The Black-Scholes Option Pricing Model Flashcards
What is the difference between the black-scholes model and the binomial model? What are the assumptions of the black scholes model?
The binomial model deals with time in a discrete way where is the BS model deals with time in a continuous manner. Assumptions include that there are no taxes transaction costs or no dividends paid, accounts only for European stocks not American, risk neutral pricing due to continuous time and assumes theta and sigma are constant. Stock prices behave randomly and tend to a log normal distribution.
What is the main advantage and disadvantage of closing out a held call before the expiration date?
Main benefit closing out a held call for it expires is that the option will be valued more if everything remains unchanged as it will have greater time value. However you do lose the chance of making more money if the stock price moves in your favour.
Why does a strap indicate you have a more bullish outlook on the economy than if you were to have taken a straddle position?
A strap (bullish strategy) involves purchasing more calls than put so if the market goes up, you profit quicker but the downside is that you have more to lose if the market decreases in value. A straddle (bearish strategy) is equal number of calls and put and you have a neutral outlook focused on volatility can profit if the asset price moves significantly in One Direction or the other.
If the stock price is 44 the exercise price is 40. The price in the market is $1.54 and the black scholes price using 0.28 as the volatility is 1.11, what will the implied volatility be?
The implied volatility will be higher than 0.28 as it is the output when the input into the BS model results in the market price of an option. Therefore as the market price is higher than the black Scholes price, the implied volatility has to be greater than 0.28.
The binomial Price will theoretically equal the BS price which of the following conditions?
- When the option is in the money
- when the implied volatility is the same
- When the number of time periods is large
- When the option is at the money
- when the number of time periods is large. This is because as a number of time periods increases the binomial model begins to closely approximate the continuous nature of the BS model. As the number of time periods approaches infinity, the binomial model converges to the Price arrived in the BS model.
What can you do if you notice the implied volatility of an option is much higher than the historical volatility calculated? What can you do to profit from this information?
You could deduce that the option is overpriced and therefore short the call/put and go long/short in the stock.
What are the two primary components that make up a stochastic process?
Pt = Pt-1 + et ; deterministic component and random component determinist follows a predictable pattern whereas the random introduces uncertainty and unpredictability.
Out of the variables in the BS model, which is the most critical?
Volatility is the most critical as options are very sensitive to volatility changes plus it is the only variable that cannot be directly observed and therefore is susceptible to being miscalculated.
What is risk neutral valuation?
The investor does not care about risk when making a decision and where their money goes rather they care more about the returns and review volatility as not a bad thing as it will give them greater potential to make a profit.
Is it difficult to ensure an option position is risk-free to stock Price changes?
Yes in reality it is hard to maintain a risk free position as it requires constant and continuous Delta hedging. Even if the stock prices don’t change, time is continuously changing and so do the Delta values and therefore your Delta neutral position.
