Abstracts

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.