Re: [Quantlib-users] Pricing swaption via Hull-White Monte-Carlo

[Amine I. <ami...@gm...>]

Hi Philippe,

I believe your forecastHandle variable - which is set to the MC curve generated for scénario i - is actually used for discounting only. discountingSwapEngine only affects the discounting and not the curves upon which the floating index is dependent. 

You need to “clone” the libor 3m index for your underlying swap and relink its curve to a MC curve as well.

Amine Ifri

> On 2 Apr 2021, at 04:11, Philippe Hatstadt <phi...@ex...> wrote:
> 
> 
> I have built a Hull-White sequence via standard method, by following precisely the method in the QuantLib Cookbook, with sigma = 10% and mean_rev = 10%.
> My goal is to ultimately build an OAS model for some Agency CMOs, for which I am building a Monte-carlo engine.
> I also built a Jamshidian engine to compute a closed-form value of a european swaption as a test, to make sure that my MC valuation converges to the theoretical value.
> The convergence doesn't work, and I think it has to do with the floating index of the swaption, so let me explain.
> 
> I first build a curve name forecastHandle of type ql.RelinkableYieldTermStructureHandle
> I then build a swaption object via my own build_swaption() function, along the lines of the swaption helpers from the Cookbook approach, which returns a ql.Swaption() object. The curve handle is passed to the build_swaption() call along with tenor, maturity and strike.
> I build the floating index as follows inside the function:
> libor_3m = ql.USDLibor(ql.Period('3M'), forecastHandle) 
> 
> Now switching to the MC calculation. I loop on all the sequences of short-term rates generated by my HW sequence. I verified that the expected value and the variance of the short-rate are the same as in the Cookbook.
> Lastly, in order to calculate the value of the swaption via MC integration, I do the following, which takes place inside a function called swaption_MC(forecastHandle, my_swaption). Importantly, forecastHandle is the same handle that was used to build the swaption, including its libor_3m index. 
> for i in range(num_paths):
>     curve = hw_discount_curve(i)
>     forecastHandle.linkTo(curve)
>     engine = ql.DiscountingSwapEngine(forecastHandle)
>     swap = my_swaption.underlyingSwap()
>     swap.setPricingEngine(engine)
>     swap_npv = swap.NPV()
>     sum_pv += max(0, swap_npv)
> return sum_pv / num_paths
> I was therefore hoping that by linking the forecastHandle to each path-wise stochastic curve, the libor 3m index would also be path dependent. but somehow, that doesn't appear to be the case, as the floating rates for each reset do not change with each stochastic curve. So I am wondering what I am doing wrong?
> 
> Help appreciated.
> 
> Philippe Hatstadt
> 
> 
> 
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> 
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