Adding an experimental analytic pricer for forward-start european options in Heston model

[jackgillett101]

…ions in Heston model

This is an implementation of S. Kruse's paper "On the Pricing of Forward Starting
Options under Stochastic Volatility", which gives an analytical form for forward start options in the Heston model.

There are still several improvements possible (implementation of the characteristic function calculator, integration choices, some numerical stability issues at distant parameters, probably more...), but as a first step I thought it made sense to add this to the experimental section of the repo.

I've tested the prices against the MC procedure and the analytic procedure where possible and they seem reliable (eg. see image below).

(the coloured lines are prices coming from this pricer, the lilac points at resetTime=0 are vanilla prices coming from AnalyticHestonEngine, and the brown dots are MC prices coming from MCForwardEuropeanHestonEngine)

[coveralls]

Coverage increased (+0.04%) to 71.213% when pulling a9bd208 on jackgillett101:analytic_heston_forward_european into 60afa35 on lballabio:master.

[lballabio]

The whole test suite sets a fixed evaluation date before starting, so I suggest using

      Date today = Settings::instance().evaluationDate();

instead.

The idea is that having the evaluation date dependent on the actual today's date makes the tests prone to spurious errors, upon which we have to increase the tolerance to pass. Using a variable date might find some actual errors, but it's unlikely and we don't run the test suite every day anyway.

(Using the fixed date might also allow you to get the tolerance back to its original value in the previous test case.)

[jackgillett101]

This certainly seems sensible. The other tests in that test suite use the current day's date as well (I'd borrowed their convention) - shall I make the change across the suite while I'm doing it?

[jackgillett101]

I've moved to the fixed date throughout the test file. All pass.

I tightened the tolerance again, needed to add some more paths as MC error s still quite large (also changed to PSR because these provide an MC error estimate which I used to track it while developing)