A New Method for Valuing Treasury Bond Futures Options by Ehud I. Ronn

By Ehud I. Ronn

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Portfolios were formed for each available striking price having positive open interest and trading volume. The empirical results are reported in Table 3. TABLE 3. 0 Note: N = number of observations. C , (P,,)is the call (put) option's market price, cjt is the time value in the call (put) option's market price. T/,, (U,,) is the model's value for the call (put) option. We thus calculated the average profit for the "all calls" and "all puts" categories as well as subcategories thereof. The choice of these subcategories was dictated by the desire to demonstrate the model's performance for options with positive time value (cj, > 0 and pjt > 0), zero model value (V,, = U,, = O), and market prices exceeding an arbitrary lower bound (Cj, r 1/16, Pi, 2 1/16).

The empirical results demonstrate convincingly that the model values can, at least to market makers trading with close to zero transaction costs, generate arbitrage profits and therefore represent more accurately the fair value of these options. Summary This analysis proposed and implemented a trinomial no-arbitrage model of state-dependent shifts in the term structure of interest rates. This model was then applied to the valuation of several important interest-dependent instruments: Treasury bond futures contracts and call and put options on these futures.

C , (P,,)is the call (put) option's market price, cjt is the time value in the call (put) option's market price. T/,, (U,,) is the model's value for the call (put) option. We thus calculated the average profit for the "all calls" and "all puts" categories as well as subcategories thereof. The choice of these subcategories was dictated by the desire to demonstrate the model's performance for options with positive time value (cj, > 0 and pjt > 0), zero model value (V,, = U,, = O), and market prices exceeding an arbitrary lower bound (Cj, r 1/16, Pi, 2 1/16).

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