All About Derivatives by Michael Durbin

Author:Michael Durbin
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2011-08-14T16:00:00+00:00

That’s the same delta as before. But let’s plug this delta back into the original equation to be extra sure it works:

Yep. This proves the value of delta is correct. And as a little bonus, it also tells us that the value of the portfolio at expiration under either scenario is $18. We’ll use this factoid in a moment.

First let’s see what our formula looks like at time zero, now that we know delta. And we know from before that the spot price of ZED is $60:

Now we’re down to two unknowns: portfolio value and the price of cZED62. Can we figure out the portfolio value? Sure can. Recall that the value of this portfolio in six months is $18 whether the stock moves to $66 or $54. So the portfolio value is just the present value of $18. Can we calculate the present value of $18? Sure can. We just need a period of time and an interest rate. The period is, as we know, six months. But what interest rate should we use? We know the payoff of this portfolio with complete certainty, that is, without risk. So the discount rate should be the risk-free interest rate. Let’s say it’s 6 percent and use continuous compounding as before:

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