Microsoft PowerPoint - PoF.ppt

232

Suppose, for example, that at a particular

point in time we know that the delta of

a call is given by 0.4 (

∆

=dc/dS=0.4). c

The riskless portfolio would consist of

ƒ

a long position in 0.4 share and

ƒ

a short position in 1 call option.

The gain or loss from the stock position

always offsets the gain or loss from the

option position so that the overall value

of the portfolio at the end of the short

period of time is known with certainty. I.e.

∆

c

is the number of units of the under

lying one should hold for each

option shorted if one wants to

obtain a riskless portfolio.

This is exactly the same reasoning as

in the binomial asset pricing model!

However, there is one important differen

ce between the binomial asset pricing

model and the BS model.

In the BS model, the position that is set up is

riskless for only a very

short period of time

.

Derivative securities: Options - Black-Scholes modelBlack-Scholes model: Main ideas