbitrage, which is not met in the case of housing assets, and ‘is simply not possible in any shape or form’; (2) that Black-Scholes assumes when constructing the dynamic hedge that the underlying asset follows a geometric Brownian motion; (3) that there is no meaningful market in deferment prices [sic] over the periods of 20-40 years most relevant to NNEGs, and furthermore a deferred interest might well be more attractive, particularly if in the form of cash-settled financial contracts, so that all the problems of current interests (nasty tenants, management costs, legal risk etc) are permanently avoided.
Let’s look at these arguments carefully.