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1965. A new method to solve Volterra integral equations for variable annuities evaluation with stochastic volatility

Invited abstract in session WC-39: Financial Modelling, stream Stochastic Modelling.

Wednesday, 12:30-14:00
Room: 35 (building: 306)

Authors (first author is the speaker)

1. Immacolata Oliva
Methods and Models for Economics, Territory and Finance, Sapienza University of Rome
2. Roberto De Marchis
Sapienza
3. Antonio Luciano Martire
MEMOTEF, Sapienza University of Rome

Abstract

A Variable Annuity (VA) differs from traditional life insurance products because, when the insurer invests the policy premium in a risky portfolio, the policyholder bears pro ts or losses according to the investment performances. In general, the dynamics of such a portfolio are defi ned via a geometric Brownian motion with constant interest rate and volatility, see e.g. Shen et al. (2016) and De Angelis et al. (2022). However, such a choice might be unrealistic, since it fails to incorporate well-known stylized facts observed in the financial market, such as the volatility smile/skew, see e.g.Heston (1993).
Moreover, the presence of an American option embedded in the structure of a VA makes it unfeasible to determine a closed-form formula for such a contract, regardless of the market model. Therefore, we have to resort to ad-hoc numerical techniques, such as finite difference methods for the associated PDE, see e.g. Shen et al. (2016). Another possible route is to refer to the integral equation characterizing the early exercise boundary, as shown in Kim (1990).
Within the latter setting, and along the lines of Adolfsson et al. (2013), in this paper, we propose a novel algorithm to solve integral non-linear two-dimensional Volterra equations in a stochastic volatility framework by exploiting specifi c features of the involved Fourier-type integrals.

Keywords

Status: accepted

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