The idea is that we can price an option in the riskless world, yet the result applies in the real (risky) world. The reason is that a higher expected return for the asset (the stock) should be met with (offset by) a higher discount rate. In this screencast example, a probability of an up step (u) of 52.5% and a risk-less rate of 4%…

translates into a real (risky) world assumption of p = 60% and a discount rate of 57%. Then the higher expected return is met with a higher discount rate, such that the option price (present value) is the same:

Screencast:

Comments

1. Lalitha Narayan 04 Apr 2009

   This is an excellent screencast on the risk-free and real world approaches to pricing an option.  The example using the spreadsheet clearly brought out how the result using a risk-free approach applies in the real world and that a higher expected return is met by a higher discount rate for the two approaches to give the same option price. The goal seek approach also highlighted how spreadsheets can be used to explain such concepts more effectively. I appreaciate the teaching aids used by you to make the concepts crystal clear. Thanks, David!

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