Abstract
We introduce the Fourier-Cosine method for pricing and hedging insurance derivatives. We implement this method for a particular problem of variable annuities under the Black-Scholes model for the investment account. The numerical results show the reliability of the Fourier-Cosine method for pricing and hedging insurance derivatives.
Highlights
We introduce the Fourier-Cosine method for pricing and hedging insurance derivatives
The lapse risk is treated as diversifiable, it is assumed as a deterministic probability of the contracts in force at maturity, for the contract provided guarantees of withdrawal benefit, the lapse risk depends on the guaranteed benefits, it will be considered in the pricing of the embed option
In this article we have introduced the Fourier-Cosine method for pricing and hedging insurance derivatives
Summary
The concept behind COS pricing method is to recover the conditional density by its characteristic function through Fourier-Cosine expansions. It can be applied for all processes as soon as the characteristic function is available, which includes all affine processes. The conditional density function of the underlying is approximated by means of the characteristic function via a truncated Fourier-Cosine expansion of order N, as follows: x) a. Replacing f ( y | x) in (2.1) by its approximation (2.2) and interchanging integration and summation, we obtain the COS algorithm to approximate the value of a European option: v x, t0. Is the Fourier-Cosine coefficient of v ( y,T ) , which is available in closed form for several payoff functions of European options. The size of the integration interval [a,b] can be determined with help of the cumulants [11]
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