Least-squares approach to risk parity in portfolio selection

The risk parity portfolio selection problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using the risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization and the equal weighting approach. In this paper, we discuss the problem of finding portfolios that satisfy risk parity over either individual assets or groups of assets. We describe the set of all risk parity solutions by using convex optimization techniques over orthants and we show that this set may contain an exponential number of solutions. We then propose an alternative non-convex least-squares model whose set of optimal solutions includes all risk parity solutions, and propose a modified formulation which aims at selecting the most desirable risk parity solution according to a given criterion. When general bounds are considered, a risk parity solution may not exist. In this case, the non-convex least-squares model seeks a feasible portfolio which is as close to risk parity as possible. Furthermore, we propose an alternating linearization framework to solve this non-convex model. Numerical experiments indicate the effectiveness of our technique in terms of both speed and accuracy.     

A perturbative approach to Bermudan options pricing with applications

In this paper we address the problem of the valuation of Bermudan option derivatives in the framework of multi-factor interest rate models. We propose a solution in which the exercise decision entails a properly defined series expansion. The method allows for the fast computation of both a lower and an upper bound for the option price, and a tight control of its accuracy, for a generic Markovian interest rate model. In particular, we show detailed computations in the case of the Bond Market Model. As examples we consider the case of a zero coupon Bermudan option and a coupon bearing Bermudan option; in order to demonstrate the wide applicability of the proposed methodology we also consider the case of a last generation payoff, a Bermudan option on a CMS spread bond.     

A synthetic factor approach to the estimation of value-at-risk of a portfolio of interest rate swaps

In this paper we decompose the interest rate swap yield curves of 10 major currencies into their common factors and find that the first two factors, interpreted as parallel shift and rotation, explain between 97.1% and 98.6% of the variation in the interest rate swap rates across all 10 currencies. The main contribution of the paper however is that we then model these two factors as simplified synthetic factors so that they may be used to develop an innovative approach to the computation of Value-at-Risk (VaR) for a portfolio of interest rate swaps.     

A market model with medium/long-term effects due to an insider

In this article, we consider a modification of the Karatzas–Pikovsky model of insider trading. Specifically, we suppose that the insider agent influences the long/medium-term evolution of Black–Scholes type model through the drift of the stochastic differential equation. We say that the insider agent is using a portfolio leading to a partial equilibrium if the following three properties are satisfied: (a) the portfolio used by the insider leads to a stock price which is a semimartingale under his/her own filtration and his/her own filtration enlarged with the final price; (b) the portfolio used by the insider is optimal in the sense that it maximises the logarithmic utility for the insider when his/her filtration is fixed; and (c) the optimal logarithmic utility in (b) is finite. We give sufficient conditions for the existence of a partial equilibrium and show in some explicit models how to apply these general results.