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51 Cards in this Set

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Who wrote the Theory of options in stocks and shares (1877)? What was its contribution
Charles Castelli
sought to explain to the public the hedging and speculation aspects of options. Not very much math in it very conceptual
Who wrote Theorie de la speculation (1900)?
Louis Bachelier
was the first work that sought to value derivative assets. contained the first profit and loss diagrams.
What were the middle years in option pricing?
Early to mid 1960's
What were the contributions to option pricing of Paul Samuelson?
wrote Brownian motion in the stock market which refered to Bacheliers earlier work.
wrote rational theory of warrant pricing
What were the contributions to option pricing of Richard Kruizenga?
wrote dissertation called put and call options:a theoretical and market analysis.
What were the contributions to option pricing of James Boness?
wrote dissertation: A theory and measurement of stock option value
he was close but had the risk free rate wrong.
Who wrote The random character of stock market prices?
Paul Cootner
What is the Black Scholes Option Pricing Model?
developed in 1973 correct model for pricing a call option- developed by Fischer, Black, and Myron Scholes
Why was the Black scholes revolutionary?
because it works, better than CAPM and constant dividend growth model. Improved version of the boness model. Proof of the the risk free rate as the correct discount factor.
What is financial engineering?
building a product with option like characteristics that is tailored to the needs of a specific customer
What is arbitrage?
riskless profit, doesn't last long
Why is Finance sometimes called the study of arbitrage?
the theory of finance is that risk and expected return are proportional, so we would not expect to find riskless profit opportunities. If they occur the market will act quickly to eliminate the arbitrage and bring the prices back into equilibrium.
Why are some arbitrage opportunities forgone?
The cost of doing them to high or the arbitrage is out of reach due to some impediment to free trade or some other restriction
What does arbitrage suggest about the pricing of equivalent assets in a well functioning marketplace?
equivalent assets should sell for the same price-equilibrium
we can solve for what an option price must be for arbitrage to be absent.
What is put/call parity?
the theory that call prices should exceed put prices by about the riskless rate of interest when the options are at-the-money and the stock pays no dividends
What are the inputs to put-call parity?
call price, put price, stock price, interest rate, and time
How does the profit loss diagram for a covered call compare to a short put?
They are identical
(they start at a set loss and level to a striaght line)
Decribe the profit/loss diagram for a long put combined with a covered call?
it is a riskless position a straight line earning the riskless rate of interest
What other combination creates a riskless position?
The combination of a short put, a short stock, and a long call.
What happens if a riskless position s-s+c-p- Sr/(1+r)=0 exists?
arbitrage is present, arbitrage profits will be exploited and become zero
Explain S-S +C -P -Sr/(1+r)=0
S-is the bank loan to buy the stock
S-buying the stock
c-writing the call
p-buying the put
Sr/(1+r)-repaying the bank loan
why is the interest charge (Sr) divided by the quantity (1+r)?
since the interest will be paid in the future it needs to be discounted to the present value.
simplify this equation
S-S +C -P -Sr/(1+r)=o
1. C-P-Sr/(1+r)=0
2. C-P=Sr/(1+r)
3. C-P/S=r/(1+r)(approx=to r)
Suppose the interest rate is 5% what is the difference on a one year call and put premium on a 25 stock?
1. c-p/s=.05/1.05=4.76%
2. c-p/25=4.76%
3. c-p=4.76%(25)
4. c-p=$1.19
According to put/call parity the at-the-money call premium should ______ the put premium.
exceed
What will happen between the at-the money call premium and put premium as the price of the stock goes up, as interest rates rise, or as time to expiration lengthens?
the difference between the premiums will become greater.
With a nondividend paying stock an at-the-money call should sell for _____ than an at-the-money put
more
When is the stock price equal to the strike price?
when its at the money
How is this formula different c-p=s- k/(1+r) from
(c-p)/s=r/(1+r)
because you are borrowing the present value of the strike price K/(1+r)
What is important about this formula C-P=S-K/(1+r)?
if you know 3 of the components S C P R you can solve for the equilibrium value of the fourth (assuming no dividend)
What is the Law of one price?
without arbitrage, equivalent financial claims should sell for the same price.
Suppose the actual put value is $3.00 and the value of the put from the formula is $3.31, what does this tell us?
This means the call price is too high (overvalued) or the actual put price of $3.00 is too low (underpriced)
Can you take advantage of option price discrepency?
Yes
Buy the underpriced and sell the overpriced
in what situation can we solve for the call value without the put value?
If we know about the possible future paths the stock price might take.
What is the Binomial option pricing model?
a model to find the value of puts and calls from future stock price paths.
Why is the binomial pricing model important?
-shows the relationships of stock values and option prices
-a predeccessor to Black Scholes
-can use it to check Black Scholes
-can use it when black scholes cannot be used
How do you set up the binomial pricing model
present-
S0-N*C solve for c

future portfolios-
S1-(S1-k)N=S1 solve for n


K=S0
What does the N represent in the Binomial Pricing Model?
how many options
How do you solve for N
S1-(S1-k)N= S1(price drop)
How do you solve for call price in binomial pricing model?
Take current stock price-(N*C)(1+r)= S1 (price drop)
plug in N and solve for C
How do probabilities affect the price of an option?
They don't option prices are independent of the expected return on the stock.
Why do we set S0-NC*(1+r)=S1 equal to the smaller of the future values?
Because either path will result in this as the portfolio value.
This is the risk free outcome
Should the put option sell for the same price as the call option in the Binomial pricing model?
No call prices are higher
c-p/s=risk free rate
if the call and the put are at the same price?
the call is too low and the put is too high
What do we know about option price relative to the probabilities associated with future stock price and expected return on the stock?
the option price is not related to either one
option prices are based on volatility
What is binomial put pricing?
setting up an arbitrage relationship with puts rather than calls
(Puts are added)
How do you solve for N in binomial put pricing?
set the two future portfolio values equal to each other and solve for N
S1=S1+N(K-S)
compare why volatile assets are more expensive to a car insurance policy?
drivers with more accidents and tickets pay a higher premium.
What is the effect of less time to expiration on call price?
it lowers it
What is pricing logic?
A riskless investment should earn the riskless rate of return or arbitrageurs will quickly act
C=S0 (prob 1)-K e^-Rt(prob 2)

explain the inputs
K is the strike price
S0 is the current stock price
(prob 2) is the prob the option will be in the money at expiration
(prob 1) is the prob that the option will be in the money at expiration adj for the degree in the money