Chapter 11 - Introduction To The Valuation Of Derivative Securities Flashcards
Derivative
A derivative is a security or contract which promises to make a payment at a specified time in the future, the amount of which depends upon the behaviour of some underlying security up to and including the time of payment.
Arbitrage opportunity
An arbitrage opportunity is a situation where we can make a certain profit with no risk.
It means that:
(a) we can start at time 0 with a portfolio that has a net value of zero (implying that we are long in some assets and short in some others). Usually called a zero-cost portfolio
(b) at some future time T:
- the probability of a loss is 0
- the probability that we make a strictly positive profit is greater than 0
Principle of no arbitrage
The principle of no arbitrage states that arbitrage opportunities do not exist.
Law of one price
The law of one price says that any two portfolios that behave in exactly the same way must have the same price. For if this were not true, we could buy the “cheap” one and sell the “expensive” one to make an arbitrage (risk-free) profit.
Intrinsic value
The intrinsic value of a derivative is the value assuming expiry of the contract immediately rather than at some time in the future.
Time value
The time value of a derivative is the excess (or the shortfall) of the total value of an option over its intrinsic value.
European call option
A European call option gives its holder the right, but not the obligation, to buy one share from the issuer of the contract at time T and at the strike price K.
European put option
A European put option gives its holder the right, but not the obligation, to sell one share to the issuer of the contract at time T and at the strike price K.
American options
American options are similar to their European equivalents, except that they can be exercised at any time up to expiry T.
Factors affecting option prices
- Underlying share price
- Strike price
- Time to expiry
- Volatility of the underlying share
- Risk-free interest rate
- Dividend rate (in case of a dividend-paying share)
What is the simplest form of derivative contract? In wat sense is it simple to price?
A forward contract is the simplest form of derivative contract. It is also the most simple to price in the sense that the forward price can be established without reference to a model for the underlying share price.
What constraint is applied when determining the forward price?
The forward price K should be set at a level such that the value of the contract at time 0 is zero (that is, no money changes hands at time 0).
State a formula for the fair forward price
K = So e^rt
How can the put-call parity be used in connection with arbitrage?
If the result was not true then this would give rise to the possibility of arbitrage. That is, for a net outlay of zero at time t we have a probability of 0 of losing money and a strictly positive probability (in this case 1) of making a profit greater than 0. In this case, the failure of put-call parity would allow an investor to sell calls and take a cash position and buy puts and shares, with a net cost of zero at time t and a certain profit at time T.
What does the put-call parity relationship not tell us?
In contrast to forward pricing, put-call parity does not tell us what ct and pt are individually: only the relationship between the two. To calculate values of ct and pt we require a model.
