17.1 Single Period

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Problem. The current stock price of All-Net is $100.00, the potential up movement / period of All-Net’s

stock price is 30.00%, the potential down movement / period of All-Net’s stock price is -20.00%, the

riskfree rate is 2.0% per period, the exercise price of an one-period, European call option on All-Net is

$90.00, the exercise price of an one-period, European put option on All-Net is $90.00, the time to

maturity for both options is 0.75 years (nine months), and the number of periods for both options is 1.

What are the current prices of the call and put?

Solution Strategy. First, calculate the date 1, maturity date items: stock up price, stock down price, and

the corresponding call and put payoffs. Second, calculate the shares of stock and money borrowed to

create a replicating portfolio that replicates the option payoff at maturity. Finally, calculate the price now

of the replicating portfolio and, in the absence of arbitrage, this will be the option price now.

FIGURE 17.1 Spreadsheet Model of Binomial Option Pricing - Single Period - Call Option.

How To Build This Spreadsheet Model.

1. Inputs. Enter 1 in cell B4. This will serve as a switch between a call option and a put option. To

highlight which type of option is being evaluated, enter =IF($B$4=1,"Call","Put") in cell G1

and copy this cell to cell A20. Enter the other inputs into the range B5:B11.

2. Enter Periods and Time. Enter the periods 0 and 1 in cells B14 and C14. The formula for Time

= Time To Maturity * (Period / Number of Periods). Enter =$B$10*(B14/$B$11) in cell B15 and

copy it to the cell C15.

3. Stock Prices. Set the Date 0 Stock Price equal to the Stock Price Now by entering =B5 in cell

B17. Calculate the Date 1 Stock Up Price = Stock Price Now * (1 + Up Movement / Period) by

entering =B17*(1+B6) in cell C17. Calculate the Date 1 Stock Down Price = Stock Price Now *

(1 + Down Movement / Period) by entering =B17*(1+B7) in cell C18.

4. Option Payoffs At Maturity. The formulas for option payoffs are:

o For a Call, the Payoff At Maturity = Max (Stock Price At Maturity – Exercise Price, 0).

o For a Put, the Payoff At Maturity = Max (Exercise Price – Stock Price At Maturity, 0).

Enter =IF($B$4=1,MAX(C17-$B$9,0),MAX($B$9-C17,0)) in cell C20 and copy it to

the cell C21.

5. Create A Replicating Portfolio. For the Replicating Portfolio, calculate the Stock Shares Bought

(Sold) using the Hedge Ratio = (Option Up Payoff – Option Down Payoff) / (Stock Up Price –

Stock Down Price). In cell B26, enter =(C20-C21)/(C17-C18). For the Replicating Portfolio,

calculate the amount of Money Lent (Borrowed) = (Call Down Payoff –Hedge Ratio * Stock

Down Price) / (1 + Riskfree Rate / Period). In cell B29, enter =(C21-B26*C18)/(1+B8). Notice

that replicating a Call option requires Buying Shares of Stock and Borrowing Money, whereas a

Put option requires Selling Shares of Stock and Lending Money.

6. Calculate the Option Price Now. In the absence of arbitrage, the Option Price Now =

Replicating Portfolio Price Now = Number of Shares of Stock * Stock Price Now + Money

Borrowed. In cell B20, enter =B26*B17+B29.

We see that the Binomial Option Pricing model predicts a one-period European call price of $17.25. Now

let's check the put.

FIGURE 17.2 Spreadsheet Model of Binomial Option Pricing - Single Period - Put Option.

7. Put Option. Enter 0 in cell B4.

We see that the Binomial Option Pricing model predicts a one-period European put price of $5.49.