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The Inflation Derivative Toolbox - Part II

Project finance or long-term rental agreements often involve fees that are fixed at a certain real level over the life of the trade: the annual payment is a fixed amount adjusted by the cumulative inflation since trade inception.


Real Annuities

Project finance or long-term rental agreements often involve fees that are fixed at a certain real level over the life of the trade: the annual payment is a fixed amount adjusted by the cumulative inflation since trade inception. Such exposures can be hedged by a real annuity swap, such as that demonstrated in Box 3. Here, the annuity (perhaps a rental income or annual management fee) is increased by an amount that mirrors cumulative inflation since trade inception. The increase is swapped into a fixed, average uplift over the life of the whole trade. Again, the important parameters to note are the index definition and the times of measurement of the index. Such structures are also useful on the demand side of the business: liability managers may have a requirement to hedge the opposite type of exposure to their clients.

Real-Coupon Swaps

For the client who needs a swap of the real yield to fixed or floating, the best solution is to mirror the design of the Canadian model inflation-linked bond. The index-linked cash-flow is similar to the real annuity: a fixed coupon uplifted from a given base to the current level of price indexation. Box 4 shows an example. The end pickup recognizes the inflation uplift of the notional principal. This structure is the basis of most asset swap deals or of new-issue hedges.

It is relatively easy to imagine additional details could be added to any of the basic structures: amortisation, stepped coupons and irregular payment schedules are all quite common and fairly trivial to incorporate into a standard structure. Somewhat more dramatic are unusual choices of index or the introduction of optionality.


For many participants, it makes sense to choose an index other than those standard in the bond market. It will often be the case that a particular asset or liability is indexed to something other than the common CPI. For example, pension liabilities in the U.S. may be linked to a myriad of local and state-specific price or wage indices. Likewise, retail banks in Europe will generally prefer to market products dependent on a domestic price index rather than euro-wide HICP. For that reason, there are active swap markets in Spanish and Italian CPI, although no sovereign bonds exist linked to these indices.

Swap trades linked to specific exposures may make perfect sense for clients, but they create headaches for dealers, who must take unhedgeable risks on the correlations between these non-standard indices and the tradable instruments. The lack of liquidity and the risks involved in the trades may lead dealers to price conservatively and users should balance this consideration against the perceived benefits of a more exact hedge.

Optionality in various guises is an increasingly popular enhancement to the standard toolkit. The most basic example is the 0% floor on a year-on-year swap. Thus the inflation payoff in Box 3 becomes:


Party B pays:



Indeed, such an enhancement is now quite standard for the year-on-year structure. Even with today's relatively low inflation environment, such an option is far out of the money, at least in the principal markets. Nonetheless, demand for protection heavily outweighs supply, meaning that by some measures prices for these floors can seem expensive.

The phrase by some measures may betray some hint of the major difficulty surrounding the embryonic inflation option market. At the moment, there is no universally accepted method of pricing, and more importantly no visible market in which to calibrate the important inputs such as volatility. Additionally, the pricing of inflation options involves subtleties, such as the relationship between the inflation rate and the discount rate which are poorly understood. Nonetheless, products such as swaptions and near-the-money caps and floors are being priced with increasing frequency, usually from historical volatility levels. Increased usage will no doubt increase the transparency and liquidity of the market.



Prospects for growth in the derivatives market are good. Issuance is well supported in all three major bond markets, with the U.S. in particular committing to a huge volume of index-linked borrowing in the coming years. Also noteworthy is Germany's expected entry to the market in the first quarter of next year. Demand continues to grow, with pension funds and retail business in particular remaining eager buyers. As prices tighten and volumes increase, we can expect new participants to become involved, including more hedge funds. The growth phase of this product is by no means over.

This week's Learning Curve was written by Joe Mulvey, a senior trader in European inflation derivatives at Barclays Capital in London.

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