What follows below is a Problem set 9 Q&A with a Finance 4335 student…

Hi Dr. Garven,

After working on problem set 9, I came across issues with 1d and question about problem 2.

On 1d – I attempted to solve for N(d1) and N(d2) using the call equation, but was never able to get to an answer due to too many variables. I did notice that the numbers for scenario d are almost all the same as scenario A. Would this make the volatility the same? If not, how am I supposed to solve without being able to calculate N(d1) and N(d2)?

On problem 2, I solved using dt = 1/6 for all parts. I noticed that the question mentions the options expire in 6 months making T = .5 , but I did not see a need for this in calculations. Is that correct or would it make dt=1/12 instead?

Any guidance you can provide is great.

Thank you!

Dear Finance 4335 student, here are Dr. Garven’s answers to your questions:

1D. Here, you are asked to calculate the standard deviation, which requires computation by trial and error (preferably via Solver, although a simple linear interpolation would suffice as well). Since 1) all parameter values for Scenarios A and D are the same except for option prices and volatility, and 2) Scenario D option prices are lower than Scenario A option prices, this implies that volatility *must also* (because of the positive relationship that exists between option prices and volatility) be *lower* under Scenario D compared with Scenario A.

2. Since the time to expiration is 6 months and each timestep lasts for 2 months, this is a three timestep problem.

See you on Tuesday,

Dr. Garven