At the close of business on March 31, Chevron sold for 107.37 per share. Call options at various strike prices expiring May 19 sold for the following prices:

Strike	Price
95	12.05
100	10.78
105	3.93
110	1.28
115	0.28
120	0.05

Graph the smile for this set of call options, using the Manaseter and Koehler (M-K) technique. The interest rate is 2 percent per year.

M-K technique:

Let ABS(z)= absolute value of z.

Given a stock price S₀, a strike price X, the interest rate r and the time to expiration T.

Our 1st estimate of implicit volatility according to the M-K method is ₁=((ABS(LN(S₀/X)+rT))*(2/T))^0.5.

The 1^st 2 terms are in the absolute value bracket.

You take the square root of the whole equation

The update formula is:

2= 1 [(C1-C*(true)) * (2)0.5 exp(d2/2)/[S0 (T) 0.5]]

where d is calculated from the 1st (or previous)iteration with your initial estimate of thestandard deviation. C*(true) is the market price of the option.