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The Actuary The magazine of the Institute & Faculty of Actuaries

Paying LPI service to market prices

Robin Thompson and Andrew Kenyon look at how liabilities linked to Limited Price Indexation can create risk


Liabilities linked to Limited Price Indexation (LPI) are common in pension schemes, as well as being transferred to insurance companies in increasing volume via the bulk annuity market. 

LPI presents a risk management challenge, though, because of increasing constraints in the supply of LPI-linked assets.

With limited LPI-linked debt issuance and all but a very small number of banks having withdrawn from the LPI swap market, this is particularly concerning for insurers needing to minimise their Solvency II capital requirements levied against asset-liability mismatches, where capital consumption can be a key distinguishing factor in the competitiveness of new business pricing.

Market dynamics 

The LPI spread to RPI – reflecting the ‘premium’ paid to acquire the cap/floor – implies that the underlying RPI distribution exhibits a strong negative skew, that is, a higher probability of extreme deflationary events than extreme inflationary events. Whilst historic RPI analysis does exhibit some skew – largely driven by events in the aftermath of the 2008 financial crisis – it is far less pronounced than LPI pricing might imply, suggesting that demand for the floor (or lack of supply) has driven prices upward.

Since 2012 (post the Consumer Prices Advisory Committee’s consultation which rejected proposed changes to the calculation method for RPI), spreads have widened every year since 2013, corresponding directly with the perceived reduction in market liquidity:

Chart 1

Risk management

Some exposures – like property market prices – can only be managed by proxy due to the lack of a functioning market in appropriate 

hedging instruments. For LPI, though, it is possible to trade RPI in a liquid swaps market or through (predominantly government-issued) RPI-linked bonds.

For many, ‘delta hedging’ LPI exposures using a combination of fixed-rate and inflation-linked instruments has become the natural substitute for scarce LPI-linked assets, making reference to an appropriate ‘real-world’ inflation model in the absence of a functioning market to mark-to.

In a functioning market, these delta values can be derived from market prices. If a liquid market does not exist, an appropriate ‘real-world’ model is required to allow us to delta-hedge our exposures.

Chart 2

Modelling considerations

Many pension schemes already make an adjustment to reduce their liabilities by removing the effect of skew – often using the Black-Scholes model to value LPI within their accounting and technical provisions bases. Adjustments like this result in a stronger balance sheet position, and some of those gains can be realised through the sale of existing LPI-linked hedging instruments:

Unlike market-consistent, risk-neutral valuations, real-world models require expert judgment to be employed in their calibration and use (see table 1). In particular:

  •  How much skew to retain
  •  Size of the distribution’s tails
  •  Correlation between real and nominal interest rates
  •  Whether the model retains the ability to converge with market prices should liquidity improve
  •  Existence of a closed-form proxy to provide pricing/valuations quickly


Insurers may also want to be able to generate scenarios covering extreme and prolonged periods of high or low inflation when calibrating capital requirements.

Table 1

What is LPI?

LPI covers the class of indexation where increases/decreases are linked to RPI (Retail Price Indexation) but subject to a maximum (cap) and/or minimum (floor) amount. LPI(0,5) – 0% floor, 5% cap – LPI(0,3) and LPI(0,∞) are all popular variants. Less frequently, the underlying inflation might be CPI.

In the early to mid-2000s, LPI supply was often derived from commercial property leases. The freeholder – often a company within a group set up purely to purchase premises leased to operating entities – made the assumption that rental income would increase in-line with RPI, subject to a cap and a floor. To increase certainty, these flows were swapped with a bank (often to receive fixed). 

In practice, though, reviews saw rents move in sympathy with market supply and demand dynamics, often with little correlation to inflation. Corporates found themselves without a natural stream of LPI cash flows to pay down their leg of the swap, combined with the ‘perfect storm’ of falling property prices and interest rates in the aftermath of the 2008 Financial Crisis.

Delta hedging

The ‘delta’ of a derivative is defined as the rate of change in the value of that derivative following a change in the value of the underlying instrument. For an equity option on a particular stock, the underlying would be the price of the stock. For LPI derivatives, the underlying is RPI.

Delta hedging refers to the process of constructing a portfolio of instruments so that the aggregate delta of the portfolio equals that of the derivative you are trying to replicate.

For a typical LPI(0,5) exposure, the actual indexation incurred is dependent on where RPI prints. At that point in time: If RPI < 0, no indexation occurs and the replicating portfolio needs to be made up of fixed income assets.

If 0 < RPI < 5, then liabilities inflate in-line with RPI, and the portfolio should be RPI-linked.

If RPI > 5, fixed indexation occurs at a rate of 5% per annum. Again, the portfolio needs to be made up of fixed income assets. In the time before the RPI print occurs, there is a chance the required indexation could be fixed or it could be in-line with RPI. The delta reflects this and requires us to allocate a portfolio that has a proportion of fixed and RPI-linked assets dependent on the distance from the bound and time to expiry. 

Dr Robin Thompson, NatWest Markets

Andrew Kenyon FIA, NatWest Markets