Option Pricing Class Problem

Here’s the Option Pricing Class Problem that I passed out in class today.  We will be working more on this class problem during our next class meeting when we examine 1) the replicating portfolio approach to pricing a put option, 2) the “delta hedging” and “risk neutral valuation” approaches to pricing calls and puts, and 3) extending these models from a single period to multiple periods.

Today, we focused our attention on replicating portfolio approaches to pricing forward contracts and (single time-step) European call options.  In the class problem, the latter concept appears in part B.  Here’s the solution to part B:

According to the Replicating Portfolio Approach, $\Delta = \displaystyle\frac{{{C_u} - {C_d}}}{{uS - dS}} = \displaystyle\frac{{12.80 - 0}}{{72.80 - 50.40}} = .5714\;$ and $B = \displaystyle\frac{{u{C_d} - d{C_u}}}{{{e^{r\delta t}}(u - d)}} = \frac{{1.3(0) - .9(12.80)}}{{1.0408(.4)}} = - 27.67$. Then ${V_{RP}} = C = \Delta S + B = .5714(56) - 27.67 = \ 4.33$.

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