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ON VALUING STOCHASTIC PERPETUITIES USING NEW LONG HORIZON STOCK PRICE MODELS DISTINGUISHING BOOMS, BUSTS, AND BALANCED MARKETS
Author(s) -
Madan Dilip B.,
Yor Marc
Publication year - 2016
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12056
Subject(s) - economics , econometrics , perpetuity , valuation (finance) , dividend , stochastic volatility , equity (law) , financial economics , volatility (finance) , finance , political science , law
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.