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question

Traders in major financial institutions use the Black-Scholes formula in a backward fashion to infer other traders' estimation of

\sigma

from option prices. In fact, traders frequently quote sigmas to each other, rather than prices, to arrange trades. Suppose a call option on a stock that pays no dividend for 6 months has a strike price of

35, a premium of

2.15, and time to maturity of 7 weeks. The current short-term T-bill rate is 7%, and the price of the underlying stock is $36.12. What is the implied volatility of the underlying security?

Plain-text mathematical notation (without MathML)

Traders in major financial institutions use the Black-Scholes formula in a backward fashion to infer other traders' estimation of σ from option prices. In fact, traders frequently quote sigmas to each other, rather than prices, to arrange trades. Suppose a call option on a stock that pays no dividend for 6 months has a strike price of 35,apremiumof2.15, and time to maturity of 7 weeks. The current short-term T-bill rate is 7%, and the price of the underlying stock is $36.12. What is the implied volatility of the underlying security?

Original LaTeX notation

Traders in major financial institutions use the Black-Scholes formula in a backward fashion to infer other traders' estimation of $\sigma$ from option prices. In fact, traders frequently quote sigmas to each other, rather than prices, to arrange trades. Suppose a call option on a stock that pays no dividend for 6 months has a strike price of $35, a premium of $2.15, and time to maturity of 7 weeks. The current short-term T-bill rate is 7%, and the price of the underlying stock is $36.12. What is the implied volatility of the underlying security?

src

theoremQA-Finance

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upstream_id / Original problem ID: 206
task_id: b124ed35-3b15-590a-8f66-d34d8715e589
task_key: default--test--206
task_revision_id: 1
config / split: default / test

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