On Cox-Ross-Rubinstein Pricing Formula for Pricing Compound Option

Main Article Content

Javed Hussain
Bareerah Khan


The fundamental objective of this paper is twofold. Firstly, to derive the Cox-Ross-Rubinstein type new formula for risk neutral pricing of European compound call option, where the underlying asset is also a European call option. Thirdly, to prove that our newly derived CRR risk neutral pricing formula for compound call option, converges in distribution to the well known, continuous time Black-Scholes formula for pricing the compound call option on call.

Article Details


  1. Agliardi, E., Agliardi, R., A closed-form solution for multi-compound options. Risk Lett. 1 (2) (2004), 12.
  2. Black, F., & Scholes, M. The pricing of options and corporate liabilities. J. Politic. Econ. 81 (3) (1973), 637-654.
  3. Cassimon, D., Engelen, P.-J., Thomassen, L., & Van Wouwe, M. The valuation of a NDA using a 6-fold compound option. Res. Policy, 33 (1) (2004), 41-51.
  4. Chiarella, C., Griebsch, S., Kang, B., A comparative study on time-efficient methods to price compound options in the Heston model. Comput. Math. Appl. 67 (6) (2014), 12541270.
  5. Chiarella, C., Kang, B., The evaluation of American compound option prices under stochastic volatility and stochastic interest rates. J. Comput. Financ. 14 (9) (2011), 121.
  6. Cortazar, G., & Schwartz, E. S. A compound option model of production and intermediate inventories. J. Business, 66 (4) (1993), 517-540.
  7. Cutland, N. J., & Roux, A. Derivative pricing in discrete time, Springer Science & Business Media, 2012.
  8. Cox, J. C., & Ross, S. A. The valuation of options for alternative stochastic processes. J. Financ. Econ. 3 (1-2) (1976), 145-166.
  9. Geske, R. The valuation of compound options. J. Financ. Econ. 7 (1) (1979), 63-81.
  10. Geske, R. The valuation of corporate liabilities as compound options. J. Financ. Quant. Anal. 12 (4) (1977), 541-552.
  11. Griebsch, S.A. The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques. Rev. Deriv. Res. 16 (2) (2013), 135165.
  12. Gukhal, C.R. The compound option approach to American options on jump diffusion. J. Econ. Dyn. Control 28 (10) (2004), 20552074.
  13. Fouque, J.-P., Han, C.-H. Evaluation of compound options using perturbation approximation. J. Comput. Financ. 9 (1) (2005), 4161.
  14. Hull, J. C. Options, futures, and other derivatives: Pearson Education India, 2006.
  15. Lajeri-Chaherli, F., 2002. A note on the valuation of compound options. J. Futures Markets, 22 (11), 11031115.
  16. Marshall, A. W., and I. Olkin, A Family of Bivariate Distributions Generated by the Bivariate Bernoulli Distribution, J. Amer. Stat. Assoc. 80 (1985), 332-338.
  17. Merton, R. C. Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3 (1-2) (1976), 125-144.
  18. Samuelson P.A. Rational Theory of Warrant Pricing. In: Grnbaum F., van Moerbeke P., Moll V. (eds) Henry P. McKean Jr. Selecta. Contemporary Mathematicians. Birkhuser, Cham. 2015.
  19. Z. Brzezniak and T. Zastawniak, Basic Stochastic Process. Springer, 1999.