Question

Consider the following stock put options:

Time to exp. Exercise price Volatility     Option Price

1. 1yr 50                  0.20             $10

2. 1yr                 50                   0.25             $10

3. 2yr                 50                   0.20            $10

4. 3yr                  50                  0.25           $10

Which put option is for the stock with the lowest stock price?

Answer 1

While comparing the years, when the number of years to maturity increase, the premium price increases. To keep the put option premium constant, we'll have to increase the stock spot price. Hence, the stock's spot price must be very high in case of option 3 and 4.

While comparing options 1 and 2, which have the same maturity of 1 year, both have same premium price but different volatility. According to Black Scholes model, if the volatility increases, the option premium increases. To keep the option premium of Put constant with the increase in volatility, stock's spot price must be high. Hence, option 2 stock price must be higher than option 1 stock price.

Thus, the put option with lowest stock price is of option 1, ie, 1 year maturity option with 0.2 volatility.