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42 Cards in this Set
- Front
- Back
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What is the importance of the BSOPM?
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we have a good understanding of what options should sell for.
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What equation is it related to in physics?
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Heat transfer equation
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What is the equation for the Black Scholes option pricing model?
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C=SN(d1)-K(e^-rt)N(d2)
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What happens to the value of a call option if the strike price decreases?
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the call option premium goes up.
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What happens to the value of a call time until expiration increases
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for both puts and calls the premium increases
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How does the current stock price affect call premium?
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the higher the stock price the more a given call option is worth.
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How does the volatility of the stock returns affect the call premium?
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the greater the price volatility of an asset the greater the call premium
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What is sigma
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It is a volatiltiy estimate
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Wjat is the annualized standard deviation?
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it is the volatilty used in Black Scholes
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Past volatiltiy is called?
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historical, statistical, or realized volatility
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Does the BSOPM adjust for cash dividends?
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no listed stock options are not adjusted for cash dividends.
but dividends indirectly decrease call prices. |
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What happens to the stock price on the ex dividend date?
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the ex dividend date is two days before the date of record, you must buy before this date to get the dividend. The stock price decreases on this day.
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What happens to the call price when the riskless interest rate increases?
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The higher the interest rate the higher the option premium
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What is the assumption in bsopm regarding the payment of dividends?
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that it pays no dividends
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Why do we use the natural logirithm in black scholes?
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it assumes continous compounding of the interest rate
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How do you plug in a stock that pays a dividend into the black scholes?
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you subtract the pv of the dividend from the current stock price and use that for s
pv of div=div*(e^-rt) |
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What is the Merton model extension?
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it accounts for dividends as a continous stream rather than a discrete payment
it produces the same exact result as pv of div in B/S |
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Does the BSOPM value europeon or american options?
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Europeon-can only be exercised on the expiration date
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What about dividends paid after the expiration date?
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They do not affect the price they are immaterial
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What does the BSOPM assume about market efficiency?
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it assumes mkt informationally efficient, meaning people cannot predict the direction of the market or a stock.
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Put/call parity states that regardless of whether you are bullish or bearish you will...
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agree on the option premium. Premiums are not affected by expected return on the stock
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What are the assumptiona about transaction costs?
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no transaction costs
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What are the assumptions about interest rates?
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that they remain flat/constant
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What is the assumption about the distribution of stock prices?
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that they are normally distributed
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What is the value of an call option?
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the difference between the expected benefit from acquiring the stock outright and paying the exercise price on expiration day
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SN(d1) means
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cash inflow- weighted expected stock price
N(d1)is the prob of being in the money adjusted for how much in the money |
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K(e^-rt)n(d2) means
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cash outflow-time value of money adjusted for expected payment @ exercise
N(d2)prob of being in the money |
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What is implied volatiltity?
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the value of sigma that causes model call premium to equal the actual call premium
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How do you solve for implied volatility?
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put in the call premium and back it out
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What does implied volatilty tell us?
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it tells us what is going to happen to the market (what the market thinks the volatility will be until expiration) only if we think the call premium is correct
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What is the difference between historical versus implied volatility?
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historical is what has happened and implied is what the model implies the volatility will be
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Is there a relationship between historical volatilty and implied volatility
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yes an ex ante (before the fact) and a ex post(after the fact)
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What did strong and dickerson find about implied volatility?
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the current level of implied volatility contains both an ex post component and an ex ante component
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Can you compare the dollar cost of two different options?
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no their are to many variables that can differ
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What is a volatiltiy smile?
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it is a contradiction to the Black Scholes which assumes a constant volatility across all strike prices
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Why the term smile?
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because of the curve you get when plotting implied volatility against strike price
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How can the Black Scholes be used to find the price of put options? equation?
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With put/call parity
P=K(e^-rt)N(-d2)-SN(-d1) |
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What is the relationship between S, K, T, Std Dev, and R (Risk free rate)and the price of a put?
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Stock Price-negative/inverse relationship
k-positive relationship t-positive relationship std dev-positive (want more volatility R-negative/inverse |
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How is B/S at pricing deep in the money or deep out of the money
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it will misprice them
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how is B/S at pricing options that have very high or low volatility
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it will misprice it is at its best with moderate volatility
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How is B/S at pricing options that only have a few days to expiration?
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it will misprice
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When does BSOPM have the best accuracy?
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for options that are at the money and within the next striking price on either side of the stock price.
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