The generalized sequential compound options pricing and sensitivity analysis

Abstract

This paper proposes a generalized pricing formula and sensitivity analysis for sequential compound options (SCOs). Most compound options described in literatures, initiating by Geske [Geske, R., 1977. The Valuation of Corporate Liabilities as Compound Options. Journal of Finance and Quantitative Analysis, 12, 541–552; Geske, R., 1979. The Valuation of Compound Options. Journal of Financial Economics 7, 63–81.], are simple 2-fold options. Existing research on multi-fold compound options has been limited to sequential compound CALL options whose parameters are constant. The multi-fold sequential compound options proposed in this study are defined as compound options on (compound) options where the call/put property of each fold can be arbitrarily assigned. In addition, the deterministic time-dependent parameters, including interest rate, depression rate and variance of asset price, make the SCOs more flexible. The pricing formula is derived by the risk-neutral method. The partial derivative of a multivariate normal integration, which is an extension of Leibnitz's Rule, is derived in this study and used to derive the SCOs sensitivities. The general results for SCOs presents in this paper can enhance and broaden the use of compound option theory in the study of real options and financial derivatives.