Derivatives and Market Consistent Valuation

It was while I was at Black Horse Life (1990-98) that I taught myself all the underlying theory behind derivatives.  I monitored the use of derivatives within Black Horse Life’s unit linked funds and Lloyds Bank Unit Trust Managers’ unit funds, checking in each case for compliance with all the legal requirements for the use of derivatives.  I built spreadsheet models to independently price all the (American and European) equity options that were held within the unit trusts – I would typically derive implied volatilities from the counterparties’ quoted prices and challenge the counterparty whenever these looked out of line with recent volatility smiles. I provided advice to the actuaries responsible for developing unit trusts with investment guarantees.

At Gen Re (1999-2000) I acted as the link between the reinsurer and the derivative house (Gen Re Financial Products, GRFP).  I used my knowledge of life insurance and of derivatives to support GRFP in selling derivatives to life insurers.  Most of our sales pitches concerned the use of swaptions to hedge guaranteed annuity options, but we also discussed the use of swaps to help maximise investment returns on assets backing annuities.  I also spent a month on secondment to GRFP trading swaps with client firms.

At PwC (2000-06) my knowledge of derivative pricing theory and my experiences at GRFP left me well placed to become the practice’s subject matter expert and a recognised industry expert on market consistent valuation.  I developed an approach to auditing market consistent economic scenario generators that was quickly adopted by the life insurance practice.  I was also the practice’s subject matter expert on the use of derivatives by life insurers, frequently asked to review firms’ derivative strategies and to explain them to my colleagues.  I invested a lot of time in training the whole life insurance practice to understand derivatives, market consistent valuation and economic scenario generators.  This training was essential to the practice: the whole industry urgently needed to learn about market consistent valuation.

In 2004, the Actuarial Profession identified the need to provide a course and exam on financial economics for those actuaries looking to increase their knowledge of a number of topics that had only recently been incorporated into the actuarial exams.  A committee was appointed to develop the course and, after the first couple of meetings, identified the need for a derivative expert to join the team.  So I was invited to join and contributed all the course material on derivatives.  I was a member of the team of examiners for the first Certificate in Practical Financial Economics exam in 2005 and chief examiner in 2006 and 2007.

At Prudential (2008-2010) everything came together.  The firm had decided that it needed to hedge some of the equity risk within the with profits fund and that, rather than buying options, it would delta hedge using futures.  I separated the problem into choosing a “benchmark option” and then delta hedging the benchmark option.
• To help senior management choose an appropriate benchmark option, I developed the concept of “solvency frontiers”.  The only data I had available was the impact on the fund’s solvency of a number of stresses to interest rates and/or equity prices.  I built a spreadsheet that would extrapolate these figures all over a two-dimensional plane with the FTSE and a particular interest rate as the axes.  I then allowed the spreadsheet user to specify a “benchmark option” and coded the spreadsheet to adjust the solvency levels all over the plane to allow for the payoffs from the option.  Finally, I coded the spreadsheet to output a graph with a single line on it: the solvency frontier, below which the fund would not cover its capital requirements.  I then used the spreadsheet to derive the benchmark option that would result in a solvency frontier lying in a position that senior management were comfortable with.  The position of the solvency frontier and the choice of benchmark option were reviewed on a regular basis.
• I agreed delta hedging procedures with the fund managers: we developed spreadsheets independently and, by using these independently, reduced some operational risks.  I developed a spreadsheet that would separate the profit/loss from futures into (i) the profit/loss that would have arisen from buying the benchmark option, and (ii) the profit/loss arising from the decision to delta hedge rather than buying the option.  I also broke down the delta hedging profit/loss into the separate mismatches for the key Greeks.  Despite the decision having already been made to delta hedge, I was also careful to explain to senior management the extra risks that this introduced.

In 2009, I was asked to join the team of examiners for ST6, the Actuarial Profession’s derivative exam. I served on the team for five years, contributing about 40% of the exam questions for the 2010-14 sittings.  As well as setting exams the team was responsible for updating course material when this was thought to be necessary: I updated all the course material on securitisations.

With the FSA and PRA (2010-14) derivative-related issues would occasionally arise, e.g. discussing firms’ use of derivatives, reviewing market consistent numbers in Pillar 2 balance sheets, needing to understand a bulk annuity provider’s use of swaps (and their impact on the valuation interest rate).

As a contractor, I reviewed the methodologies and assumptions used by a bulk annuity provider within their mark to model valuations of certain unlisted assets.  These included a bond with LPI linked coupons and a number of bonds where the issuer had the option to repay at specified prices.  An understanding of derivative pricing was essential within the review.

While the industry has taken huge steps forward in this area, I still can’t help feeling that the issue of sampling error hasn’t been given the attention it deserves.  I’m keen to help firms to calculate confidence intervals for all stochastically derived numbers and to show them how to use variance reduction techniques (like control variate technique) to narrow them down to a width that they are comfortable with.