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This drift comes from making the discounted stock a martingale in the risk-neutral measure $\mathbb Q$ You start with a stock in $\mathbb P$ having this form: $$ dS_t = \mu S_t dt + \sigma S_t dW_t $$ You also have a discount factor $e^{rt}$. The idea is to remove the drift of the discounted process in $\mathbb Q$ so you get (after applying Girsanov's ...


3

You only have one asset in your portfolio which means that you can only statically hedge. By the definition of self financing, $V_0=\phi_0 S_0$, $V_1=V_0+\phi_1 (S_1-S_0)$, and $V_1= \phi_1 S_1$. Putting these last two together, $V_0=\phi_1 S_0 $. Hence $\phi_1=\phi_0$ and you have a static position. Intuitively, this is because you cannot trade in ...


2

The first consideration is to set prices which do not generate arbitrage opportunities. The existence of a risk-neutral probability measure ensures that the model is arbitrage-free. In the Black-Scholes setting, as you mentioned, the market is complete and there as a unique martingale measure, hence only one possible price for each derivative. In a ...


1

I would consider the financial applications of the Greeks: hedging. The "main" greeks, viz. Delta, Gamma, Theta, Vega and Rho, all have intuitive financial meanings. Gamma is the rate of change of your Delta (how many shares of stock to own) with respect to the stock price, so a high Gamma implies you will be rebalancing in large quantities (often ...



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