Inferring Yield Volatility from Bond Option Prices
Summary
The document outlines two ways to infer yield volatility from bond option prices. One approach expresses a put payoff on bond price in terms of yield differences and the bond’s price sensitivity to yield. Assuming normally distributed yields, it then applies the Bachelier option pricing formula and solves for the implied yield volatility.
A second approach builds a one-period recombining binomial tree for interest rates, with upward and downward moves around the current rate. Risk-neutral probabilities and discounted payoffs can be matched to the observed option price to estimate the size of the rate moves; their probability-weighted dispersion gives a volatility estimate. The discussion is brief and provides no worked example or comparison of the methods. The binomial description also leaves details such as calibration and model assumptions unspecified, so the resulting estimate depends on the chosen setup.
Key ideas
- Bond option prices can be translated into yield volatility using a bond option pricing model.
- A normal yield assumption allows implied volatility to be found with the Bachelier formula.
- A recombining rate tree can be calibrated to an observed option price using risk-neutral probabilities.
- The probability-weighted dispersion of rate outcomes provides a volatility estimate.
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# Extract yield volatility from bond option prices # Extract yield volatility from bond option prices Is there a way to extract yield volatility from bond option prices or to convert implied bond prices to yield volatility? ## Answer by Andrea (score 0) https://quant.stackexchange.com/a/81165 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 ## Answer by Hritabrata Das (score 0) https://quant.stackexchange.com/a/85759 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.
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