Problem Set 9 helpful hints – part 2 of 2

Here are some helpful hints for Problem Set 9, problem 2:

Scenario A requires solving for call and put option prices using the Black-Scholes-Merton option pricing formulas. See the Part 2 option pricing lecture note, page 21, for a numerical illustration of how to do this.
Scenario B requires finding the current price of the underlying asset, where the call, put, and exercise prices are all given. Solve the put-call parity equation ( $C + K{e^{ - rT}} = P + S$ ) for S.
Scenario C requires finding the exercise price, where the call, put, and underlying asset prices are all given. Solve the put-call parity equation for K.
Scenario D requires finding $\sigma$ for a call option worth $2.38 and a put option worth $3.60. Feel free to use the Black-Scholes spreadsheet from the course website, or better yet, create your own Excel spreadsheet in which you solve for the call and/or the put by varying $\sigma$ (this can be accomplished either via trial and error or better yet, by using either Solver or Goal Seek). An important lesson you’ll learn from this part of problem 2 is that call and put option prices are positively related to $\sigma$ .