Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model

Jarrow, Robert A.; Yıldırım, Yıldıray

doi:10.2307/4126754

Cited by 167 publications

(34 citation statements)

References 22 publications

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“…Because of the inflation adjustment, the coupon paid at 8 Kerkhof (2005) provides an excellent introduction to the inflation swap market. Also, see Jarrow and Yildirim (2003) and Hinnerich (2008). Fleckenstein (2012) extends our analysis to other inflation-linked bond markets including the United Kingdom.…”

Section: The Arbitrage Strategymentioning

confidence: 67%

The TIPS‐Treasury Bond Puzzle

Fleckenstein¹,

Longstaff²,

Lustig

2014

The Journal of Finance

226

145

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We show that the price of a Treasury bond and an inflation‐swapped Treasury Inflation‐Protected Securities (TIPS) issue exactly replicating the cash flows of the Treasury bond can differ by more than $20 per $100 notional. Treasury bonds are almost always overvalued relative to TIPS. Total TIPS‐Treasury mispricing has exceeded $56 billion, representing nearly 8% of the total amount of TIPS outstanding. We find direct evidence that the mispricing narrows as additional capital flows into the markets. This provides strong support for the slow‐moving‐capital explanation of arbitrage persistence.

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Section: The Arbitrage Strategymentioning

confidence: 67%

The TIPS‐Treasury Bond Puzzle

Fleckenstein¹,

Longstaff²,

Lustig

2014

The Journal of Finance

226

145

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show abstract

“…This will be relevant in Section 4 when we calibrate some specific rational pricing models. Jarrow and Yildirim (2003) produce an important generalization that allows for the pricing of inflation-linked securities with stochastic interest rates. In practice, the popular model specification is to assume that the nominal and the real interest rates have Hull-White dynamics.…”

Section: Comparison With Other Modelsmentioning

confidence: 99%

“…In Section 2 we first present the model in full generality and demonstrate the measure changes and the models' relation to the Jarrow and Yildirim (2003) framework. In Section 3 we derive option pricing formulae under different assumptions in the driving process, and in Section 4 we end with an example that shows how the model can be simultaneously calibrated to inflation derivatives and to a multiple-curve nominal market.…”

Section: Introductionmentioning

confidence: 99%

Rational Models for Inflation-Linked Derivatives

et al. 2018

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We construct models for the pricing and risk management of inflation-linked derivatives. The model is rational in the sense that affine payoffs written on the consumer price index have prices that are rational functions of the state variables. The nominal pricing kernel is constructed in a multiplicative manner that allows for closed-form pricing of vanilla inflation products suchlike zero-coupon swaps, caps and floors, year-on-year swaps, caps and floors, and the exotic limited price index swap. The model retains the attractive features of a nominal multi-curve interest rate model such as closed-form pricing of nominal swaptions. We conclude with examples of how the model can be calibrated to EUR data. for inflation-linked bonds. These bonds are typically government-issued debt where the principal is indexed by the consumer price index (CPI) or similar. The bonds often have an embedded YoY floor protecting the principal from being adjusted down by deflation. Finally, Limited Price Index (LPI) products come with both a lower and upper bound on the adjustment on the principal creating a path-dependent collar on inflation. Despite its exotic nature LPIs have been in high demand by pension funds.All products should ideally be priced in a consistent manner using a tractable arbitragefree model. Cap/floor products naturally display volatility skews and non-flat term structures of volatility, both of which the model also should be able to capture. In addition, the model should yield closed-form solutions for the price of the most traded derivatives, here the YoY and the ZC cap/floor. Hughston (1998) develops a general arbitrage-free theory of interest rates and inflation in the case where the consumer price index and the real and nominal interest rate systems are jointly driven by a multi-dimensional Brownian motion. This approach is based on a foreign exchange analogy in which the CPI is treated like a foreign exchange rate, and the "real" interest rate system is treated as if it were the foreign interest rate system associated with the foreign currency. The often cited work by Jarrow and Yildirim (2003) makes use of such a setup and considers a three factor model (i.e., driven by three Brownian motions) in which the CPI is modelled as a geometric Brownian motion, with deterministic timedependent volatility, and the two interest rate systems are treated as extended Vasicek-type (or Hull-White) models. Similar to Jarrow and Yildirim (2003), Dodgson and Kainth (2006) use a short-rate approach where the nominal and the inflation rates are both modelled by Hull-White processes while they discard entirely the idea of a real economy. A GBM-based model for the CPI provides the baseline framework for how one might understand implied volatility in such a market, but any GBM model for the CPI does not, by construction, reproduce volatility smiles.Further development of inflation models has paralleled that of interest rates models. For example inflation counterparts to the nominal LIBOR Market Model, see for example Brigo and Me...

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“…Real prices (inflation adjusted) correspond to prices in foreign currency, whereas nominal prices correspond to domestic prices in local currency, and the CPI corresponds to the spot exchange rate and follows a lognormal process. Jarrow and Yildirim (2003) compute the price of CPI options when both the real and nominal term structures are stochastic by using a three factor model following Heath, Jarrow, and Morton (1992). In their model, the price level process is exogenous and follows a log-normal distribution.…”

Section: Inflation Derivative Pricingmentioning

confidence: 99%

Inflation Derivatives Under Inflation Target Regimes

Avriel

Hilscher

Raviv

2012

Journal of Futures Markets

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Inflation targeting—the central bank practice of attempting to keep inflation levels within fixed bounds around a quantitative target—has been adopted by more than 20 economies. Such practice has an important impact on the stochastic nature of inflation and, consequently, on the pricing of inflation derivatives. We develop a flexible model of inflation targeting in which the central bank's intervention to steer inflation toward the target depends on past deviations and the policymaker's ability and will to enforce the target. We use our model to price inflation derivatives and demonstrate the impact of inflation targeting on derivative pricing.

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Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model

Cited by 167 publications

References 22 publications

The TIPS‐Treasury Bond Puzzle

The TIPS‐Treasury Bond Puzzle

Rational Models for Inflation-Linked Derivatives

Inflation Derivatives Under Inflation Target Regimes

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