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## New answers tagged derivatives

2

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price, also known as the principle of no riskless arbitrage and which you may already have heard of in the following terms: "there is no free lunch in financial markets". This law is at the heart of securities' relative valuation, see this very nice paper by ...

2

Note that, \begin{align*} \frac{\partial{C}}{\partial{\sigma}} &=\frac{S_0}{\sqrt{2\pi}}{e^\frac{-d_+^2}{2}}(\frac{-1}{\sigma})(d_-)-\frac{Ke^{-rt}}{\sqrt{2\pi}}e^{\frac{-d_-^2}{2}}(\frac{-1}{\sigma})(d_+)\\ &=\frac{1}{\sqrt{2\pi}}e^{\frac{-d_+^2}{2}}\left[-\frac{S_0 d_-}{\sigma} + \frac{Ke^{-rt}d_+}{\sigma} e^{\frac{d_+^2}{2} - \frac{d_-^2}{2}} ...

0

On the second question, you have the choice to pay (S_t - K) at t or (S_T - K) at T. The value at t of deciding to pay now versus later is: Value at t of paying (S_t - K) at t - Value at t of not paying (S_T - K) at T. = -(S_t - K) + exp(-r(T-t)) (F(t,T) - K) where F(t,T) is the forward price of the index. Now F(t,T) = S_t exp(r-d)(T-t) where d is ...

3

As with everything else it is determined by competition: little or no competition => very high fees (or more correctly large bid-ask spreads). That is one reason why many IB try to develop new derivatives: they can be very profitable when no one else trades them yet. Then the cost comes down somewhat when competitors come in. Lack of transparency in pricing ...

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