The Greeks and Volatility

Can implied volatilities be expected to vary for options on the same stock with the same exercise price but different expiration?

- Yes - The volatility is supposed to be the volatility of the stock over the life of the option so it can indeed vary with a different time to expiration

What factors contribute to the difficulty of making a delta hedge be truly risk-free?

- inability to trade at no cost over a very small time interval - Transaction costs discourage frequent trading and make it impossible to actually earn the risk-free rate

Vega

- measures the change in the option price for a change in the volatility - nearly linear when the option is at-the-money - option price is very sensitive to the volatility

Why and how are implied volatilities used to quote option prices

- option price could be quoted by stating its implied volatility, while another option on the same stock could be quoted by stating a different implied volatility - then use Black-Scholes-Merton to find actual price - easier to see more expensive options

Theta

- relationship between the option price and the time to expiration - European calls, the theta is negative meaning that the option price will fall as expiration approaches

Gamma

- the change in delta for a given (again very small) change in the stock price - measures the risk involved in not adjusting the hedge ratio to equal the delta - large when the option is at-the-money and nearly zero when the option is deep in- or out-of-the-money

Delta

- the change in the call price for a given change in the stock price - applies only when the stock price changes by a very small amount - hedge ratio - 0-1, 0 out-of-the-money, 1 in-the-money

Implied Volatility of a particular option is substantially higher than the theoretical volatility. What action should you take?

-If you accept the "theoretically correct" standard deviation as the true volatility, then the market price of the option is implying a higher volatility of the stock than is reasonable - implied volatility obtained by setting the Black-Scholes-Merton price equal to the market price is higher than it should be - mkt price too high - selling overpriced option with purchase of stock

Can implied volatilities be expected to vary for options on the same stock with the same expiration but different exercise price?

-implied volatilities should not vary for options on the same stock with the same expiration and different exercise prices - actually multiple volatilities, which is often referred to as the volatility smile or skew

Rho

-the change in the option price when the risk-free rate changes - nearly linear and is fairly weak - the call price is not very sensitive to the risk-free rate