Case Objective

To understand delta hedging in the binomial option pricing model.

Key Concepts

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

Case description

There is one stock, one zero-coupon bond, a put option and a call option.  Both options are European style options.  The market lasts for three periods.  The stock price is initially 400.  The uptick parameter is 1.090513 and the downtick parameter is 0.917.  The interest rate each period is 1%.  Both options expire at the end of the third period, and have a strike price of 410.   Prices for the stock are fixed at 400 initially, and then follow the binomial process.   You are endowed with an initial short position in one of the two options and a positive amount of cash.

Case Data

The following table shows the cash flows from each security at the end of period 3 depending on the number of upticks and downticks that occur.   Thus, “udd” in the table means that there was an uptick followed by two downticks.  There are no cash flows in intermediate periods.

 uuu uud udu udd duu dud Ddu ddd Stock 518.74 436.21 436.21 366.80 436.21 366.80 366.80 308.44 Bond 103 103 103 103 103 103 103 103 Put 0 0 0 43.20 0 43.20 43.20 101.56 Call 108.74 26.21 26.21 0 26.21 0 0 0

In this trading case you are only permitted to trade in the Stock and the Bond.  You are a price taker for the stock and as such do not face any liquidity constraints.  You are free to both make and take market in the bond.  That ism, the trading crowd can discover prices for the bond.

In the trading period market securities are traded using market cash.  Three trading periods are equivalent to one trial.  If at the end of any trial you have a closing balance of \$5000 market cash then you will earn \$8 grade cash.  If you have a closing balance of market cash that is lower than \$5000 then you will earn zero grade cash.  Any amount of market cash that is greater than \$5000 and less than or equal to \$10,000  earns grade cash as follows:

You trade a number of independent trials and a record of your cumulative grade cash is maintained.