Mathematical Modeling in Finance with Stochastic Processes

88 CHAPTER 2. BINOMIAL OPTION PRICING MODELS

the value of such a cash-or-nothing binary option with payoff $100 at

expiration 2 time units in the future and strike price $100? Assume a

simple interest rate of 10% in each time period.

4. Along strangle option pays max(K 1 −S, 0 ,S−K 2 ) if it expires when
   the underlying stock value isS. The parametersK 1 andK 2 are the
   lower strike price and the upper strike price, andK 1 < K 2. A stock
   currently has price $100 and goes up or down by 20% in each time
   period. What is the value of such a long strangle option with lower
   strike 90 and upper strike 110 at expiration 2 time units in the future?
   Assume a simple interest rate of 10% in each time period.


5. Along straddle option pays|S−K|if it expires when the underlying
   stock value isS. The option is a portfolio composed of a call and a
   put on the same security withKas the strike price for both. A stock
   currently has price $100 and goes up or down by 10% in each time
   period. What is the value of such a long straddle option with strike
   priceK = 110 at expiration 2 time units in the future? Assume a
   simpleinterest rate of 5% in each time period.

Outside Readings and Links:

1. Peter Hoadley, Options Strategy Analysis Tools. A useful link on ba-
   sics of the Black Scholes option pricing model. It contains terminology,
   calculator, animated graphs, and Excel addins (a free trial version) for
   making a spreadsheet model. Submitted by Yogesh Makkar, September
   9,2003.


2. Binomial Tree Option Pricing by Simon Shaw, Brunel University The
   web page contains an applet that implements the Binomial Tree Option
   Pricing technique, and gives a short outline of the mathematical theory
   behind the method. Submitted by Chun Fan, September 10, 2003.