Pricing inflation products with stochastic volatility and stochastic interest rates

Abstract

We consider a Heston type inflation model in combination with a Hull-White model for nominal and real interest rates, in which all the correlations can be non-zero. Due to the presence of the Heston dynamics our derived inflation model is able to capture the implied volatility skew/smile, which is present in the inflation option market data. We derive an efficient approximate semi-closed pricing formula for two types of inflation dependent options: index and year-on-year inflation options. The derived pricing formulas allow for an efficient calibration of the inflation model. We also illustrate our approach using a real-life pension fund example, where the Heston Hull-White model is used to determine the value of conditional future indexations.

Pricing variance swaps under stochastic volatility and stochastic interest rate

“…Grzelak et al [58] and Singor et al [99] compared their Heston-Hull-White hybrid model with the SZHW hybridization for pricing inflation dependent and European options respectively. Their techniques differ in the way that the former applied square-root approximation method in [55], whereas the latter extended the space vector into one additional dimension.…”

“…Regarding pricing discretely-sampled variance swaps with full correlation among all asset classes, we may perform some calibration procedure to obtain the correlation parameters as explained in [99]. Besides that, an empirical study on comparison between the relative performance of the Heston-CIR model and other hybridizations of stochastic volatility and stochastic interest rate models with full correlations may also be investigated.…”

Deflation Risk and Implications for Life Insurers

“…For instance, Ang et al [12] and Ahlgrim and D'Arcy [8] use time series of realized inflation rates, which is technically the same as using the index level. 5 Inflation option market prices were used by Singor et al [10], and Kitsul and Wright [15]. Fleckenstein et al [7] employed swap prices and option data, as in this study.…”

“…The proposed method contrasts with other methods used in the literature (i.e., calibration techniques and multi-stage estimations). On one hand, calibration methods such as the one used by Singor et al [10] select the model parameters based on a given day's available prices. Even though this methodology can give a set of parameters that is consistent with market prices, it is impossible to know whether these are robust in time.…”

Inflation Prediction and Inflation Volatility for Turkey

“…For this reason, it is not a least demanding task to measure inflation volatility in order to craft systematic behaviour for different market players. Although different studies have been done so for to measure the inflation volatility such as ((EDGE & GÜRKAYNAK, 2010 ;Berument & Sahin, 2010;Berganza & Broto, 2012;Castillo, 2014;Singor, Grzelak, van Bragt, & Oosterlee, 2013;Ginindza & Maasoumi, 2013;Clark & Davig, 2011;Kim, 2004;Castelnuovo, 2010)) that provide an overview and postulate that under unsystematic monetary policy inflation deviation is unpredictable, while for systematic monetary policy, it is desirable to assume that government does not intervene in the monetary policy. In this paper, we choose a mathematical technique to measure inflation volatility and inflation prediction for Turkey.…”