I want to price a quanto option using a Stochastic Volatility model (like Heston model, 1993).
Normally, what we do is:
- Calibrate the stochastic volatility model,
- draw a binomial tree consistent with the model, with numerous steps and
- derive the option price from the binomial tree.
This process is given as an example in this book on page 284, where an European vanilla option is priced under a stochastic volatility model.
But what about for a quanto option? How can I draw a binomial tree to price this option? That is, a binomial tree that takes into consideration the correlation among the underlying asset and the exchange rate?
Is there some way to apply a stochastic volatility model to price a quanto option? Could you please help me with the detailed steps?
The quanto option pricing formula is given in this paper.
[EDIT - being more specific] Suppose I already have:
- The correlation among the underlying asset ($S$) and the exchange rate. I have it. I know it is, say, 0.7.
- I have a well calibrated Heston model for the volatilities of both the underlying asset ($S$) and the exchange rate.
I want to know:
- How to get, from my Heston model, the volatilities that I need to put into the quanto option pricing formula? In the formula of this paper, the vols are supposed constant. How can I treat stochastic vols using this formula? I do not know what vols I shoul put into the quanto option pricing formula. I want to know how to get the vols that I need from the Heston model.