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Consider the call option above. After each period, there is a 40% chance for the stock price to go up, 25% chance to stay the same, and 35% chance to go down. Assume μ is the same as the risk-free rate. Stock price is $62. Call option price is 5.83 (calculated from previous problem) (a) Find the up-factor u and down-factor d = 1/u.

This is the second part of the problem. First problem asked to find option price which i did and it came out to $5.83 using excel. every problem we were given we were always given u and d. this one gives percentages and asking to find u and d. i don't even know where to start to find u.

manny singh
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    So $u$ and $d$ are risk-neutral probabilities - are the percentages the real-world probabilities? In any case you can right a set of equations for the top and the set of equations for the bottom plus closure condition $p_u + p_d + p_s = 1$ where $p_s$ is the probability of staying the same. – Chinny84 Apr 25 '17 at 02:15
  • Ok so i put .40+.35+.35=1 how do i get u from it? And no the probabilities are not real world. – manny singh Apr 25 '17 at 02:21
  • Setting those equation will give me 3 probabilities that is the next question i have to answer which i can do. But how do i find u? – manny singh Apr 25 '17 at 02:22
  • Two things 1) i assume the tree is recombining (if so then see here and compute the $u$ and $d$ after using your probabilities to compute the variance) 2) I lied it was just the one thing. – Chinny84 Apr 25 '17 at 02:33
  • Going backwards in this to solve option price. That link doesnt help it states how to solve u using sigma, here sigma is not given just the probabilities. – manny singh Apr 25 '17 at 02:35

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