What volatility should be used for each option series
What volatility should be used for each option series hence the theoretical Black–Scholes price and the market price are similar?
Expert
Though, we have the Black–Scholes formula as a function of volatility for option values, here is no formula for the implied volatility like a function of option value; this must be computed using several bisection, Newton–Raphson, or another numerical technique for getting zeros of a function. There plot these implied volatilities verses strike, one curve per expiration. It is the implied volatility smile. When you plot implied volatility against strike and expiration both as a three-dimensional plot then it is the implied volatility surface. Frequently you will find as the smile is quite flat for long-dated options, although getting steeper for short-dated options.
Otobai Motor Company is currently paying a dividend of $1.40 per year. The dividends are expected to grow at a rate of 18% for the next three years and then a constant rate of 5% thereafter forever. What is the vlaue of its current stock price? Assuming that the discount rate is 10%.{Hint: pages 84-
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