The current price of Chipotle is $50. There are European and American put and ca

Question

The current price of Chipotle is $50. There are European and American put and call options written on Chipotle The expiration date for all these options is in 2 months. The effective risk-free rate of interest over a month is .001 (ie, 1%) per month for the next 2 months (note: this is not the annualized rate.) In order to capture the volatility of Chipotle, assume that in any month Chipotle's stock price will either rise 1096 or fall 1596. 1. Write down the possible evolutions of the stock price of Chipotle on the binomial tree below: t-0 t-1 t-2

Explanation / Answer

The size of upmove ie U=10% = 1.1
The size of downmove ie D=15% = 0.85

Probability of upmove = 1+Rf-D / U-D = 1+0.001-0.85 / 1.1-0.85 = 0.151 / 0.25 = 0.604
Probability of down move = 1-U = 1-0.604 = 0.396

See excel for the tree:

t=0

t=1

t=2

60.5

55

50

42.5

36.125

t=0

t=1

t=2

60.5

55

50

42.5

36.125

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