Choosing Volatility and Rates for Binomial American Put Pricing

Summary

The document asks how to choose volatility and interest-rate inputs when pricing American puts with a binomial model and comparing estimates with market prices. The author proposes using the standard deviation of recent log returns for volatility and considers a Treasury yield matching the option’s duration for the rate. They are unsure how to interpret the yield’s compounding convention and report that either convention still gives prices far from market values.

The only evidence offered is a basic implementation check: with invented inputs, the binomial result is close to a Black–Scholes European option value and slightly higher, as expected for an American put. This does not validate the model’s market calibration or answer the input-selection questions. The document contains no practical response, data analysis, or guidance on other pricing inputs, so it serves as a statement of unresolved modeling concerns rather than a complete method.

Key ideas

• The document asks how to estimate volatility and interest rates for binomial pricing of American puts.
• It considers recent log-return variability as a possible volatility estimate.
• It questions which compounding convention applies to Treasury yields used as the risk-free rate.
• A comparison with a European pricing result checks only a basic expectation and does not resolve market mispricing.

Tags

# How to estimate $\sigma$ and $r$ in binomial pricing model?


# How to estimate $\sigma$ and $r$ in binomial pricing model?












I am writing a program to price American put options with binomial pricing model and to compare it with the market price.

When I used made-up numbers for $\sigma$ and $r$, the price by binomial pricing model is very close to its European counterpart by Black-Scholes equation. (And always a little bit higher which makes sense since American puts should be worth more than European puts). So my code should be correct in this sense.

And my question is what volatility and interest rate I should use? 1. If the duration of the option is 1 month, should I use $std(log(\frac{S_{i+1}}{S_i}))$ for the past month as the volatility $\sigma$ in the model? 2. For the interest rate $r$, I found that some people suggest to use the treasury rate for the corresponding duration of the option. However, I found no source saying whether the rates on https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield are continuously compounded or annually compounded. I tried using both. But both of the resulted option prices are still way off from the market value.

Any other related suggestions are more than welcome. If anyone with practical experience can answer these naive questions, I'd really appreciate it.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.