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Criado por mho1
aproximadamente 9 anos atrás
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Setting up the continuous time model
we wish to look at the return on investments... how should this be modeled?
For the Black-Scholes model we model the return on investments...
contingent claim
(continuous time)
ECC
Portfolio
(continous time)
Value of a portfolio
(continuous time)
A portfolio is said to be replicating if....
and self-financing if....
In out B-S model, self-financing means:
Stochastic exponential and SDE it satisfies
What is the probability measure that we define in order for the discounted stock price to be a martingale?
The probability measure for which the discounted stock price is a martingale
What type of stochastic process does the discounted stock price follow?
Claim martingale
Apply the martingale representation theorem to the claim martingale
Black-Scholes Portfolio
Value of the Black-Scholes portfolio
arbitrage price of an option under the B-S model
Derive the B-S pricing formula for a general ECC
Black-Scholes pricing formula for a general ECC, X
Black-Scholes pricing formula for a European Call option
Black-Scholes PDE
Delta hedging
Foreign Exchange set up
What does the market look like from the point of view of a dollar investor?
What is the arbitrage price (in dollars) of a contingent claim X?
What does the market look like from the point of view of a sterling investor?
What is the arbitrage price in sterling of a contingent claim X?
So that arbitrage opportunities are not created there must be certain relationships between U(t) and V(t), and the respective martingale measures, what are these?
Continuous dividend payments, continuously reinvested into the stock
How do you price Z(t)?
dividends paid at regular intervals, payments immediately reinvested into the stock