Continuous time option pricing Flashcards
Assumptions about stock prices as Stochastic processes
Stock prices evolve randomly over time
Stock prices incorporate expectations about the future.
Hence, stock prices only change with news.
News cannot be forecasted & arrives in a random fashion over time.
Weak-form of market efficiency
The spot price impounds all the information contained in past prices.
Historical prices contain no info about future prices.
Technical trading is therefore futile.
Competition ensures that the markets are weakly efficient.
why can we setup a riskless portfolio
The stock price & the option price are affected by the same underlying source of uncertainty (i.e., stock price movements).
Over a short period of time the stock price and the option price are perfectly correlated.
δ can be chosen so that the gain (loss) from the stock position is offset by the loss (gain) from the option position.
