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by MartinGale7
August 31st, 2018, 6:07 pm
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

Thank you all for your help, especially Alan. I've been experimenting with this method and can't seem to get anything that works well enough for for pricing options at T based on empirical CDFs (of log returns to expiry T). I might just resort to (numerically) integrating the payoffs over the probab...
by MartinGale7
August 30th, 2018, 3:03 pm
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

Thank you Alan. I understand what you mean about bound now. I have a model which is forecasting the CDF of future log returns. I'm trying to use these CDFs to price options. These CDFs are 11 segment cubic splines (although I can fudge on tails to plus and minus infinity if necessary). Alternatively...
by MartinGale7
August 30th, 2018, 10:42 am
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

Are you suggesting we need to find (possibly different) b for each strike we are trying to price?
by MartinGale7
August 30th, 2018, 10:33 am
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

Thank you Alan. I found both of your posts helpful. I hope you don't mind if we illustrate this with a worked example?   This is hypothetical (of course). Let’s say that I am confident that the log returns of a given stock are uniformly distributed between -10% and +10% at a specific future point T....
by MartinGale7
August 29th, 2018, 5:56 pm
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

Hi Alan (or anyone else kind enough to help), Thanks for your posts. I have been doing some experimental modelling of this. I usually work in another area, so am no means an expert (forgive me for this :)). I am wondering if you can lend a hand. I now have my empirical cumulative distribution D(ln(S...
by MartinGale7
August 20th, 2018, 3:15 pm
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

Thank you. That is enough to get me started.
by MartinGale7
August 20th, 2018, 2:43 pm
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

Thank you. I will give this a go and update the thread once I have a result. BS will be using the new distribution. I have a few reasons for asking this question on the N() and uses for this in my modelling. I currently have my own model for creating CDFs based on empirical data. However, as an alte...
by MartinGale7
August 20th, 2018, 10:32 am
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

Re: The N() in Black Scholes Option Pricing

I am tempted to try this using Monte Carlo. Ie, I can define a distribution arbitrarily which describes market returns (at time of option expiry). I can make this anything I want. I can then price straddles (by average expiry price) at various moneynesses and then back out the IM using BS (with the ...
by MartinGale7
August 18th, 2018, 9:26 am
Forum: General Forum
Topic: The N() in Black Scholes Option Pricing
Replies: 27
Views: 5589

The N() in Black Scholes Option Pricing

A nice simple question (forgive me - this is not my usual field of expertise). In the equation for pricing a European call option we have N(), ie the cumulative standard distribution. However returns are not normally distributed. Because of this, we end up with non-flat volatility surfaces (as we ba...
by MartinGale7
August 17th, 2018, 6:21 pm
Forum: General Forum
Topic: Implied vol skew/smirk if market was risk-neutral?
Replies: 8
Views: 1939

Re: Implied vol skew/smirk if market was risk-neutral?

@Alan Thank you. I will do some research on those.
by MartinGale7
August 17th, 2018, 3:04 pm
Forum: General Forum
Topic: Implied vol skew/smirk if market was risk-neutral?
Replies: 8
Views: 1939

Re: Implied vol skew/smirk if market was risk-neutral?

@Alan No. I expected that if I messed with the 1min data to change the distribution of returns (fat left tail) then I would see smirk. Even pricing a 5min straddle based on 1min bars with a very fat left tail still doesn't seem to produce smirk.
by MartinGale7
August 17th, 2018, 2:43 pm
Forum: General Forum
Topic: Implied vol skew/smirk if market was risk-neutral?
Replies: 8
Views: 1939

Re: Implied vol skew/smirk if market was risk-neutral?

(I think I realise the problem above. I was forecasting straddle prices 60min ahead based on 1min bars. I changed the distribution of the 1min bars, however by central limit theorem, the 1min bars might now have a larger left shoulder but once stacked together, over a longer time frames will resembl...
by MartinGale7
August 17th, 2018, 2:14 pm
Forum: General Forum
Topic: Implied vol skew/smirk if market was risk-neutral?
Replies: 8
Views: 1939

Re: Implied vol skew/smirk if market was risk-neutral?

Thank you for this. I have been programming this up. There are really two parts to the question - (1) Does the distribution of returns (fat-tails) cause those strikes further out of the money to have higher implied volatilitys? You have said yes to this and my modelling confirms this. (2) Does a fat...
by MartinGale7
August 17th, 2018, 7:30 am
Forum: General Forum
Topic: Implied vol skew/smirk if market was risk-neutral?
Replies: 8
Views: 1939

Implied vol skew/smirk if market was risk-neutral?

A quick question. The BS assumes that returns are normally distributed. We know the tails tend to be fatter in reality. We also know that in equity markets, large downward returns happen rarely but more often than large upward returns. Despite this, the drift tends toward (at least in theory) the fu...
by MartinGale7
January 23rd, 2018, 4:24 pm
Forum: Numerical Methods Forum
Topic: Which solver to use?
Replies: 20
Views: 9194

Re: Which solver to use?

Yes, I hope so. In my case I think there is only one (local) minimum as long as I am using an error squared cost. If using abs error then I can try multi-start, ie using different starting points to confirm they all up at the same (local) minimum.

Happy days.
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