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1

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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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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In an interview on Tastytrade, NYU's Phil Maymin talks a bit about this exact question: https://www.tastytrade.com/tt/shows/what-else-ya-got/episodes/dr-philip-maymin-skew-10-22-2014?locale=en-US A full example of this is also covered in Maymin's book, Financial Hacking.


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It also depends on at what levels of the spot the higher vol gets realized. In your example: if you buy an option on a 40 vol expiring in a month and over the next month stock the average vol of the stock is 60 and you dynamically hedge, are you guaranteed to make money? If not could you please give me a simple example perhaps where you'd wind up ...


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Options on the spread between crude oil and petrol are traded on the cme http://www.cmegroup.com/trading/energy/refined-products/rbob-crack-spread-swap-futures_quotes_globex_options.html http://www.cmegroup.com/trading/energy/refined-products/heating-oil_quotes_globex_options.html#optionProductId=566


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I know this is almost a month old, but... Unless it is a homework assignment, you could have a look at this paper by Del Moral and Shevchenko, which gives a different estimator than the one you're probably using. It gives both a crude Monte Carlo-estimator and a sequential Monte Carlo-estimator. You probably just want the crude Monte Carlo one. Eq. (27) ...


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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 ...


2

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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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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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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What the author is arguing is that the current price exactly at this instant takes into account all the views of the market participants as expressed by orders (which would be correct). Note that those views may change almost instantaneously generating orders thus causing price to change. An example is you have an expected future price of 10 and the current ...


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Mark has rightly pointed. You may think like this, If there is high probability price would go up in future(in very short period), lets say 90% then investors would continue to buy until they no longer expect price to increase with such a high probability. Or until this strategy of buying shares with high probability of going up is not profitable(excess ...


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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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Isn't the option's delta a close approximation for the probability the option will be in the 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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COS method is an efficient way to recover the distribution function from the characteristic function in the Heston model. For other methods, you may refer to "Inverting Analytic Characteristic Functions and Financial Applications".


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In options pricing language, the probability of a spot process being above a given level $K$ at time $T$ is the undiscounted price of a digital call option on that spot process. In the Heston model, there is an analytic expression for this in terms of Fourier transform. You can find this in various standard references, e.g. Alan Lewis's book "Option ...


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Interactive Brokers provide access to those. Here is a link to the product list in question.


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If you have access to an Interactive Brokers account - you can get historical data from them - they support EUREX options according to their site's product page: https://www.interactivebrokers.com/de/?f=/en/trading/exchanges.php?exch=dtb&showcategories=&ib_entity=de To get the data - you can use their API's, or alternatively - use a third-party ...



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