PORTFOLIO INSURANCE UNDER ROUGH VOLATILITY AND VOLTERRA PROCESSES

Affine Volterra processes have gained more and more interest in recent years. In particular, this class of processes generalizes the classical Heston model and the more recent rough Heston model. The aim of this work is hence to revisit and generalize the constant proportion portfolio insurance (CPPI) under affine Volterra processes. Indeed, existing simulation-based methods for CPPI do not apply easily to this class of processes. We instead propose an approach based on the characteristic function of the log-cushion which appears to be more consistent, stable and particularly efficient in the case of saffine Volterra processes compared with the existing simulation techniques. Using such approach, we describe in this paper several properties of CPPI which naturally result from the form of the log-cushion’s characteristic function under affine Volterra processes. This allows to consider more realistic dynamics for the underlying risky asset in the context of CPPI and hence build portfolio strategies that are more consistent with financial data. In particular, we address the case of the rough Heston model, known to be extremely consistent with past data of volatility. By providing a new estimation procedure for its parameters based on the PMCMC algorithm, we manage to study more accurately the true properties of such CPPI strategy and to better handle the risk associated with it.

Spanning With Binary Options: A Vector Lattice Approach

The issue of portfolio insurance is one of the prime concerns of the investors who want to insure their asset at minimum or appropriate cost. Static hedging with binary options is a popular strategy that has been explored in various option models (see e.g. (2; 3; 4; 7)). In this thesis, we propose a static hedging algorithm for discrete time models. Our algorithm is based on a vector lattice technique. In chapter 1, we give the necessary background on the theory of vector lattices and the theory of options. In chapter 2, we reveal the connection of lattice-subspaces with the minimum-cost portfolio insurance strategy. In chapter3, we outline our algorithm and give applications to binomial and trinomial option models. In chapter 4, we perform simulations and analyze the hedging errors of our algorithm for European, Barrier, Geometric Asian, Arithmetic Asian, and Lookback options. The study has revealed that static hedging could be suitable strategy for the European, Barrier, and Geometric Asian options as these options have shown less inclination to the rollover effect.

Spanning With Binary Options: A Vector Lattice Approach

The issue of portfolio insurance is one of the prime concerns of the investors who want to insure their asset at minimum or appropriate cost. Static hedging with binary options is a popular strategy that has been explored in various option models (see e.g. (2; 3; 4; 7)). In this thesis, we propose a static hedging algorithm for discrete time models. Our algorithm is based on a vector lattice technique. In chapter 1, we give the necessary background on the theory of vector lattices and the theory of options. In chapter 2, we reveal the connection of lattice-subspaces with the minimum-cost portfolio insurance strategy. In chapter3, we outline our algorithm and give applications to binomial and trinomial option models. In chapter 4, we perform simulations and analyze the hedging errors of our algorithm for European, Barrier, Geometric Asian, Arithmetic Asian, and Lookback options. The study has revealed that static hedging could be suitable strategy for the European, Barrier, and Geometric Asian options as these options have shown less inclination to the rollover effect.