Chap 7 Going from One Step Per Time Period to Many

Pascal’s triangle – a building block

 Starting value is positive

 Assuming that V 0 = $20, that u = 1.2, that X = $21, and that the risk-free rate equals 10 percent.

 All of the states of nature where n ＜ a have zero payoffs because the call option will not be exercised.

 V 0 equal $100, let u = 1.5 (i.e.,150% per year), the exercise price be $250, the life of the option be seven periods, and the annual risk-free rate equal 10 percent, we have the parameters of Exhibit7.6.  There are eight end states.  The number of up movements ranges from zero to seven.  Given an exercise price of $250, the option is in the money only for the three uppermost states where n, the number of up movements, is 5,6, or 7.  Therefore, the value of the border state, state a, is 5.  The risk-neutral probability is p = ( )/( ) = 0.52.

The limit of the binomial option pricing model is the Black-Scholes formula

 Step 1 defines the uppermost ending branch of the tree, the first of two seed cells.  Step 2 copies this cell down column I from cell I32 to cell I39.  Step 3 is the coding of the first cell, B32 as the value of the option if exercised.  Step 4 is to copy the cell across the first row up to but not including the last column (up to cell I31)  Step 5 defines a second seed cell, C33. It is coded as an “if statement.”

 Step 6 copies cell C33 across the columns up to and including cell H33