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1

In the link you provided, by noting the construction of array p[], p0 and p1 are respectively the discounted $\texttt{down}$ and $\texttt{up}$ probabilities. Since $d=\frac{1}{u}$, then \begin{align*} p0 &= e^{-r \Delta T}\, \frac{u-e^{(r-q)\Delta T}}{u-d}\\ &= \frac{\big(u\,e^{-r \Delta T} -e^{-q\Delta T}\big)u }{u^2-1}, \end{align*} and ...


1

Is the option perpetual? If so, the $C=1/H$ answer looks suspicious and $C=1$ is more plausible for the reasons detailed below. If $C<1$, you borrow \$$C$, buy the option, wait until the underlying hits the barrier, receive \$1 payout, repay the \$$C$ debt (we have assumed 0 interest) and pocket the difference. Similarly, if $C>1$ then one can ...


2

This option is a perpetual one touch option. Its price depends on the model used; additional assumptions are required to get a model-independent price. Let us first consider 3 important example models for stock price $S$. Constant: $S(t) \equiv 1.$ There is $0$ probability that the perpetual one touch pays off, so its price is $0.$ Black-Scholes: $S$ ...


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Consider a portfolio where I sell $\frac{1}{H}$ in stock and use that to buy an option. This is a 0 cost portfolio. When I hit the barrier the price of this portfolio is also 0. Law of one price would suggest that this portfolio should be zero cost at all times. So the price of the option at any time must be $$ C_t = \frac{1}{H}*S_t $$ Also, the option ...


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There are a few careers dedicated to identifying better ways to compute the value of various sets of option contract terms under different assumptions. If beta is a Greek letter that comes to mind when, you could probably still get something out of the Wikipedia article on Black-Scholes. Branch from there. If you want to move toward applications I would ...


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Whatever pricing model you use you will almost always have the time to maturity as an input somewhere, agree? So if you have an option with a current time to maturity of e.g. 1 year, in order to get the time value in e.g. 6 months from now; you pretty much just run the pricing with time to maturity of 6 months as an input. No rocket science necessary there. ...


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When a company distributes a special dividend or there is other corporate action, it affects the deliverable of the option contracts. Thus, the option is adjusted and becomes special. For example, a standard option contract is on 100 shares of ABC. The company goes through a corporate action (including special dividends), and the deliverable now is 90 ...


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Your prayers were heard ;-) The following article gives you all you need, especially the function getOptionQuote() which lets you download option chains for any ticker symbol with one line of code! You find the article here (with full R code): ...


1

The mean of bid and ask for a fill is not realistic and this will impact your analysis a lot in options. The market maker is quoting the spread because that's how they intend to get paid for the risk if you bring them one leg. Use the worst pricing assumption on this, even though you should probably still rest orders in practice for anything that has a ...


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First of all, thank for your answer and your time. Having looked all over the place, I come to realize that stock price cannot be rewritten using log return. That is St = S0 * r1,0 * r2,1 * ..., with rt+1,t = log(St+1/St) For the 1st case, that is the Asian geometric option. If you use the fact that the definition of geometric mean can be rewritten such ...


2

The price of the April option will be more than $5.00, correct. How much more depends on the implied volatility ($\sigma$) of the option and the interest rates ($r$). The higher $\sigma$ and $r$ are, the higher the time value of money and the value of the April option. I highly recommend playing around with this calculator to gain an intuitive ...


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Conversion to a butterfly can mitigate or even eliminate all risk taken by opening a initial debit spread or long option position. This is possible only if the underlying moved in your favor after your initial position is open. To convert to a butterfly you simply sell and buy enough options (for a credit) that together with your initial position forms a ...


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Maybe you need to make your position gamma neutral in the first place. Once the underlying has decreased significantly, if you weren't delta and gamma neutral in the first place, you can't prevent a loss.


2

Intuitive, no math explanation: Imagine two call options, option A expiring tomorrow and option B expiring in two months. Both of the options are way out of the money and have the same strike price. Due to some event the implied volatility of the stock spikes. Let's assume stock price stays the same. Does the chances of option A expiring in the money ...



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