1Consider the binomial model for an American call an d put on a stock whose price is $60. The exercise price for both the put and the call is $45. The standard deviation of the stock returns is 30 percent per an num, and the risk-free rate is 5 percent per annum. The options expire in 90 days. The stock will pay a dividend equal to 3 percent of its value in 50 days . (a) Draw the three-period stock tree and the corres ponding trees for the call and the put. [7.5 marks] (b) Compute the price of these options using the th ree-period trees. [7.5 marks] (c) Explain when, if ever, each option should be ex ercised

2. ABC is currently trading at $78 per share. Your pre

vious calculation of the

historical volatility for ABC indicated an annual s

tandard deviation of return of 27

percent, but examining the implied volatility of se

veral ABC options reveals an

increase in annual volatility to 32 percent.

There are two traded options series that expire in

245 days as show in the

following table:

X = 75

X = 80

Call

Put

Call

Put

DELTA

0.6674

-

0.3326

0.574

-

0.426

GAMMA

0.0176

0.0176

0.019

0.019

The options have $75 and $80 strike prices respecti

vely. The current 245-day

risk-free interest rate is 4.75 percent per annum,

and you hold 2,000 shares of

ABC.

Construct a portfolio that is DELTA - and GAMMA- ne

utral using the call options

written on ABC. Show all calculations.

BEA380 Assignment 1 1 1A/Example: Put Option*** t=120/4 =30 days=30/365 years; K=80 2 DivAdj=(1.0-0.03)*** days 30 60 90 120 3 S'*(1-0.03) 4 5 K=80 6 1B/Example: Call Option 7 K=80 8 2/Example*** 9 10 11 * Early Exercise 12 13 3/Example*** 14 15 4/Example*** 16 17 S'=S-D1-D2 18 19 20 C=max(C1,C2,C3) 21 5/Example 22 23 24