Pricing models for inflation linked derivatives in an illiquid market

Recent nancial crises have highlighted the sensitivity and vulnerability of nancial marketsto ination, which reduces the value of money and a ects the net returns of nancial instruments.In response to this, investors who are concerned with maintaining their investment'spurchasing power rather than its market value are resorting to ination linked (IL) productsto hedge their ination risk. Consequently, the ination market has been rapidly growing forthe last decade and has further great potential growth worldwide. It is highly probable thatination linked derivatives will eventually be as common as conventional products. Anothercause of the ination market boost is the growing extension of the time frame of nancialtransactions, which has generated an increase in ination expectation; since 1980 the averagetime to maturity of long-dated transactions went from one decade to three decades.This is, in part, due to the ageing population in the developed world. This research investigatessome alternative models in order to improve the match between model prices andobserved prices in the American and South African ination markets. It takes into accountthe relative illiquidity of IL products. The main tools used are L evy distributions, macroeconomicfactors, no-arbitrage and pricing kernel models. L evy processes can replicate thebehaviour of the return innovations of a wide range of nancial securities. Adding a stochastictime change to the L evy process randomises the market clock, thus generating stochasticvolatilities, higher stochastic return moments and eventually stochastic skewness. These areobserved stylised facts most conventional models do not achieve. Moreover, in contrast tothe hidden factor approach, each L evy process component and its stochastic time changecan readily be assigned an economic meaning. This explicit economic mapping facilitatesthe interpretation of current models and provides a more intuitive approach to buildingnew models that capture other observed behaviours. Finally, L evy processes also providetractable formulas for derivative pricing and market estimations. In general, ination is aconsequence of macroeconomic factors. Exogenous dynamics of the most signi cant of thesefactors are used to deduce the endogenous ination dynamics in some of the consideredmodels. In these cases, the calibration of the pricing kernel models requires little historical data on IL derivatives. In fact, the required macroeconomic historical data is easily availablebecause of the current national and international legislation.