Instead of the Binomial model developed in class, assume that now the stock pric
ID: 2817970 • Letter: I
Question
Instead of the Binomial model developed in class, assume that now the stock price follows a ternary one-period model, that is, at time 0 the stock price can go up by a factor u, down by a factor d, and stay somewhere in between with the factor m (u> 1> d,u> m > d). The positive probabilities of the stock going up, middle, and down are pu,Pm.Pd, respectively (probabilities of course sum up to one). The stock market is assumed to consist of the money market account paying interest rate r, the stock, and a call option. In general, what makes it impossible to price the option in such a model? Please provide a rigorous argument for your answerExplanation / Answer
Option is a derivative contract ,with option of performance , i.e the buyer has right to perform the contract in case of ITM only . In case of Call Strike price < the spot price , while in case of Put Strike price > the spot price.
The valuation model used in Binomial is based on the concept of performance or under observation to be an option contract ITM. In any case the value of option only change with the change of the spot price , may go up , down or remain at same . The value of option remain un changed at any lattice , if price remain unchanged . So,the ternary model is not possible for valuation at first order in given circumtances.