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The binomial model was first proposed by William Sharpe in the 1978 edition of Investments (ISBN 013504605X), [2] and formalized by Cox, Ross and Rubinstein in 1979 [3] and by Rendleman and Bartter in that same year. [4] For binomial trees as applied to fixed income and interest rate derivatives see Lattice model (finance) § Interest rate ...
In mathematical finance, the Cox–Ingersoll–Ross (CIR) model describes the evolution of interest rates. It is a type of "one factor model" (short-rate model) as it describes interest rate movements as driven by only one source of market risk. The model can be used in the valuation of interest rate derivatives.
Least Square Monte Carlo is a technique for valuing early-exercise options (i.e. Bermudan or American options).It was first introduced by Jacques Carriere in 1996. [12]It is based on the iteration of a two step procedure:
Rubinstein was a senior and pioneering academic in the field of finance, focusing on derivatives, particularly options, and was known for his contributions to both theory and practice, [5] especially portfolio insurance and the binomial options pricing model (also known as the Cox-Ross-Rubinstein model), as well as his work on discrete time ...
Ross is best known for the development of the arbitrage pricing theory (mid-1970s) as well as for his role in developing the binomial options pricing model (1979; also known as the Cox–Ross–Rubinstein model). He was an initiator of the fundamental financial concept of risk-neutral pricing.
As above, these methods can solve derivative pricing problems that have, in general, the same level of complexity as those problems solved by tree approaches, [1] but, given their relative complexity, are usually employed only when other approaches are inappropriate; an example here, being changing interest rates and / or time linked dividend policy.
John Carrington Cox is the Nomura Professor of Finance Emeritus at the MIT Sloan School of Management. He is one of the world's leading experts on options theory and one of the inventors of the Cox–Ross–Rubinstein model for option pricing, as well as of the Cox–Ingersoll–Ross model for interest rate dynamics .
A variant on the Binomial, is the Trinomial tree, [10] [11] developed by Phelim Boyle in 1986. Here, the share price may remain unchanged over the time-step, and option valuation is then based on the value of the share at the up-, down- and middle-nodes in the later time-step. As for the binomial, a similar (although smaller) range of methods ...