Multivariate digital options with memory

Abstract

We study a class of multivariate digital products called Altiplanos. These products may be structured according to two general features: (i) they may be univariate or multivariate; (ii) they may be European or with barrier. In addition to that, they may be endowed with exotic characteristics. One of these is the so-called memory feature, which prescribes that the first time when the underlying event takes place, coupons are paid for all the previous periods in which it had not occurred. The task of this paper is to provide new results for the evaluation of this clause. We show that the memory features provide the products with the presence of a digital option paying all coupons in the final date, and that this option plays a dominant role in the evaluation. Concerning sensitivity, the value of digital products with memory are positively sensitive to an increase in cross-section correlation and to a decrease in temporal correlation.

Keywords:

• copula functions
• Markov processes
• multivariate options
• memory feature
• correlation products