Question

Check my work You observe a premium of $46.00 for a call option on Birdwell Enterprises common stock, which is currently selling for $46. The strike price on the call option is $47. The option has four months to maturity. The stock pays no dividends. The current risk-free interest rate is 3.50%. What is the implied volatility of the stock? (Round your answer to the nearest whole percent.) Implied volatility %

Answer 1

Let me tell you upfront that there is something not correct with the question. A call premium of $ 46.00 on a stock with current price of 46.00 is nearly unbelievable. Anyways, I have proceeded with the solution below. The answer is exceptionally high. Please don't down vote merely because of this.

Implied volatility is 1515%

Please try this answer and let me know in the comments section.

Black Scholes formula:

Value of call = S N (d1) - Kert Nd2) where di = od d2 = d1 - 0 Vt

We will populate the inputs and run a goal seek in excel to get the answer.

Please see the screenshots below. I have set up the Black Scholes model using an arbitrary volatility of 5% in the green colored cell. The output is in yellow colored cell. We run goal seek.

Output of goal seek:

Goal Seek ? X 1 7 Inputs 8 S gt 100 11 K 12r 13 Output 14 d1 15 d2 16 N(d1)= 17 N(D2) 18 Value of the call option, C 46.00 Set cell: 018 0.33 4 months = 4/12 years To value: 5% By changing cell: $C$101 47 Strike price of call option OK Cancel 3.50% Values Formula Used -0.326417857 =(LN(C8/C11)+(C12+C10^2/2)*C9)/(C10*SQRT(C9)) -0.355285371 =C14-C10*SQRT(09) 0.372054114 =NORMSDIST(C14) 0.361187907 =NORMSDIST(C15) 0.335558 |=C8*C16-C11*EXP(-C12*09)*C17

gt 7 Inputs 8 s 46.00 0.33 4 months = 4/12 years 10 O 1515% 11 K 47 Strike price of call option 12r 3.50% 13 Output Values Formula Used 14 d1 4.371671821 =(LN(C8/C11)+(C12+C10^2/2)*(9)/(C10*SQRT(09)) 15 d2 -4.373921992 =C14-C10*SQRT(09) 16 N(d1)= 0.999993835 =NORMSDIST(C14) 17 N(d2)= 6.1017E-06 =NORMSDIST(C15) 18 Value of the call option, c. 45.999433 |=c8*c16-C11*EXP(-C12*09) *C17