Lattice model (finance)

Binomial Lattice for equity, with CRR formulae
Tree for an (embedded) bond option returning the OAS (black vs red): the short rate is the top value; the development of the bond value shows pull-to-par clearly

In finance, a lattice model[1] is a technique applied to the valuation of derivatives, where a discrete time model is required. For equity options, a typical example would be pricing an American option, where a decision as to option exercise is required at "all" times (any time) before and including maturity. A continuous model, on the other hand, such as Black–Scholes, would only allow for the valuation of European options, where exercise is on the option's maturity date. For interest rate derivatives lattices are additionally useful in that they address many of the issues encountered with continuous models, such as pull to par.[2] The method is also used for valuing certain exotic options, where because of path dependence in the payoff, Monte Carlo methods for option pricing fail to account for optimal decisions to terminate the derivative by early exercise,[3] though methods now exist for solving this problem.

  1. ^ Staff, Investopedia (17 November 2010). "Lattice-Based Model".
  2. ^ Hull, J. C. (2006). Options, futures, and other derivatives. Pearson Education India.
  3. ^ Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option pricing: A simplified approach. Journal of financial Economics, 7(3), 229–263.