•We propose a general joint model for log-returns and their volatility.•We use multivariate time changed Lévy processes.•Volatility and leverage are originated by both continuous and discontinuous ...drivers.•We provide expressions for the characteristic function and its “forward extension”.•Robust calibration performance is achieved with purely discontinuous dynamics.
We propose a novel flexible framework for the joint evolution of stock log-returns and their volatility based on time changed Lévy processes. The novelty of the approach stems from the generality of the jump structure we endow our model with, and the ability of the model to generate leverage effects out of the pure jump component. We derive the characteristic function and the forward characteristic function of the log-returns, which allow for the efficient pricing of vanilla and forward-start-like option contracts by Fourier transform methods. The proposed framework achieves robust calibration performance properties especially in the case of pure jump specifications. The results offered in this paper could have potentially interesting implications in terms of design of models and hedging strategies, and their development.
•We propose a multivariate structural model for credit default using Lévy processes.•We use the model for setting the problem of Credit Value Adjustment pricing.•We accompany the model with an ...efficient calibration procedure and pricing scheme.•We apply the proposed framework to the case of oil swaps.•The approach allows to cater for collateralization, netting and initial margin.
This paper proposes an integrated pricing framework for Credit Value Adjustment of equity and commodity products. The given framework, in fact, generates dependence endogenously, allows for calibration and pricing to be based on the same numerical schemes (up to Monte Carlo simulation), and also allows the inclusion of risk mitigation clauses such as netting, collateral and initial margin provisions. The model is based on a structural approach which uses correlated Lévy processes with idiosyncratic and systematic components; the pricing numerical scheme, instead, efficiently combines Monte Carlo simulation and Fourier transform based methods. We illustrate the tractability of the proposed framework and the performance of the proposed numerical scheme by means of a case study on a portfolio of commodity swaps using real market data.
This paper proposes an integrated pricing framework for convertible bonds, which comprises firm value evolving as an exponential jump diffusion, correlated stochastic interest rates movements and an ...efficient numerical pricing scheme. By construction, the proposed stochastic model fits in the framework of affine jump diffusion processes of Duffie et al. Econometrica, 2000, 68, 1343-1376 with tractable behaviour. We define the firm's optimal call policy and investigate its impact on the computed convertible bond prices. We illustrate the performance of the numerical scheme and highlight the effects originated by the inclusion of jumps, stochastic interest rates and a non-zero correlation structure between firm value and interest rates.
This paper proposes a market consistent valuation framework for variable annuities (VAs) with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based ...on a hybrid model for the financial market and uses time-inhomogeneous Lévy processes as risk drivers. Further, we allow for dependence between financial and surrender risks. Our model leads to explicit analytical formulas for the quantities of interest, and practical and efficient numerical procedures for the evaluation of these formulas. We illustrate the tractability of this approach by means of a detailed sensitivity analysis of the fair value of the VA and its components with respect to the model parameters. The results highlight the role played by the surrender behaviour and the importance of its appropriate modelling.
The aim of this paper is to analyze the performance of hedging strategies based on snow and temperature options developed by ski operators to protect their profitability under adverse changes in ...climatic conditions. The setup is based on a joint non-parametric model for snow and temperature aimed at providing a modelling support for the assessment of the impact of these weather variables on the number of visitors at the ski resort. The analysis is carried out considering the case of Austrian Alps, and examines: i) the ability of the proposed approach to provide a realistic representation of the true data-generating process; ii) the variability reduction in the Profit and Loss of the ski operator offered by the suggested strategies; and iii) the tradeoff between the budget earmarked for hedging and profitability protection.
•We carry out an analysis of snow level and temperature dynamics highlighting the relevance of non-parametric modelling.•Visitor number fitted model is transformed into future revenues projections.•We develop hedging strategies for protection of ski resorts' profitability against adverse climate conditions.•Weather variables' generated sample trajectories form the basis of profit and loss calculations.•We identify best-performing hedge portfolios with periodic reset of snow options, and combined snow-temperature options.
This paper proposes a framework for the valuation and the management of complex life insurance contracts, whose design can be described by a portfolio of embedded options, which are activated ...according to one or more triggering events. These events are in general monitored discretely over the life of the policy, due to the contract terms. Similar designs can also be found in other contexts, such as counterparty credit risk for example. The framework is based on Fourier transform methods as they allow to derive convenient closed analytical formulas for a broad spectrum of underlying dynamics. Multidimensionality issues generated by the discrete monitoring of the triggering events are dealt with efficiently designed Monte Carlo integration strategies. We illustrate the tractability of the proposed approach by means of a detailed study of ratchet variable annuities, which can be considered a prototypical example of these complex structured products.
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