Pricing Ratchet equity-indexed annuities with early surrender risk in a CIR++ model
نویسندگان
چکیده
In connection with a problem posed by Kijima and Wong [11], we propose a lattice algorithm for pricing simple Ratchet equity-indexed annuities (EIAs) with early surrender risk and global minimum contract value when the asset value depends on the CIR++ stochastic interest rates. In addition we present an asymptotic expansion technique which permits to obtain a first order approximation formula for the price of simple Ratchet EIAs without early surrender risk and without global minimum contract value. Numerical comparisons show the reliability of the proposed methods. Key-words: Ratchet Equity-indexed annuities; stochastic interest rates; early surrender risk; lattice methods; asymptotic expansions This research was supported by MIUR (Prin 2007) and by NSFC (No. 10801139) ∗ China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, China, [email protected] † Dipartimento di Scienze Economiche e Statistiche, Via Tomadini 30/A, Università di Udine, 33100 Udine, Italy (E-mail: [email protected], [email protected]) ha l-0 07 21 96 3, v er si on 1 31 J ul 2 01 2 Pricing de Ratchet sur action avec risque de rachat anticipé et utilisant le modèle CIR++ Résumé : Suite au problème posé par Kijima et Wong, nous proposons un algorithme de treillis pour le pricing du Ratchet sur action avec risque de rachat anticipé. Il inclut aussi une valeur minimale globale lorsque l’actif dépend du processus CIR++ du taux d’intérêt. Par ailleurs, nous présentons une technique de développement asymptotique permettant une approximation de premier ordre pour le prix du Ratchet EIAs, sans risque de rachat anticipé ni valeur minimale. Des expériences numériques montrent une bonne qualité des résultats obtenus par la méthode proposée. Mots-clés : Ratchet sur action, taux d’intérêt stochastiques, méthode de treillis, risque de rachat anticipé, développement asymptotique ha l-0 07 21 96 3, v er si on 1 31 J ul 2 01 2 Pricing Ratchet equity-indexed annuities with early surrender risk in a CIR++ model 3
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