A Quadratic Gaussian Year-on-Year Inflation Model

Gretarsson, Hringur

doi:10.2139/ssrn.2274034

Cited by 2 publications

(3 citation statements)

References 29 publications

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“…There is enough flexibility in the b \mathrm{ (t) function to fit the YoY swap rates without error, but direct calibration results in a quite volatile b \mathrm{ (t) function, which is hardly desirable. Therefore we instead fit an eight-knot Hermite polynomial with a nonsmoothness penalty---a similar choice is made in [18]---and we find that the loss of accuracy when doing this is insignificant. The flexible shape means that the correlation parameter b and volatility parameter a \mathrm{ in practice cannot be identified simultaneously with b \mathrm{ (t) from the YoY swap curve.…”

Section: H T Dam a Macrina D Skovmand And D Slothmentioning

confidence: 99%

“…While these models can reproduce smiles---augmented with stochastic volatility or jumps---they rely on numerically intensive algorithms or approximations for the pricing of ZC cap/floors, in particular. One may say similarly of the models in [29], [18], and [37], which, in a similar manner use forward inflation, or in the case of [20], the forward inflation swap rate, as the model primitive. [47] builds an inflation counterpart to the nominal model of [16] and [28].…”

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confidence: 99%

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Rational Models for Inflation-Linked Derivatives

Dam¹,

Macrina²,

Skovmand³

et al. 2020

SIAM J. Finan. Math.

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We construct models for the pricing and risk management of inflation-linked derivatives. The models are rational in the sense that linear 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, year-on-year swaps, caps and floors, and the exotic limited-price-index swap. We study the conditions necessary for the multiplicative nominal pricing kernel to give rise to short rate models for the nominal interest rate process. The proposed class of pricing kernel models retains the attractive features of a nominal multicurve interest rate model, such as closed-form pricing of nominal swaptions, and it isolates the so-called inflation convexity-adjustment term arising from the covariance between the underlying stochastic drivers. We conclude with examples of how the model can be calibrated to EUR data.

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Section: H T Dam a Macrina D Skovmand And D Slothmentioning

confidence: 99%

mentioning

confidence: 99%

Rational Models for Inflation-Linked Derivatives

Dam¹,

Macrina²,

Skovmand³

et al. 2020

SIAM J. Finan. Math.

View full text Add to dashboard Cite

show abstract

“…While these models can reproduce smiles-augmented with stochastic volatility or jumps-they rely heavily on numerically intensive algorithms or approximations for the pricing of ZC cap/floors, in particular. One may say similarly of the models by Kenyon (2008), Gretarsson et al (2012), and Mercurio and Moreni (2009) who in a similar manner use forward inflation, or in the case Hinnerich (2008) the forward inflation swap rate, as the model primitive. Waldenberger (2017) builds an inflation counterpart to the nominal model of and Keller-Ressel et al (2011).…”

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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A Quadratic Gaussian Year-on-Year Inflation Model

Cited by 2 publications

References 29 publications

Rational Models for Inflation-Linked Derivatives

Rational Models for Inflation-Linked Derivatives

Rational Models for Inflation-Linked Derivatives

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