Inflation Derivatives Pricing with Macroeconomic Foundations
Gabriele Sarais (Imperial College London, UK)
Joint work with Damiano Brigo

Tuesday June 3, 16:30-17:00 | session 3.5 | Options, Futures | room G

We develop a model to price inflation and interest rates derivatives using continuous-time dynamics that have some links with macroeconomic monetary DSGE models equipped with a Taylor rule: in particular, the reaction function of the central bank, the bond market liquidity, inflation and growth expectations play an important role. The model can explain the effects of non-standard monetary policies (like quantitative easing or its tapering) and shed light on how central bank policy can affect the value of inflation and interest rates derivatives.
The model is built under standard no-arbitrage assumptions. Interestingly, the model yields short rate dynamics that are consistent with a time-varying Hull-White model, therefore making the calibration to the nominal interest curve and options straightforward. Further, we obtain closed forms for both zero-coupon and year-on-year inflation breakevens and options. The calibration process is fully separable, which means that the calibration can be carried out in many simple steps that do not require heavy computation.
The advantages of such structural inflation modelling become apparent when one starts doing risk analysis on an inflation derivatives book: because the model explicitly takes into account economic variables, a trader can easily assess the impact of a change in central bank policy or growth expectation on a complex book of fixed income instruments, which is normally not straightforward when using standard inflation pricing models.

Finite-Jump Tangent Lévy Models
Emmanuel Leclercq (Swiss Finance Institute at EPFL, Switzerland)
Joint work with Damir Filipovic and Loriano Mancini

Tuesday June 3, 17:00-17:30 | session 3.5 | Options, Futures | room G

The aim of the paper is to develop a practicable continuous-time dynamic arbitrage-free model for the pricing of European contingent claims. Using the framework introduced in Carmona and Nadtochiy (2011, 2012), the stock price is modeled as a semi-martingale process and, at each time t, the marginal distribution of the European option prices is coded by an auxiliary process that starts at t and follows an exponential additive process. The jump intensity that characterizes these auxiliary processes is then set in motion by means of stochastic dynamics of Itô’s type. Our model is a modification of the one proposed by Carmona and Nadtochiy, as only finitely many jump sizes are assumed. This crucial assumption implies that the jump intensities are taken values in only a finite-dimensional space. In this setup, we provide explicit necessary and sufficient consistency conditions that guarantee the absence of arbitrage. Then, a practicable dynamic model verifying them is proposed and estimated, using options on the S&P 500. As an application, we finally consider the hedging of a variance swap contract, via a variance-minimizing hedge.