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Exotic Options with the Binomial Model

Exotic Options with the Binomial Model. Zhang Zhuozhuo Calum Johnson Waldemar Pietraszkiewicz. Binomial Model. The binomial model is a very useful and popular technique for pricing an option.

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Exotic Options with the Binomial Model

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  1. Exotic Options with the Binomial Model Zhang Zhuozhuo Calum Johnson WaldemarPietraszkiewicz

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

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

  7. Binary options • Diagram of cash-or-nothing call and put options, with a payout 10 and strike price 50. • CallPut

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

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

  10. Power options • 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 whereS – a stock with given price, K – strike price

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

  12. Solution

  13. Solution

  14. Conclusion • 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. The End Any Questions?

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