Question

This is for my finance class and I am a bit stuck. We're asked to use the Delta hedging formula (i.e. how much stock to hold) for the multiperiod binomial model to confirm that a financial derivative paying the stock price at time t=N (i.e. V_N = S_N) must be priced with V_0 = S_0 today.

Answer 1

Multiperiod Binomial Model

We assume in the multi-period model at point two that the stock price, even by a factor of u and d, rises or decreases again. The following

S2(H H) = uS1(H) = u 2S0, S2(HT) = dS1(H) = duS0,

S2(T H) = uS1(T) = udS0, S2(T T) = dS1(T) = d 2S0

It is possible to perform this method repeatedly for any number of N times to form Binomial model for N-period

For n = 1 , 2, ..., N, in the One period binomial model theorem, the random variable Vn (ω1ω2...ωn) is the need to be the price of the derivative protection at time n if the results of the rest n tosses are ω1ω2...ωn. The derivative security price is the need at time zero to be V0. Notice that the number of shares of stock that should be held at n is ∆n(ω1ω2...ωn). Since ∆n relies on the first n coin tosses, we claim that ∆0, ∆1, ..., ∆N−1 is an adapted phase of the portfolio. What this implies is that in the replicating portfolio process, the number of shares of stock is changed at each time point. The above theorem works by calculating the value of the option, taking into account the binomial model of the N-period, at the time N (where N = n+1) and then working backwards recursively until the option value at the time