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The current price of a non-dividend paying stock is $35. Use a two-step tree to value...

The current price of a non-dividend paying stock is $35. Use a two-step tree to value an American put option on the stock with a strike price of $33 that expires in 12 months. Each step is 6 months, the risk free rate is 6% per annum (continuously compounding), and the volatility is 15%. What is the option price? Show work in detail and use a tree diagram (Use 4 decimal places).

Solutions

Expert Solution

Parameters of Option Binomial Model –

There are three parameters of Option Binomial Pricing Model

  • up factor (u)
  • down factor (d)
  • probability (P)

up factor and down factor used to calculate rise in price and fall in price of underlying assets in one period. Probability is measure probability of rise in price and (1-P) is probability of price fall.

Cox-Rox-Rubinstein has suggested following formula to calculate these factors,

And,

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

Cell reference -

Thus, Value of American Put option = $0.6486

Please note - Early exercise of this put option is not beneficial as at Node-C, the payoff is less than the value of option.

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.


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