•We propose a multivariate model for FX and assets log returns using Lévy processes.•We show the model preserves natural inversion and triangulation symmetries.•We accompany the model with an ...efficient calibration procedure to market quotes.•We joint calibrate on real data a triangle of implied volatility surfaces.•The approach gives access to the implied correlation matrix.
We propose an integrated model of the joint dynamics of FX rates and asset prices for the pricing of FX derivatives, including Quanto products; the model is based on a multivariate construction for Lévy processes which proves to be analytically tractable. The approach allows for simultaneous calibration to market volatility surfaces of currency triangles, and also gives access to market consistent information on dependence between the relevant variables. A successful joint calibration to real market data is presented for the particular case of the Variance Gamma process.
Estimation of Multivariate Asset Models with Jumps Ballotta, Laura; Fusai, Gianluca; Loregian, Angela ...
Journal of financial and quantitative analysis,
10/2019, Letnik:
54, Številka:
5
Journal Article
Recenzirano
Odprti dostop
We propose a consistent and computationally efficient 2-step methodology for the estimation of multidimensional non-Gaussian asset models built using Lévy processes. The proposed framework allows for ...dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets because it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail in an empirical illustration.
In this paper we propose a new method for approximating the price of arithmetic Asian options in a Variance-Gamma (VG) economy, which is then applied to the problem of pricing equityindexed annuity ...contracts. The proposed procedure is an extension to the case of a VG-based model of the moment-matching method developed by Turnbull and Wakeman and Levy for the pricing of this class of path-dependent options in the traditional Black-Scholes setting. The accuracy of the approximation is analyzed against RQMC estimates for the case of ratchet equityindexed annuities with index averaging.
The aim of this paper is to provide an assessment of alternative frameworks for the fair valuation of life insurance contracts with a predominant financial component, in terms of impact on the market ...consistent price of the contracts, the embedded options, and the capital requirements for the insurer. In particular, we model the dynamics of the log-returns of the reference fund using the so-called Merton (
1976
) process, which is given by the sum of an arithmetic Brownian motion and a compound Poisson process, and the Variance Gamma (VG) process introduced by Madan and Seneta (
1990
), and further refined by Madan and Milne (
1991
) and Madan et al. (
1998
). We conclude that, although the choice of the market model does not affect significantly the market consistent price of the overall benefit due at maturity, the consequences of a model misspecification on the capital requirements are noticeable.
In this paper we consider the problem of hedging an arithmetic Asian option with discrete monitoring in an exponential Lévy model by deriving backward recursive integrals for the price sensitivities ...of the option. The procedure is applied to the analysis of the performance of the delta and delta-gamma hedges in an incomplete market; particular attention is paid to the hedging error and the impact of model error on the quality of the chosen hedging strategy. The numerical analysis shows the impact of jump risk on the hedging error of the option position, and the importance of including traded options in the hedging portfolio for the reduction of this risk.
In this note we introduce a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain deferred annuity pension-type contracts in the UK. The ...valuation approach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath–Jarrow–Morton framework for the term structure of interest rates. Numerical results are investigated and the sensitivity of the price of the option to changes in the key parameters is also analyzed.
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