New answers tagged options
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As @Valometrics suggests, the only way you portfolio can be worth 65 is indeed that you are short that call. Otherwise it wouldn't make sense for it to be worth only 65 instead of 67
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If you are long the call option (you purchased it), the value will be as you said $22*3+1=67$.
If you are short the call option (you sold it), the value becomes:
$22*3-1=65$
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The BS implied vol is the vol parameter in the BS formula that makes it hit the observed price of an European option.
To price an American option you need an assumption on the underlying dynamics, say geometric Brownian motion with constant diffusion coefficient (which happens to be also named BS dynamics). Then you need to get the derivative pricing PDE (...
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The HestonModelHelper in QuantLib expects a spot value, strike and BlackVol.
In theory, you could convert the strike of your FX Options (which are normally quoted in Delta terms) into an absolute strike (Check this post for details), and then calibrate the model as if the instruments were options on an equity where the foreign rate would be the dividend.
I ...
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Finite difference method is used to compute derivatives of functions as it is the case for greeks estimation. Regarding the IV computation, one can use an algorithm to get volatility by inverting the theoritical price formula to match quoted prices.
As for Heston model, we can use finite difference method to approximate the solution but its calibration ...
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Implied volatility is obtained by taking the observed market price of an option and solving for the necessary volatility in the Black Scholes formula to give that price. The finite difference method is just a numerical method to solve PDEs like the Black Scholes equation on a computer.
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This is a very common real-world task in quantitative finance, because new underlyings or options series pop up frequently.
Single Volatility
At its simplest, a volatility surface can be represented by a single constant parameter, $\sigma_C$, which to first approximation can be taken equal to the historical return volatility of your hypothetical underlying ...
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In order to erase the remaining P&L, you should gamma hedge your options. Actually, this is due to the non linearity of the options price.
This can be done by going long or short options with important gamma to make the gamma of your hedge portfolio equal to your options one. This way, the change of your delta will be hedged.
If you want to know how ...
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That is not the traditional representation of VaR. Normally, a VaR measure reflects the current risk exposure of the portfolio and measures its loss based on market movements, i.e. via an instantaneous shock to those positions, whether those market movements are supposed to reflect 1-day, 5-day, 50-day or 1-year, for example.
Generally VaR does not account ...
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The only missing point is that, by NA, if an asset has zero volatility, it is riskless and must therefore grow at the risk-free interest rate: $\mu \equiv r$ (Else, you buy the highest yielding asset and sell the lowest yielding).
In such situation, the valuation of an option is straightforward: it is the discounted payoff $e^{-r\left(T - t\right)} \left[...
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There is a simple way to find the number of rolls with the minimum of 4:
the number of rolls with the minimum of 6 is 1.
The number of rolls with the minimum of 5 is the number of rolls for which all outcomes are 5 or 6 minus the number of rolls with the minimum of 6:
2*2*2-1=7.
The number of rolls with the minimum of 4 is the number of rolls for which ...
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This isn't really an option as it is an exercise in probability.
How many rolls have a minimum of 6?
1 = 3C3 (6s)
How many rolls have a minimum of 5?
7 = 3C3 (5s) + 3C2 (5s6s) + 3C1 (5s6s)
How many rolls have a minimum of 4?
19 = 3C3 (4s) + 3C2 (4s5s) + 3C1 (4s5s) + 3C2 (4s6s) + 3C1 (4s6s) + 3P3 (4s5s6s)
How many rolls have a minimum of 3?
...
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Depends on how accurate you need your analysis.
And do you want the Spot price or the Forward price?
You seem to be using put call parity to solve for the underlying:
$$ c + Xe^{-rT} = S + p $$
and so:
$$S = (c-p) + Xe^{-rT}$$
You can find the market implied price of the underlying through a regression (for a given maturity), because:
$$(c-p) = S - Xe^{...
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Put-call parity is a basic no-arbitrage requirement of any option pricing engine. Why would you consume computation time and get numerical errors in pricing the call AND the put? Alternatively, you could only have some numerical error on the, say, put, and then an internally consistent call price at almost no extra computational cost.
In practice, pricing ...
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Interest rate options should be priced with risk neutral methods regardless of your opinion of interest rate trends. If you have a view on interest rates, you can express it by taking a delta position. If you were to bias your option prices , you would just end up paying the wrong price for the option.
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You are in luck, as these days there are many exchange-traded funds that track indexes. An option on one of these is therefore equivalent (for Lévy copula purposes at least) to an option on a weighted index of stocks.
So, for example, you can look at options on SPY as options on a weighted sum of 500 different US stocks. These are very liquid so you will ...
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May not be exactly what you are looking for but in Bloomberg you can use the securities finder (SECF <GO>) to get European equities with options.
Choose "Equities" as the category
Go to the "Equity Options" tab, or any other (Index Options or Options on Eqty Future)
Filter by Currency, Exchange or whatever you want
Click the export button to download ...
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You should always use the biggest volatility to minimise the risk and hedge the option correctly. Don't forget to multiply daily volatility by square(252) to annualize it.
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