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hrad
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Posts: 8
Joined: February 3rd, 2012, 2:01 pm

Pricing Options Using Copulas

August 15th, 2020, 11:26 pm

Hi all,

I have a implied black scholes volatility surfaces for European style options on futures. I need to be able to price basket options and spread options.

As far as I understand I can derive a cumulative distribution function for each underlying futures contract by pricing very tight put spreads or call spreads using my implied volatility surfaces ie replicating digital options. I have read that I can impose a dependence structure on these CDF’s to be able to price basket and spread options consistently with the vanilla options. Honestly the maths is a bit too intense for me to fully get my mind around. I’ve bought 3 books now, Dong Qu’s ‘Manufacturing and Managing Customer-Driven Derivatives’, and Umberto Cherubinis ‘Copula Methods in Finance’ and ‘Dynamic Copula Methods in Finance’. I understand the maths enough that I get the concept, I love the concept, I desperately want to implement it, but even after all the reading I genuinely don’t even know where to begin to make it happen.

If someone can help me by showing me in excel or pointing me in the right direction of how to implement in excel (long story but it needs to be excel) it would be so amazing.
 
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nikol
Posts: 5
Joined: January 29th, 2002, 9:14 pm

Re: Pricing Options Using Copulas

December 1st, 2020, 8:43 pm

Rough method which can help you to get an idea:
1. "empirical" CDF per underlying will help you to convert it into normal CDF's
2. transform normal CDFs with correlation matrix into correlated normal CDFs 
3. transform normal correlated CDFs back into "empirical" CDF space.
4. price whatever you want
Note, that you have to carefully define and measure correlations, otherwise you might get some inconsistencies. That's where the complexity enters.