New answers tagged options
First off, volatility smiles are often drawn over a delta space. Since you're asking, I'll assume you're trying to draw a volatility smile over strike prices, log moneyness, or some similar metric. If you have neither the spot price nor any strike prices associated with your data, I don't believe it's possible to back out both of those values. Not ...
With 0% interest rates r-q is almost always < 0. Dividends are pretty much never continuous, so for an American option if the dividend you collect and interest you forgo collecting (or paying) being short the stock is larger than the value of the put (since when you punch a call you sell that call and buy 100 shares, thus selling the put). It's also worth ...
I see a theta of -0.03ish. Delta is about the order of magnitude of your number, maybe you mixed them up?
The excercise should happen if the present value of the dividend yield minus risk free interest exceeds the value of the related put. As noted before this is only true if a position is deep in the money and volatility is low. On single stocks this decision is usually done right before dividend ex-date.
You can use the "Merton Jump Diffusion Model" to price European Options with jumps. The other points of your question are rather of practical relevance only. The negative drift of the underlying is usually not important, because the pricing goes under the riskneutral measure $Q$.
in addition to the answer above: If the option is settled on an exchange, the terms will be standardised and a secondary market will exist making it a liquid instrument (with dedicated counterparties offering to match each side of the trade). A warrant will be more thinly traded and will trade over the counter (OTC), and will have terms that are specific to ...
Stock markets? Not that I know of. I would say ICE and NYMEX have OTC power contracts but I believe they have pretty big margins and account minimums for that kind of contract. Just at looking at today's settlements I see very little traded on Clearport.
A warrant represents the option to receive a share of stock, newly issued by the company, which in general causes dilution. An option is usually the right to receive an already outstanding share of stock, purchased from a third party.
It's because of the settlement days you passed when you initialized the flat volatility curve. You're creating the spot, forward and flat volatilities as: boost::shared_ptr<BlackVarianceSurface> volatilitySurface( new BlackVarianceSurface(todaysDate, calendar, maturityArray, strikeArray, ...
I think that for any $q>0$ it becomes optimal to exercise an American call for a sufficiently high spot price $S$: if the spot increases enough, the dividend yield corresponds to sufficient cash dividend to render exercise optimal. This would happen irrespective of the value of $r$ or the sign of $r-q$. What matters is that, for a given strike $K$, the ...
VG belongs in the family of variance-mean mixture models. Given a horizon $T$ the distribution of log-returns $f$ is a mixture of Gaussians $f_G$ with randomised mean and variance. The randomisation density is $g$ and its mean and variance increase with $T$. For the VG process this randomised factor is Gamma-distributed. More concretely, denote with ...
For forward libor models, one can hedge interest rate options by using bonds. (Note that forward libor is a tradeable security under the forward measure). See http://www.columbia.edu/~mh2078/market_models.pdf For affine yield models (like Vasicek or CIR models) the inverse problem is the most useful. Given an interest rate process, I can compute a ...
Selling 2 ATM calls against 100 underlying shares result in Delta neutral. "Given the extra downside protection, and potential need for a stop order if the asset price rises too high, is the added risk of the naked leg justified?" The risk is if the move is more than extrinsic premium collected. One thing to watch out this type of trade is skewness. ...
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