Extract yield volatility from bond option prices

External question — Quantitative Finance Stack Exchange Author: sigma1988 Original post: https://quant.stackexchange.com/questions/80690 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Is there a way to extract yield volatility from bond option prices or to convert implied bond prices to yield volatility?

External answer — Quantitative Finance Stack Exchange Author: Andrea Original post: https://quant.stackexchange.com/a/81165 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. You will need a Bond Option Pricing Formula which uses the yield volatility. There is another question around Bond option on price vs bond option on yield So, the payoff of your bond option is $(K_P-P_T)^+ = (Y_T - Y_K)^+ \cdot (-P'_y)$ You assume normal yield distribution, use the Bachelier formula and imply the yield volatility. See this answer as well: Bachelier model call option pricing formula

External answer — Quantitative Finance Stack Exchange Author: Hritabrata Das Original post: https://quant.stackexchange.com/a/85759 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. If you know the bond price, option price , strike rate , current interest rate for the time period, you can first create a recombining binomial tree with one up and one down movement of current interest rate + x % and current interest rate - x% respectively. Once done, use risk-neutral probability to equate current option price with that of what you would find by discounting the up and down states after adjusting for their corresponding probabilities - that would give you your x value , that gives actual implied normal yield volatility of up and down movements in the binomial tree derived from market prices. Then you basically find standard deviation of that - take variances of option prices of each up and down movements from expectation, adjusted for their risk-neutral probabilities again and sqaureroot it to find the implied volatility.