Some extraordinary developments this week including the resignation of Simon Thomas as Chief Financial Officer of Just Group, and the somewhat stormy presentation by Kevin Dowd and myself at the LSE. I shall comment on the latter tomorrow, today I shall discuss the Institute of Actuaries’ response to CP 13/18.
The paper is signed by the IFoA president, Jules Constantinou, but it seems to have been the work of the anonymous Equity Release Working Party. We can only guess at the make up of the Party, and of the ‘Joint Review board’ which is supervising a further independent discussion paper. Yet the introductory section states ‘We [the Institute] strive to act in the public interest by speaking out on issues where actuaries have the expertise to provide analysis and insight on public policy issues’. If in the public interest, why is the composition of the Working Party such a closely guarded secret?
There are three lines taken in the paper. First, that the proposals could have an adverse impact on the supply of equity release mortgages to consumers. Second, that the point of transitional arrangements was for firms to have an orderly transition to the Solvency II regime, yet the PRA is now waiving these arrangements for equity release products. I will not comment on these points today. The third point I shall deal with now. Movements in a house price index are autocorrelated, which supposedly invalidates the use of the Black Scholes framework.
Under geometric Brownian motion the volatility increases with the square root of time while for other models it does not; the value for long term derivatives such as NNEG could materially differ from that assumed under the Black-Scholes model.
I shall deal with the third point now, because the response shows such a profound misunderstanding both of practical options pricing, and of the detail of CP 13/18, the paper it is supposed to be replying to.
When we are taught options theory, we told that the derivation of the Black Scholes depends on a a number of assumptions. This section of the Wikipedia article ‘Black Scholes’ fairly represents the standard textbook approach. Prices must follow a lognormal distribution, they must be random, no arbitrage opportunity, short selling possible etc. These are all sufficient conditions for the derivation to hold. However, it is well known to options practitioners that most if all of these conditions can be relaxed: they are sufficient, but not necessary. Black Scholes calculates the value of hedging the option by replicating it with linear instruments. It is completely unnecessary, for example, that the price series is random. I can replicate an option on a lognormally distributed price series which has been sorted in order of magnitude, i.e. largest price fall first, followed by next largest, continuing through to smaller falls, then to positive rises right through to the largest price rise. Completely non-random, yet an option on the final price in this series can still be replicated, so long as we can accurately forecast the volatility of the series. In the coming weeks, I shall give more examples of price series which in no way reflect the classic Black Scholes assumptions.
The Institute also fails to understand the key points of CP 13/18 which in no way depend on the textbook assumptions of Black Scholes. Principle II states that a rational investor would value an ERM (expiring at time t) less than either the present value of the loan (which is obvious) and the present value of deferred possession. Thus the two curves in the chart above represent an upper bound on the value of the ERM, and a lower bound on the value of the NNEG. It is irrelevant whether the property price series is random, log normal, autocorrelated or not. If you deny this upper bound, you are biting on granite.
As Kevin commented in his presentation last night, the failure by actuaries to adopt the latest (i.e. post 1950s) developments in financial economics and financial markets was the result of entrenched commercial interests. This was supposed to have been corrected after the Morris Review in 2005. Yet the Institute has just published a paper that (a) shows complete ignorance of developments in financial economics and (b) is almost certainly the product of entrenched commercial interests. I rest my case.