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riazp94
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Posts: 18
Joined: September 11th, 2017, 6:48 pm

Implied volatilities under stochastic interest rates

November 20th, 2018, 5:13 pm

Hi all,

As part of my masters dissertation I have to implement the hybrid Heston-Hull-White (HHW) model. There is no closed form solution for the characteristic function of this model. In https://staff.fnwi.uva.nl/p.j.c.spreij/ ... 0Rates.pdf  , Lech A. Grzelak and Cornelis W. Oosterlee provide a couple of methods for approximating the HHW model so that a closed form expression for the characteristic method can be found. 

On page 273 and 274 of the paper (table 1 and attached), the authors provide a pricing comparison of these approximated models with the full model, obtained via Monte Carlo simulation. The comparison is done in terms of implied volatilities. It is not immediately clear to me how one would compute Black Scholes implied volatilities when there is a stochastic interest rate. 

Does anyone have any thoughts on this?
Attachments
Screenshot 2018-11-20 at 19.09.37.png
Table 1, Page 273 and 274
 
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bearish
Posts: 5188
Joined: February 3rd, 2011, 2:19 pm

Re: Implied volatilities under stochastic interest rates

November 20th, 2018, 5:29 pm

I would guess that they use the implied vol from a standard Black-Scholes model with the constant interest rate set equal to the initial yield curve’s spot rate to the option maturity date. And from a quick glance, that initial curve seems to be flat at 2%.