Bootstrapping the underlying's price history prices options where no option market exists

The pipeline starts from a single observed discounted price series. An AR(1) fit takes out the linear predictability, and a stationary block bootstrap of the residuals preserves the dependence that remains after that fit ^[3]. Only then comes the no-arbitrage step, and it is one number: a scalar correction following Duan and Simonato [1998] that enforces the martingale condition required by the Fundamental Theorem of Asset Pricing ^[4]. Whatever shape the bootstrapped distribution has is otherwise left alone, and no parametric distributional assumption is imposed beyond what the data itself exhibits ^[13].

That single correction is also the limit of what the study claims. The author wrote that the construction does not recover the risk-neutral measure itself in the usual economic sense; it is a pricing measure obtained by disturbing the historical dynamics as little as possible, to verify the FTAP ^[5].

Validation is against a real surface: the implied volatility surface of DAX index European options quoted July 5, 2002, with prices compared directly instead of implied volatilities ^[6]. Those quotes sit about 24 years before the conference the study was accepted for ^[11]. The reported validation covers one index on one quote date ^[15]. The post does not report how large the pricing errors were ^[12].

Standard practice would assume a parametric family for the underlying's dynamics, geometric Brownian motion or stochastic volatility or jump-diffusion, then calibrate that family's parameters to observed option prices ^[8]. The study's motivation is that this works where a liquid option market exists and does not help where one does not: an Asian option on a private index, an option embedded inside an insurance product, a participation certificate ^[8][9]. Because no option-market input enters at any stage, the same construction runs on path-dependent payoffs, which the study illustrates on arithmetic Asian options ^[7].

So the DAX comparison is a check on the one class of contract the method is not needed for. A new pricing measure is ordinarily in exactly this position, and it is worth stating plainly.

The author is asking for the argument now: "I'm now interested in constructive remarks and feedback on the study, that will allow to enrich, improve and robustify the methodology," the post says ^[10].