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4

there are a number of ways to do this. You do have to make some modelling assumptions, however. eg continuity, BS model holds, or log stock price process is independent of level. The most common way is to take the pay-off and geometrically reflect in the barrier. (i.e. pass to log coordinates and reflect). i.e. write the function as $f(x)$ where $x= \log ...


2

if you hedge it means that your USD return equals (neglecting hedging cost) your EUR return. You just change the name. If you want to know what the return measured in EUR is, then you either calculate the price of S&P in EUR and then take returns or equivalently you calculate the product of the local return and the return of the USD in EUR in the ...


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Commonly used procedures: A) hedge when a 1 sd move has happened B). Hedge when your delta position exceeds some risk limit. C) hedge once a day D) hedge based on your desired delta position All are used. I personally prefer B.


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There has been a lot of work in recent years on the pricing and hedging of volatility derivatives, leading to some non-obvious, even startling results. It is summarized in Mark Joshi's book More Mathematical Finance among other places. It all started with the work of Anthony Neuberger on the Log Contract in 1994, which seemed to be a theoretical result ...


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The EUR is normally quoted as EURUSD, i.e. the value of one euro measured in dollars, currently about 1.1281. If the S&P index is $sp_t$ and the EURUSD rate is $eu_t$ then the S&P converted into Euros is $sp(t)/eu(t)$. The arithmetic 1 day return on this is $-1+\frac{sp_t}{sp_{t-1}}\frac{eu_{t-1}}{eu_t}$. The logarithmic return is ...


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You need to hedge future cash flows (not future value) using a fixed for fixed currency swap (equivalent to a series of forwards). This translates into a "cash flow hedge". Hedging present value would be hedging the "fair value" of the bond with a fixed-for-float currency swap. Using a fixed for fixed swap will convert your cash flows into desired currency ...


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The most rigorous approach I have seen so far eliminating the risk premium is this one: Emanuel Derman: The Perception of Time, Risk and Return During Periods of Speculation (2002) Equation 2.23 on page 11 derives $\mu$ ~ $r$ but it only holds in the limit when you hypothesize countless uncorrelated stocks in a diversifiable market. Still an interesting ...



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