2902055
| Question | Answer |
| 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 | We want to obtain a martingale from the contingent claim X, must assume that E(X)<infinity |
| 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 |
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