Problem set 6 important hints

The deadline for Problem Set 6 has been moved from 2 pm today to 5 pm tomorrow.

In problem set 6, problems 1 and 2 feature the same time to expiration, T = 1 year. For problem 1, we define T= \delta t, while for problem 2, T= 2\delta t.  Broadly, this sets the stage for examining the dynamics between the discrete-time Cox-Ross-Rubinstein (CRR) model and the continuous-time Black-Scholes-Merton (BSM) model, where T= n\delta t, and n corresponds to the number of time-steps that occur from the beginning of the binomial tree to the array of terminal nodes that exist at the expiration date T.  As you will see toward the end of today’s lecture, CRR model prices and probabilities converge to  BSM model prices and probabilities as the number of time steps becomes arbitrarily large.

Furthermore, as the number of steps, n, increases, \delta t becomes smaller. This leads to a corresponding decrease in the risk-neutral probability q and adjustments to the up (u) and down (d) factors.

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