# Tag Info

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To answer your questions: Is the trading p&l meant to be the delta-hedging p&l? Yes, in his example it concerns delta hedged pnl. how come p&l is raising steadily even when stock price is rising? the trader should be losing money on the delta hedging because he is short gamma? He is short gamma but long theta. He is initially making money ...

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You can write $$\mathbb{E}\left[ \max(a X_T + b X_S -K,0)\right] = \mathbb{E}\left[ \max(a X_S Y_{S,T} + b X_S -K,0)\right],$$ with $Y_{S,T} = X_T/X_S.$ For a given value of $X_S$ we can write $$\mathbb{E}\left[ \max(a X_S Y_{S,T} + b X_S -K,0)\right] = X_S \mathbb{E}\left[ \max(a Y_{S,T} + b -K/X_s,0)\right],$$ since $Y_{S,T}$ is log-normal this can ...

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I don't believe you will necessarily find a cite-able source as, I believe, this comes from a practical rather than theoretical motivation. As you know option prices are a function of: future prices, discount rates and implied volatility, volatility surface skew and other supple/demand factors. So when you are trading these instruments, you need to ...

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Yes, the greenshoe option, technically called overallotment option is described in the prospectus. Yes, in the event the greenshoe option is exercised by the underwriters, the company issues additional shares and receives additional proceeds. Essentially it is as though a small secondary offering took place.

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Your Vega of 188.48 is correct, in the sense that matches my calculation. What it means is that if the volatility increase by 1 (i.e. by 100 percentage points, from 19.14% to 119.14%) the call will increase by 188 dollars. Obviously that is an unrealistic move. More realistically if the volatility increases by 0.01 (i.e. 1 percentage point, from 19.14% to ...

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In short answer, Yes: the backward PDE solution with $v(t,L)=0$ and the expectation coincides under the Black-Scholes market. In the one dimensional case, this topic is mathematically treated in the theory of the scale function and the spead measure. See Revez-Yor 3rd.ed. Ch.VII.3 for details. I don't know whether there are some rigorous theories on the ...

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As the other comments already suggest this topic has been discussed many times and the references / links that are provided are far more detailed than my quick solution below. In the construction / replication of a variance swap one tries to achieve a CONSTANT dollar gamma. This is done by buying a strip of calls and puts, weighted by 1/K^2 as you ...

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If you assume that IV of different expiration options is equal, then it mathematically follows that you are correct. Weeklies would give you the maximum theta decay. That is the theoretical answer. In practice, you may not have weeklies on every stock or index and you might have them but they trade too thinly. Wide bid/ask spreads etc. Also sometimes there ...

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well, the current share price reflects fair value. So you'd expect it to be close to its expected price, but slightly below because of risk aversion and discounting. If it was very far off its expectation, it would either be over or under valued and people would trade accordingly.

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