# Tag Info

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If you're using greeks for your past trading session's analysis , you should use historical Vol If you intend to make trading decisions in future and want to have a future outlook of greeks, you should use implied Vol.

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While implementing this strategy , you're taking risk of downside movement of your long equity position, as others have pointed out. If your market is quite volatile , and you can use the stop losses effectively , you can have minimal profit.

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For question a). From the assumptions, in particular, that $R=0$, \begin{align*} \pi_l + \pi_m + \pi_u &=1\\ \frac{1}{2}\pi_l + \pi_m + 2\pi_u&=1. \end{align*} Set $\pi_m=x$, and solve for $\pi_l$ and $\pi_u$, \begin{align*} \pi_l &= \frac{2}{3}(1-x)\\ \pi_m &= x\\ \pi_u &= \frac{1}{3}(1-x), \end{align*} where $0<x<1$. The option ...

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First, we have $P(t)+S(t)=C(t)+B(t,T)\cdot K$, Then, $\frac{\partial P(t)}{\partial S(t)} + \frac{\partial S(t)}{\partial S(t)} = \Delta^{\text{put}}_{t}+1$ and $\frac{\partial C(t)}{\partial S(t)} + \frac{\partial [B(t,T)\cdot K]}{\partial S(t)} = \Delta^{\text{call}}_{t}+0$. Finaly, $\Delta^{\text{call}}_{t}-\Delta^{\text{put}}_{t}=1$. This relationship ...

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Trinomial trees give incomplete markets so there is a range of possible risk neutral prices. So you have to find the possible probabilities that make the tree risk-neutral and see what prices you get. You have the correct expressions. Now just have to parametrize the set of solutions. It is one-dimensional and all the probabilities are positive so you need ...

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A very decent place to get options data is https://www.historicaloptiondata.com. It is not free and I do not know anywhere you would be able to download such data for free. Re: options greeks there was discussion recently historical options data

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The expected value of the option at maturity is simply $$\mathbb{E}[(S_T-K)^+]$$ Note that this is under the real world measure. In a B-S framework this value is given by $$e^{rT}C(\alpha;S_0, K, \sigma, T)$$ Where $C(r; S_0, K, \sigma, T)$ is the B-S call option price. Hence the expected growth rate (using a simple return) is $$\frac{e^{rT}C(\alpha;S_0, ... 0 The "best" approximation comes from the one of the greeks: \Theta. This is the derivative of the option value with respect to time-to-maturity. For a call option it is given by:$$\Theta(\tau) = -\frac{\sigma}{2\sqrt{\tau}}S\phi(d_+) - r K e^{-r\tau} \Phi(d_+)where \tau = T - t is the time to maturity, t is the current time, T is the maturity ... 1 OP is absolutely right in his approach and this is the underlying idea behind risk neutral valuation or even BS model. If Black-Scholes model assumptions hold, then a derivative payoff can always be replicated in such a way it would never provide return more than risk free interest rate, otherwise it will lead to arbitrage opportunities. But assumption never ... -3 I've been collecting daily option prices for all symbols/strikes since beginning 2014. If anyone interested, let me know (not free) 0 Probably Option Metrics which you can find on WRDS is what you are looking for. 1 Note that, for K_1 < K < K_2, \begin{align*} -(K_2-K_1) \le (S_T-K_2)^+ - (S_T-K_1)^+ \le 0. \end{align*} Taking the conditional expectation with respect to information set \mathcal{F}_t, \begin{align*} -(K_2-K_1)B_t(T) \le C(T, K_2, S, t) - C(T, K_1, S, t) \le 0. \end{align*} That is, \begin{align*} -B_t(T) \le \frac{C(T, K_2, S, t) - C(T, K_1, ... 3 For the case where \sum_{i=1}^n \lambda_i =1, you need only note that the payoff \begin{align*} (x-K)^+ \end{align*} is a convex function in x. That is, \begin{align*} \Big(\sum_{i=1}^n \lambda_i S_i -K\Big)^+ \le \sum_{i=1}^n\lambda_i(S_i-K)^+. \end{align*} Then \begin{align*} e^{-rT}E\left(\Big(\sum_{i=1}^n \lambda_i S_i -K\Big)^+\right) \le ... 3 you just add in any auxiliary variables accumulated along the path that determine the pay-off to the regression variables. So path-dependence is not a problem. If you have previous decisions, you may need to do different regressions based on their possible values or make them into a continuous variables that can be used for regression. 2 The easiest way to think of this is as follows: Settlement Price - Price at which the exchange margins all accounts for those options. Closing Price - Mid/Bid/Ask of Active Market at the exchanges last trade time. E.g. for TY Contracts this is at 5pm EST vs. a Settle Time of 3pm EST. Last Trade Price - Not all options trade every day. This is the price ... 0 One example could be someone using option strategies and its underlying dividends. In these cases, the trader could use early excersise to capture the dividend value. Google it for more information. 3 Options are in zero net supply (like futures and other derivatives), so for evry long there is a short and for every short there is a long. The open interest is the sum of the longs which also equals the sum of the short positions. 2 You should not use the Feller condition as a constraint. In many cases its violation will be required for a good fit to the market data. 0 There was a recent thread discussing this historic options data That data source mentioned there is commercial, though reasonably priced. Their data in CSV format readily ingestible by Excel. One note of caution is options' daily closing quotes are not always accurate. 1 it is not a "newbie question". actually it is very deep question, especially if you are trying to trade options in some way. all Greeks are about change in premium of the option. Premium consists of two components: time value + intrinsic. Greeks cannot tell you anything about this decomposition, they deal only with total sum (i.e. with overall premium). So ... 0 From e.g. the CBOE web site you are able to download a full table of option quotes (delayed) for a specific stock (menu quotes - delayed quotes). Take it from there, appply data manipulation (Excel VBA, R, Python..) to the extent needed and then you should be be able to end up with the desired result. This wouldn't be a simple copy & paste procedure; ... 5 If you want to know what Greeks the market assigns to an option, i.e. the market implied Greeks, then you would use the implied volatility. And that is what traders like to look at. 0 Check out BarchartOnDemand. They have CME EOD data as an API...it may not be advertised but I know is available via their API (http://www.barchartondemand.com/api.php ). Pricing is not published but should be reasonable for an individual just looking for EOD. You can also get the same data through QuantGo.com but have to use it on your own computer instance ... 0 To get IV I do the following: 1) change sig many times and calculate C in BS formula every time. That can be done with OIC calculator All other parameters are kept constant in BS call price calculations. The sig that corresponds to C value closest to the call market value is probably right. 2) without OIC calculator for every chosen sig I am using old ... 2 You can guesstimate by vega weighted implied vol. This is why: Say that you have a portfolio of options with prices P_j. Each one of them has a different pricing function f_j (as function of vol) and a different implied vol \sigma_j. For each option f_j(\sigma_j)=P_j. Now you put them together in a single product. If the implied vol of the product ... 3 For the US market nearly all options on securities are american whereas the options on indexes are european. What you can do is to use a database such as OptionMetrics which adjusts the stock american options to european options by taking into account the early exercise premium. 3 Using the answer from: Chris Taylor, on math stackexchange (link): Let the price of an option at strike K be given by V(K). To say that the price is convex in the strike means thatV(K-\delta) + V(K+\delta) > 2 V(K) for all $K>0$ and $\delta>0$. Let's assume that the opposite is true, i.e. that there exist tradeable option contracts ...

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