Embedded theoretical quality option pricing in Treasury bond futures—Starting from the definition deviation of conversion factor

Unlike ordinary futures, Treasury bond futures are a kind of complex financial derivatives with multiple Treasury bonds as the underlying, which can be settled on multiple dates. China's Treasury bond futures contract embeds a quality option, rolling timing option, and month end timing option, and these options restrict each other, making the pricing of Treasury bond futures extremely difficult. Quality option plays a dominant role in these three options. This article creatively divides quality options into theoretical quality option caused by the definition deviation of conversion factor and disturbance quality option caused by the market factors except for interest rate. Using the bond valuation method based on the yield to maturity curve, this article puts forward the embedded theoretical quality option and China's Treasury bond futures pricing models. For the empirical test, the dataset covers a 10‐year Treasury bond futures contract in 151 working days. The results show that the relative error between our model and the actual closing price of the Treasury bond futures is small compared with the cost of carry model, which excludes any embedded options. This research constructs a practical and straightforward pricing model of embedded theoretical quality option.