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