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You can use the "Merton Jump Diffusion Model" to price European Options with jumps. The other points of your question are rather of practical relevance only. The negative drift of the underlying is usually not important, because the pricing goes under the riskneutral measure $Q$.


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nice point. One way of looking at it, I think, is that you have just two Brownian motions, so in a sense your space is just 2 dimensional. Thus, as long as $V$ and $V_1$ are not "linearly dependent", you're spanning the space, and you're done, and it doesn't really matter what $V_1$ you're choosing. Now, this is of course a very hand-waving argument, in ...


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For question 2): At time T, we need to pay 100*S_T/S_t (in domestic currency, say \$). To do this, we need to buy 100\$ worth of shares at time $t$: that gives us $N=100/S_t$ shares, with the desired final value of $N\,S_T = 100*S_T/S_t$ at expiry. Needless to say, today's PV of 100\$ at time $t$ is $100\,B(0,t)$. However, then at time $t_1$, we hold $N$ ...


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Stock markets? Not that I know of. I would say ICE and NYMEX have OTC power contracts but I believe they have pretty big margins and account minimums for that kind of contract. Just at looking at today's settlements I see very little traded on Clearport.


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We can explicitly value the Inverted Option under Black-Scholes Model as follows: Then the delta-hedging ratio is given as:


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Note that, for a smooth function and constant a $$f(S_t) = f(a) + f'(a) (S_t-a) + \int_a^{\infty}(S_t-x)^+f^{''}(x)dx + \int_{0}^a(x - S_t)^+f^{''}(x)dx.$$ Then, the payoff $1/S_t$ can be approximately hedged by call and put options: $$\frac{1}{S_t} = \frac{1}{a} -\frac{1}{a^2}(S_t-a)+ 2\bigg[\int_a^{\infty}\frac{(S_t-x)^+}{x^3}dx + \int_{0}^a\frac{(x - ...



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