Black Scholes calls/puts/options

Question

I'm working on the Black Scholes method for calls/puts/options. Using the table below.

I don't know how to answer these two questions:

"What is the option's speculative value at $215".

"What is the implied volatility on the call option assuming it is currently trading for $7.25"

My table:

Stock Price Call Price Intrinsic Value

$7.25 2.32

$180 .11 -

$185 .30 -

$190 .69 -

$200 1.44 -

.....

$215 10.24 7.00

$220 13.99 12.00

... and so on...

Answer 1

We will ignore interest and dividends as you have given neither. Your chart is a bit misleadiing (columns don,t line up) if the stock price were 208 the stock would be at the money. at 215 it would have time value of 3.24 and intrinsic value of 7. at 2.20 the intrinsic value i 12 an TV is 1.99. The TV of the 200 strike is 1.44. If TV is symmetric about ATM strike the the stock price is closer to 220 than it is to 210. The option is currently in the money. A good guess for the time value with the stock price at 210 is EXP(ln(3.24) +(ln(3.24)-ln(1.99)) = 5.24. At a stock price of 2.10 intrinsic value is 2 and TV = 5.24 which is roughly 7.25. So the stock is trading around 210. We can not determine implied volatilituy from Black Scholes without knowing the maturity. If there is another column which I don't see. I have traded option for the big banks and hedge funds for more than 30 years. If you need an expert in options you would be hard pressed to find anyone better.