Table of Contents
- 1 What do you use for volatility in Black-Scholes?
- 2 Why does Black-Scholes assume constant volatility?
- 3 What causes volatility smile?
- 4 How is option price volatility calculated?
- 5 Is the volatility smile predicted by the Black-Scholes model?
- 6 What is the Black-Scholes equation for implied volatility?
- 7 Can Black-Scholes be used to determine the value of an option?
What do you use for volatility in Black-Scholes?
Plugging the option’s price into the Black-Scholes equation, along with the price of the underlying asset, the strike price of the option, the time until expiration of the option, and the risk-free interest rate allow one to solve for volatility. This solution is the expected volatility implied by the option price.
Why does Black-Scholes assume constant volatility?
Volatility Skew Black-Scholes assumes stock prices follow a lognormal distribution because asset prices cannot be negative (they are bounded by zero). Often, asset prices are observed to have significant right skewness and some degree of kurtosis (fat tails).
What are volatility smiles describe the key features of volatility smiles and why do you think they exist?
A volatility smile is a common graph shape that results from plotting the strike price and implied volatility of a group of options with the same underlying asset and expiration date. The volatility smile is so named because it looks like a smiling mouth.
What causes volatility smile?
Volatility smiles are created by implied volatility changing as the underlying asset moves more ITM or OTM. The more an option is ITM or OTM, the greater its implied volatility becomes. Implied volatility tends to be lowest with ATM options. Extreme events can occur, causing significant price shifts in options.
How is option price volatility calculated?
16.1 – Calculating Volatility on Excel
- Calculate the average.
- Calculate the deviation – Subtract the average from the actual observation.
- Square and add up all deviations – this is called variance.
- Calculate the square root of variance – this is called standard deviation.
What is option Moneyness?
Moneyness describes the intrinsic value of an option in its current state. The term moneyness is most commonly used with put and call options and is an indicator as to whether the option would make money if it were exercised immediately.
Is the volatility smile predicted by the Black-Scholes model?
The volatility smile is not predicted by the Black-Scholes model, which is one of the main formulas used to price options and other derivatives. The Black-Scholes model predicts that the implied volatility curve is flat when plotted against varying strike prices.
What is the Black-Scholes equation for implied volatility?
The Black-Scholes equation must be solved to determine the implied volatility. The other inputs for the Black-Scholes equation are the price of the underlying asset, the strike price of the option, the time until expiration of the option and the risk-free interest rate.
What is the Black-Scholes model?
The Black-Scholes model is the standard formula that is used for pricing derivatives, especially options. When the implied volatility of options is plotted against the corresponding strike prices, the Black-Scholes model predicts that the curve obtained is flat.
Can Black-Scholes be used to determine the value of an option?
As with any equation, Black-Scholes can be used to determine any single variable when all the other variables are known. The options market is reasonably well developed at this point, so we already know the market prices for many options.