Luiz Vitiello

Actuarial Transform Pricing

This article studies four transform pricing methods in the context of general equilibrium (GE) framework. The four methods, viz. the Esscher transform, indifference pricing, the Wang transform, and the standard deviation loading, are popular among actuarial literature and practice. The transform pricing methods offer a convenient solution to contingent claim pricing problem when the underlying risk exposure cannot be fully hedged. We show analytically that these four methods are similar and close to the GE approach if the utility has an exponential function, and the underlying distribution is Normal. When the payoff distribution is non-gaussian, prices produced by the four methods vary widely. Moreover, some transform methods may lead to prices that are not coherent, violating one or more of the following properties: additivity, homogeneity, scale invariance and monotonicity. We discuss the implications of our findings on incomplete market pricing.

Pricing GDP Linked Securities

We propose a simple model for the valuation of sovereign growth linked bonds. The model is calibrated to potential GDP, output gap, real exchange rate and rating implied historical default probabilities. Bond prices are obtained by applying the Esscher transform on the simulated cash flows with the risk aversion parameter calibrated to match market prices of vanilla bonds of the sovereign (or a comparable sovereign). The model was applied to Argentinian data and its US

Jump Mis-Specification and International Portfolio Selection

vanilla bonds before being used to price Argentinas GDP warrants. Results indicate that our model produce valuations that are close to observed market prices.

General Equilibrium and Risk Neutral Framework for Option Pricing with a Mixture of Distributions

In this paper we make a distinction between systemic co-jumps and independent idiosyncratic jumps, and examine the impact of their mis-specification on asset allocation. We discuss how jumps mis-specification may lead to jumps mis-estimation and to a suboptimal portfolio. Specifically, we develop a framework where security prices have three distinct parts: a diffusion component, a systemic co-jump component, and an independent idiosyncratic jump component. In our model, the intensity and the timing of systemic co-jumps is the same across all assets whilst the timing and intensity of the idiosyncratic jump is, obviously, asset specific. The recognition that stock market returns jump together as well as separately is crucial for cross-market asset allocation policy. Univariate jump diffusion is estimated through a Markov Chain Monte Carlo (MCMC) method for weekly MSCI index returns of eleven developed and emerging markets from 1988 to 2009. The MCMC procedure produces sample paths of the latent univariate jump processes which were used in estimating the systemic and idiosyncratic jumps between series. Our results suggest that in developed markets, the omission of (idiosyncratic) jumps has little impact on portfolio selection. Developed markets are more homogeneous and their stock returns tend to jump together. The covariance matrix absorbed a large part of the linear co-jump risks producing an optimised portfolio that is not too dissimilar to one produced by a diffusion model with only the possibility for co-jumping. However, we find that, for emerging markets that tend to have idiosyncratic jumps, the assumption of co-jumps produced biased jump estimates. Losses in portfolio certainty equivalence due to this wrong jump dependence assumption are economically significant.