Question: For the Microsoft option prices below (prices at closing on June 4, 2023), the Risk-free rate R f = 3.84. Q: what is the annual

For the Microsoft option prices below (prices at closing on June 4, 2023), the Risk-free rate R_{f =}3.84.

Q: what is the annual implied volatility of returns of MSFT shares in the options?

Microsoft's current stock price is $335.40; Assume no dividends; Expiry of options December 15, 2023 (assume 190 days to expiration). Please provide calculations, formulas used, and step-by-step explanations.

Calls (Expiration: 12/20/2023); Puts (Expiration 12/20/2023)

Strike	Price	Intrinsic value	Implied Variance		Strike	Price	Intrinsic Value	Implied Variance
325	$36.46	10.4	26.06		325	$16.75	N/A	16.75
350	$22.04	N/A	22.04		350	$28.90	14.6	14.3

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