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Current stock price for XYZ $50.00 3% 0% Interestrate Dividend rate Option PUT PUT PUT PUT CALL CALL CALL CALL Strike Expiration Option Price $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months $50.00 6-months $50.75 6-months $55.00 6-months $60.00 6-months $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Delta Implied Vol (AOption/AS) -0.023 40% 32% 22% 21% 22% 21% 19% 15% -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favourite 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 implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend 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" price of the option Numerally compute the derivative AOptions/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 delta analytically by taking the partial derivative (with respect to 5) of the functions C(S,t) and P(S,t). 1. The $55-stike call is priced at $1.20. Suppose the price of the stock moved up from $50 to $52. For this $55-strike call what would be its approximate updated price if it got priced at the same implied volatility (19%) as before?

Current stock price for XYZ $50.00 3% 0% Interestrate Dividend rate Option PUT PUT PUT PUT CALL CALL CALL CALL Strike Expiration Option Price $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months $50.00 6-months $50.75 6-months $55.00 6-months $60.00 6-months $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Delta Implied Vol (AOption/AS) -0.023 40% 32% 22% 21% 22% 21% 19% 15% -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favourite 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 implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend 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" price of the option Numerally compute the derivative AOptions/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 delta analytically by taking the partial derivative (with respect to 5) of the functions C(S,t) and P(S,t). 1. The $55-stike call is priced at $1.20. Suppose the price of the stock moved up from $50 to $52. For this $55-strike call what would be its approximate updated price if it got priced at the same implied volatility (19%) as before?

Survey of Accounting (Accounting I)
Survey of Accounting (Accounting I)
8th Edition
ISBN:9781305961883
Author:Carl Warren
Publisher:Carl Warren
Chapter15: Capital Investment Analysis
Section: Chapter Questions
Problem 15.2.2MBA
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Please use the Black-Scholes formula 

Current stock price for XYZ $50.00 Interestrate 3% Dividend rate 0% Option PUT PUT PUT PUT - CALL CALL CALL CALL Strike Expiration $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months $50.00 $50.75 $55.00 $60.00 6-months 6-months 6-months 6-months Option Price $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Implied Vol 40% 32% 22% 21% 22% 21% 19% 15% Delta (AOption/AS) -0.023 -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favourite 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 implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend 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" price of the option Numerally compute the derivative AOptions/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 delta analytically by taking the partial derivative (with respect to S) of the functions C(S,t) and P(S,t). 1. The $55-stike call is priced at $1.20. Suppose the price of the stock moved up from $50 to $52. For this $55-strike call what would be its approximate updated price if it got priced at the same implied volatility (19 %) as before?
Transcribed Image Text:Current stock price for XYZ $50.00 Interestrate 3% Dividend rate 0% Option PUT PUT PUT PUT - CALL CALL CALL CALL Strike Expiration $30.00 6-months $40.00 6-months $50.00 6-months $50.75 6-months $50.00 $50.75 $55.00 $60.00 6-months 6-months 6-months 6-months Option Price $0.14 $0.77 $2.74 $2.97 $3.48 $2.97 $1.20 $0.15 Implied Vol 40% 32% 22% 21% 22% 21% 19% 15% Delta (AOption/AS) -0.023 -0.123 -0.431 -0.470 0.569 0.530 0.299 0.065 XYZ stock is currently trading at $50 per share. We ask our favourite 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 implied volatility. The tables also gives the deltas: the derivative of each option price with respect to the stock price. As you know this means: Leave the implied volatility, the interest rate, and the dividend 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" price of the option Numerally compute the derivative AOptions/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 delta analytically by taking the partial derivative (with respect to S) of the functions C(S,t) and P(S,t). 1. The $55-stike call is priced at $1.20. Suppose the price of the stock moved up from $50 to $52. For this $55-strike call what would be its approximate updated price if it got priced at the same implied volatility (19 %) as before?
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