XYZ stock is currently trading at $50 per share. We ask our favorite trading desk to...
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XYZ stock is currently trading at $50 per share. We ask our favorite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information. For each option price we've run the price through the Black-Scholes formula and solved for the implied volatility. The table also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied vol, the interest rate, and the dividend rate unchanged; Change the current price of the stock by a small amount up and down, say +/- $0.01; Apply the call-price or the put-price formulas, C(S,t) or P(S,t), and obtain the "stock- price-up" and "stock-price-down" prices of the options; Numerically compute the derivative AOption/AS. This is the option's delta at that value of the underlying stock and that implied volatility. It's a measure of how sensitive the option price is to the price of the underlying stock. Note that we could also obtain the delta analytically by the taking the partial derivative (with respect to S) of the functions C(S,t) and P(S,t). XYZ stock is currently trading at $50 per share. We ask our favorite trading desk to price a bunch of 6-month options on XYZ: 4 puts and 4 calls. The table above gives the information. For each option price we've run the price through the Black-Scholes formula and solved for the implied volatility. The table also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied vol, the interest rate, and the dividend rate unchanged; Change the current price of the stock by a small amount up and down, say +/- $0.01; Apply the call-price or the put-price formulas, C(S,t) or P(S,t), and obtain the "stock- price-up" and "stock-price-down" prices of the options; Numerically compute the derivative AOption/AS. This is the option's delta at that value of the underlying stock and that implied volatility. It's a measure of how sensitive the option price is to the price of the underlying stock. Note that we could also obtain the delta analytically by the taking the partial derivative (with respect to S) of the functions C(S,t) and P(S,t).
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Related Book For
Financial Markets And Institutions
ISBN: 978-0132136839
7th Edition
Authors: Frederic S. Mishkin, Stanley G. Eakins
Posted Date:
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