Financial Jeorpardy

22 Pages Posted: 26 Jul 2015 Last revised: 23 Dec 2016

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: December 21, 2016

Abstract

Learning the pre limited liability value process of equity claims and its relationship to the stock price is an answer to the financial jeorpardy question when observed option prices are the answer being given by the market. Constant dollar equity holder values, prior to the imposition of limited liability, are the signed conditional expectations of the integral of discounted net residual equity claims through all time. The stock is modeled as a limitied liability claim imputing positive dividend flows to shareholders in certain circumstances coupled with a call option written on the integral of all discounted net residual equity claims.The underlying signed value has a known characteristic function when revenues and expenses are modeled as independent gamma processes. The stock price is a positive function of this signed underlying value, given by the solution of a partial integro differential equation. Options on the stock are then options on this function of the signed underlying value and are solved for using its density obtained by Fourier inversion of the characteristic function. The calibration of model parameters, the imputed dividend function and the terminal call strike is conducted on option prices at a single maturity for four underliers, AMZN, SPY, GOOG and JNJ. In all these cases it is observed that risk neutrally, up moves arrive more frequently and are generally smaller while down moves are less frequent and are larger. The terminal option strikes were in the money for SPY and JNJ and out of the money for AMZN and GOOG.

Keywords: uniformly integrable martingale, variance gamma, stochastic perpetuity

JEL Classification: G10, G11, G13

Suggested Citation

Madan, Dilip B., Financial Jeorpardy (December 21, 2016). Robert H. Smith School Research Paper No. RHS 2635635, Available at SSRN: https://ssrn.com/abstract=2635635 or http://dx.doi.org/10.2139/ssrn.2635635

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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