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Take a look at Espen Gaarder Haug. The Complete Guide to Option Pricing Formulas Hardcover, 2nd edition (2007).


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There is an abundance of different strategies and option types. If you are only looking at vanilla strategies, i.e. combinations of puts and calls, then I'd suggest looking at the payoff charts here. Some of the intuition behind these payoffs is useful as well. You can even come up with more fancy strategies and names such as seagull options or wedding cake ...


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For plain-vanilla options I would generally recommend Hull, J. C. (2012) Options, futures, and other derivatives. For example, in the 7ths edition it's on page 183.


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Asian options are the most liquid markets for options on commodities which are delivered over time such as electric power and natural gas. Some metal smelters also use Asian options since their plant runs every day and so their costs (power, ore) are well-approximated by an average over time. (Hence why the LME has some Asian options.) Asian options may ...


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I guess you ask if there is a difference if you model them via stochastic vol as opposed to local vol for example? If so, yes. The effect is called decorrelation. Since SV has vols fluctuate as opposed to deterministic, you get more variation in the price of the underlyings. Hence, your effective realized correlation is smaller in SV.


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You are competing against thousands of firms, many of them doing this professionally and employing people like the ones you see in the Vola Dynamics link I provided in the comments. So my answer is, no you will not find trading opportunities. I go even further and claim you probably never will (on your own). If you use vendors liker Bloomberg, SuperD, and ...


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Unless I am missing the obvious, I do not see the question being answered? In my opinion trying to understand in simple language what $\alpha, \beta, \rho$ mean requires an explanation what these parameters do and why it is useful. Here is my attempt: Black (all Black Scholes formulas) assume(s) that Implied Volatility is independent of strike (constant and ...


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Chapter 5.5.2 (Hedging with One Stock) paragraph that includes (3) does not assume that the value of the payoff at any $t$ is Markovian, that is, it is a function of $S(t)$ only, so there is no "delta" as in (1) to use. Summary 6.7 has the answer to what Shreve does want to say about formula (3) (in particular the three paragraphs I highlighted; ...


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$$S(t_n)-D_n-Ke^{-r(T-t_n)}\geqslant S(t_n)-K$$ means that if LHS (lower bound of option price) $\geqslant$ RHS (what you get if you exercise early), it cannot be optimal to exercise. This is an assumption, not a claim that it is true or must hold under any circumstances. The rest is just reformulation to have $D$ on one side. Hence, iff $$D_n \leqslant RHS$$...


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If quick and simple works, the formula by Malz is quite easy to implement. If you have access to an automated data import tool, I suspect you use one of the common vendors. In this case it may be worth to ask if they have an API that pulls you the exact value based on a request for say 35DC with expiry in x days. E.g. Bloomberg would allow you to pull single ...


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I doubt anyone will provide or have a vol surface for this. Well, if it is sold, your market maker will price that but that is a different story in my opinion. It's like buying insurance for your car vs a Bugatti Chiron. The latter will not follow standard logic and likely have a hefty premium to a "theoretical" price of insurance. Long term vol ...


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No difference really if you look closely. Looking at the table, you see delta of a put is negative; delta of a call is positive. To the left of the middle of the chart (50 Delta) you have out the money puts, to he right, out the money calls. Now, delta is associated with a strike. For the same strike, you have ITM calls, if OTM puts and vice versa. In the ...


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Nice question. The short answer is of course that if $C>P$ you could make riskless profits by buying puts and stocks and writing calls. But the prices of long dated securities can indeed look counterintuitive. For example Warren Buffett has said that the Black-Scholes model gives strangely high prices for very long dated puts (like 100 year maturity). It ...


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I do not think there is any problem. Firstly, you also did not use OIS but LIBOR now, although the "appropriate" risk free rate would be OIS. You also did not compare the two. To address the risk that one or more IBORs are discontinued while market participants continue to have exposure to that rate, counterparties are encouraged to agree to ...


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An index itself doesn‘t have any gamma. Even for the options on an index (spot? futures? ETF?) it‘s a zero sum game since for every long position you have a matching short position. Now it gets a bit more interesting if you look into the type of players that trade options. Very simplified you have two main players. Firstly, there are real money investors ...


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You can re-write the payout as $C = S_2 \, max( S_1 / S_2 - K, 0)$ and then value the option in units of $S_2$ at first. Say $S_2$ is the IBM share price, then we would value in units of IBM shares. In that case it is a simple option with payout $max( S_1 / S_2 - K, 0)$. If the volatilities are $\sigma_1$ and $\sigma_2$ and the correlation is $\rho$, the ...


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This is a rainbow option with two assets $S_1$ and $S_3=KS_2$. $S_3$ also follows the Black & Scholes stochastic equation with initial value $KS_2(0)$ and the same other parameters as $S_2$. You can find in section 3 (The Result of Margrabe) of the following article the formula to price these kind of products: http://finmod.co.za/Pricing%20Rainbow%...


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Frequently, American options are de-Americanized. Afterward, you "simply" use the standard model you use to construct your VOL surface based on European prices. In reality, things are quite messy though: You need data filtering to ensure the reliability of the inputs (do you use several exchanges vs most liquid, stale prices, unreliable bid-ask ...


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Better late than never. There are lots of nuances to consider when pricing options. The help desk should have been able to point you towards a solution. I do not think they will (be able to) replicate completely but should at least provide generic examples. Personally, I do not like domestic vs foreign. Tends to cause confusion in my humble opinion. I will ...


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"Warrant Arbitrage", the attempt to take advantage of warrants mispricing in volatility terms was one of the first applications of the Black Scholes theory decades ago. I don't know where things stand today, but I doubt that there are large volatility discrepancies today (although as pointed out in other answer warrants are not very liquid so it ...


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"And why don't other banks exploit too expensive warrants by buying them from their peers and hedge the position at the EUREX?" If the warrants are expensive relative to options, the way to exploit them is to sell them and buy the cheaper options as a hedge, not to buy the warrants. And that is the reason why they cannot be exploited in the way you ...


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"how can we say that an index options for example SPY is gamma negative ?" I believe the chart shows an estimate of dealers' net gamma position for QQQ as a function of price. It is not the gamma for a single option on an index. This kind of analysis has been discussed elsewhere, and I believe previously on StackExchange.


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Yours is the (backward Kolmogorov) PDE of a Black-Scholes model with time-varying short rate and volatility. Now, have you considered at all risk-neutral evaluation and Feynman-Kač representation? See e.g. Bjork chap 5. Because, the infinitesimal generator of that PDE is the same of the following SDE: $$ dS(t) = r(t) S(t)dt + \sigma(t) S(t) dW(t) $$ where $W(...


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I am assuming you do NOT refer to Investopedia: Forward Premium which does not change the way you value an option. I assume you mean the following: Wikipedia: Garman-Kohlagen The call formula (similar for put) can also be expressed in terms of Fwd instead of S (covered interest rate parity) which yields: $$exp^{-r_d*t}[FN(d_1) - KN(d_2()]$$ where $r_d$ is ...


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What do you mean by solving it? A heat equation can be solved by a simple sin(x) exp(-x t) function as it will satisfy the equation. I think what you really mean is satisfy the boundary conditions. Without the boundary condition there are various solutions possible. Assuming you are looking to solve for call option where boundary values are determined using ...


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This is just like any other option. For example, if you are trading an IBM option, you hedge with IBM stock, which doesn't expire at all, (obviously). You then sell your hedge in the gamma-storm that enuses at expiry. For longer term options where you have an expiry that goes way past the futures you have two choices: Trade the rolls periodically and/or ...


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I just published a blog post on how to backtest options strategies with R: Backtesting Options Strategies with R In the post, I provide the fully documented R code for your own experiments. The "trick" is to use the often publicly available implied volatility as a proxy for option prices (which are often hard to come by and/or very expensive). For ...


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