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Lecture8_ImpliedVol

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Unformatted text preview: we have found using “ImpliedVol1” code is consistent with our earlier Goal Seek results (note that our sigma increases by 0.1% at each step) each Goal seek (Vol2 Strike price Market's call price ImpliedVol1 tab) 12.44% 100 7.00 12.50% 11.16% 105 4.00 11.20% 13.19% 110 3.00 13.20% 13.89% 115 2.00 13.90% 13.18% 120 1.00 13.20% 15.60% 125 1.00 15.70% 15-16 Implied Volatility for American Options 15-17 VBA for Implied Vol. (American Options) (1) To compute the implied options for American To options, we can only rely on VBA options, See the “ImpliedVol_VBA2” tab Use the “ImpliedVol3” function in VBA Use (“Alt+F11”) that compute the implied volatility based on given market price based Binomial_all2 is the function we have Binomial_all2 constructed before to use binomial tree pricing for European/American options pricing We let sigma (implied volatility) increase 1% We every step to approximate the market price every 15-18 VBA for Implied Vol. (American Options) (2) Check if our VBA code “ImpliedVol3” works fine First, we use the binomial_all2 VBA code to First, compute the market price of European option given volatility 40% and 100 steps, it’s 17.3648 (Why do we use European option here? We just want to confirm with our earlier results; the result 17.3648 is slightly different from 17.4034 due to approximation error – we can make the approximation more precise by increasing the step numbers, but it take much longer; thus, I just go with 100 steps) go 15-19 VBA for Implied Vol. (American Options) (3) Then, we import the 17.3648 as the market price Then, into the VBA function “ImpliedVol3” and get the implied volatility = 40.00%, which confirms that our code is good (at least at the European part) our 15-20 VBA for Implied Vol. (American Options) (4) Now, when we use the ImpliedVol3 to compute Now, the implied volatility of American options the First, we use the binomial_all2 VBA code to First, compute the market price of American option given volatility 40% and 100 steps, it’s 17.3648 (it’s the same as European option) (it’s Then, we import the 17.3648 as the market price Then, into the VBA function “ImpliedVol3” and get the implied volatility = 40.00%, which confirms that our code is good our 15-21 A real example – S&P 500 option (1) Now, let’s try to use the ImpliedVol3 VBA function Now, to compute the implied volatility in a real case – the S&P 500 index option the We select S&P500 option as t...
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