1. Zhang Zhuozhuo Calum Johnson Waldemar Pietraszkiewicz

2.  The binomial model is a very useful and popular technique for pricing an option.  The binomial option pricing formula is based on assumption that the stock price follows a multiplicative binomial process over discrete intervals.

3.  The rate of return of the stock over each period can have two possible values: u-1 with the probability q, or 1-d with the probability 1-q.

4.  The Cox-Ross-Rubenstein formula is the most popular formula for constructing binomial trees so it is what we use in our model.  where Δt is the time interval between observations of the price and σ the volatility.

5.  Binary options are options with discontinuous payoff.  The most common Binary options are: ◦ Cash-or-nothing call ◦ Cash-or-nothing put ◦ Asset-or-nothing call ◦ Asset-or-nothing put

6.  Binary Call and Put Options pay either: ◦ a fixed cash settlement amount or, ◦ nothing at all, depending on the underlying price at expiration.

7.  Diagram of cash-or-nothing call and put options, with a payout 10 and strike price 50.  Call Put

8.  Cash-or-nothing options are valued by: where Q is the amount paid at time T and r is the risk-free interest rate.

9.  Asset-or-nothing options are valued by: where S is the initial stock price, q is the dividend rate.

10.  Power options are exotic options in which the payoff is multiplied by some power x of the stock.  For a call power option the payoff is  For a put power option the payoff is where S – a stock with given price, K – strike price

11.  The value of a power call option is given by:  while the value of a put is:  where and

14.  We presented: ◦ information about a binomial model which valuates cash-or-nothing and asset-or-nothing options ◦ the theoretical research and presented information about the binomial model and binary options ◦ a program written on MS Excel which valuates the European cash-or-nothing and asset-or-nothing options.

15. Any Questions?