Option Pricing under Extended Vasieck Model

[[abstract]]The binominal option pricing model developed by Cox, Ross, and Rubinstein (1979), is an efficient numerical procedure for computing American option prices. As CRR model is path independent, the discrete state space efficiently approximates the continuous time state space. Besides CRR, other examples of such discrete-time model approximation include: Boyle (1986,1988), Boyle, Evinine, and Gibbs (1989), Madan, Milne, and Shefrin (1989), He (1990), Nelson and Ramaswamy (1990), Amin (1991), Kamrad and Ritchken (1991), Tian (1993), and Ritchken (1995). However, these models are only useful in the environment of constant interest rate, they cannot be applied to long-dated European- or American-style options in which the term structure risk is important. Hence, in this study, I first provide the forward price tree to mimic the evolution of forward price of underlying asset. Furthermore, based on forward price tree method, using martingale pricing methodology, I create the binomial or trinomial implied spot-tree trees that can price equity derivatives which are sensitive to domestic short-term rate, exchange rate, foreign short-term rate, domestic or foreign stock prices such as European- or American-style long-dated stock options, currency options, and Quantos. The nodes of binomial tree and trinomial tree for each date n is 1 + n and 1 2 + n , respectively. The model execution will be the same as the traditional lattice methods and can be implemented with arbitrary deterministic volatility functions of interest rate and stock price. Hence, they are timesaving and suitable for the practical application.[[note]]NSC91-2416-H327-02