Question 2:

Given a call price, stock price, exercise price, firsk-free return and time to maturity, it is possible to calculate the implied volatility - that is the sigma in the call pricing equation from the previous question that makes the market price and calculated prices of the call option equal. In that sense, it is very much like calculating yeild to maturity or internal rate of return. Once you have the bond pricing equation in the case of yield to maturity, or net present value equation in the case of internal rate of return, it is easy to set up a search for the interest rate, or in the case of the call option the volatility parameter, that makes market price and calculated price equal.

Note, however, that in contrast to the yield to maturity and internal rate of return calculations, where an increas in the interest rate causes the present value of the cash flow stream to drop, an increase in the sigma input to the call option pricing equation will cause the estimated price to increase.

(35 pts)

In [10]:

def implied_vol(C,S,X,r,T): # Fill in the missing code return k, sigma # where k is the number of passes through the search loop and sigma is the # resulting volatility estimate. 

In [ ]:

# Test the function using the call price check figure and other input data (except for sigma) shown # in the previous question.