On Valuing Stochastic Perpetuities Using New Long Horizon Stock Price Models Distinguishing Booms, Busts, and Balanced Markets

33 Pages Posted: 10 Mar 2016

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland

Marc Yor

Université Paris VI Pierre et Marie Curie

Date Written: April 2016

Abstract

For longer horizons, assuming no dividend distributions, models for discounted stock prices in balanced markets are formulated as conditional expectations of nontrivial terminal random variables defined at infinity. Observing that extant models fail to have this property, new models are proposed. The new concept of a balanced market proposed here permits a distinction between such markets and unduly optimistic or pessimistic ones. A tractable example is developed and termed the discounted variance gamma model. Calibrations to market data provide empirical support. Additionally, procedures are presented for the valuation of path dependent stochastic perpetuities. Evidence is provided for long dated equity linked claims paying coupon for time spent by equity above a lower barrier, being underpriced by extant models relative to the new discounted ones. Given the popularity of such claims, the resulting mispricing could possibly take some corrections. Furthermore for these new discounted models, implied volatility curves do not flatten out at the larger maturities.

Keywords: martingale limits, variance gamma, generalized gamma convolution, discounting process, abnormal earnings

Suggested Citation

Madan, Dilip B. and Yor, Marc, On Valuing Stochastic Perpetuities Using New Long Horizon Stock Price Models Distinguishing Booms, Busts, and Balanced Markets (April 2016). Mathematical Finance, Vol. 26, Issue 2, pp. 296-328, 2016, Available at SSRN: https://ssrn.com/abstract=2745638 or http://dx.doi.org/10.1111/mafi.12056

Dilip B. Madan (Contact Author)

University of Maryland

Marc Yor

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013
France

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