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I am trying to reproduce the results of the paper Bond Variance Risk Premiums. In the online appendix A they noted their metholodology. I have a data set of American future and option prices on these futures and I want to transform them into European forward prices. Based on that my questions:

How do I calibrate the market price of risk in step 2? I would try to do a golden section search with a formula like min [real-option-prices - theoretical-option-prices-calculated-with-the-market-price-of-risk-as-variable]. Is there such a closed form formula with the market price of risk as variable or how do I get the market price of risk out of option data?

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