Case Objective

To understand the two-period binomial option pricing model.

Key Concepts

Binomial option pricing model; option replication; dynamic trading strategies.

Case description

There is one stock, one bond, a put option and a call option.  Both options are American style options. Each trial of the trading case covers two months of calendar time.  The FTS markets are open for the first trading day of each month and during this day each American option can be exercised if desired.  To exercise you need to put in the quantity and then click on the button Exercise (see Generic Trading Screen below).  Actual exercise is executed at the end of the current trading period and the number to be exercised is indicated with an additional /num in relevant position cell.

That is, at the end of the first trading day time “flashes by” and then end of month one realizations occur.  Shortly after, the first trading day of the second month opens.  The stock price at the beginning of the first month is 20, and at the end of the month, it either goes up to 40 or down to 10.    You can trade at this realized stock price (i.e., either 10 or 40) during the first day of month two.  At the end of the second month, the stock value again either doubles or is halved (i.e., three possibilities 5, 20, or 80 see below).  At the end of each trading day the interest rate is 1% for the remaining  month.  That is, any surplus (shortfall) of cash earns (pays) 1% per month.  Both options expire at the end of month two, and have a strike price equal to 25.

In summary, the price of the stock is fixed at 20 at the beginning of month 1, and then at either 40 or 10 at the beginning of month 2, depending on whether an uptick or downtick was realized.  An up or down tick is equally likely.  All other prices are determined by the traders as a result of their limit and market orders.

Case Data

The following binomial tree shows the cash flows from each security at the end of period 2.   There are no cash flows in period 1.

The objective is to accumulate as much grade cash per trial (two trading periods) as possible.  Your realized final market cash position determines your grade cash as follows: