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4

As you can see from the wiki page, the delta of a put is $$\Delta = -e^{-qT}N(-d_1)= -e^{-qT} \left(1-N(d_1)\right)$$ Recall that this $\Delta$ is the derivative of the value of the put $p$ with respect to the value of the underlying stock $S$: $\frac{\partial p}{\partial S}$. So this means that if the underlying goes up by 1, the price of the put change ...


3

Here's one scenario: dealer is long a deep in the money American put (say strike is K and the current stock price is S < K ), versus being short a european put with the same strike and final expiration. If the dealer exercises early the American put, he is now short the European put at K with a short stock hedge against it. Thus he is synthetically ...


2

Here's the example of what is in the quote: dealer is long an ITM call. As a hedge the dealer is also short OTM put (with the same strike) and short stock. This is a "riskless" position, equivalent of a bond. The underlying pays a dividend, and a day before the ex-date dealer exercises the call. The shares that dealer received from exercise are netted ...


2

This spread can't be statically synthesized. However you can synthesize it dynamically by trading in the underlying contracts. You would first value the option using standard theory (this involves solving a two-dimensional PDE, or using Monte Carlo) to get a price $V(F_1,F_2)$ in terms of the prices of the underlying futures contracts. Then the holdings in ...



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