Bounds for present value functions with stochastic interest rates and stochastic volatilityBounds for present value functions with stochastic interest rates and stochastic volatility
Faculty of Applied Economics
Faculteit Toegepaste Economische Wetenschappen
Mathematics, Statistics and Actuarial Sciences
Antwerpen :UA, 2001[*]2001
Research paper / Faculty of Applied Economics UFSIA-RUCA ; 2001:037
University of Antwerp
The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather complicated, and is known only for special cases. An interesting solution to this difficulty consists of determining computable upper bounds, as close as possible to the real distribution. In the present contribution, we want to show how it is possible to compute such bounds for the present value of cash flows when not only the interest rates but also volatilities are stochastic. We derive results for the stop loss premium and distribution of these bounds.