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Social ScienceThe current price of XL Corporation stock is $40. In each of the next two years, this stock price can either go up by $15.00 or go down by $15.00. XL stock pays no dividends. The one-year risk-free interest rate is 15% and will remain constant. Using the binomial pricing model, calculate the price of a two-year American straddle option on XL stock with a strike price of $40.
The current price of XL Corporation stock is $40. In each of the next two years, this stock price can either go up by $15.00 or go down by $15.00. XL stock pays no dividends. The one-year risk-free interest rate is 15% and will remain constant.
Using the binomial pricing model, calculate the price of a two-year American straddle option on XL stock with a strike price of $40.
Expert Answer
Calculate the probabilities:
p is 57.37% and 1-p is 42.63%.
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S55 ($40+S15) P $40 1-P $35 ($40-S15) (555x(P)+(S35x (1-P) =(s40x (e15 $55P $35-$35P = $46.4733 65 11.473365 P = 20 =0.573668 or57.3 7% 1-P [1-57.37% =42.63%
Create a binomial model:
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$70 ($40+$15+$15) $55 ($40+$15) Stock Price $40 Strike Price = $40 $40 ($40+$15-$15) $35 ($40-$15) $20 ($35-$15)
Calculate the Price of the Option:
Note that 2.71828 denotes the numerical value of exponential (e).
Excel Spreadsheet:
...
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B 1Strike Price 2 Probability 3 1-Probability 4 Payoff at $40 5 Payoff at $20 6 Riskfree Rate 7 Price of Option $40 57.37% 42.63% $0 $20 15% $2.8738
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