Question

5. (a) The stock price is 80 the volatility of the stock is 20%. Assuming that the time to expiration is 3 months and the interest rate is 1% per annum calculate the price P of the European call option with strike 81. (b) Calculate ?, ?, ?, Vega using formulas for these parameters. Calculate the same parameters approximately using the options calculator. (c) Check that following relationship holds ? + rx? + \frac{1}{2}?²x²? = rP

          5. (a) The stock price is 80 the volatility of the stock is 20%. Assuming that the time to expiration is 3 months and the interest rate is 1% per annum calculate the price P of the European call option with strike 81.
(b) Calculate ?, ?, ?, Vega using formulas for these parameters. Calculate the same parameters approximately using the options calculator.
(c) Check that following relationship holds
? + rx? + \frac{1}{2}?²x²? = rP

5. (a) The stock price is 80 the volatility of the stock is 20%. Assuming that the time to expiration is 3 months and the interest rate is 1% per annum calculate the price P of the European call option with strike 81.
(b) Calculate ?, ?, ?, Vega using formulas for these parameters. Calculate the same parameters approximately using the options calculator.
(c) Check that following relationship holds
? + rx? + (1)/(2)?²x²? = rP

Added by Marc L.

Horngren’s Cost Accounting

Srikant M. Datar, Madhav V. Rajan 16th Edition

Instant Answer

Solved by Expert Oluwadamilola Ameobi

09/14/2023

Step 1

01 σ = volatility = 20% = 0.20 T = time to expiration = 3 months = 0.25 years Calculating d1: d1 = (ln(80/81) + (0.01 + (0.20^2)/2) * 0.25) / (0.20√0.25) d1 = (ln(0.9877) + (0.01 + 0.02/2) * 0.25) / (0.20√0.25) d1 = (-0.0123 + 0.015) / (0.20 * 0.5) d1 = 0.0027 / Show more…

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(a) The stock price is 80 the volatility of the stock is 20%. Assuming that the time to expiration is 3 months and the interest rate is 1% per annum calculate the price P of the European call option with strike 81 . (b) Calculate Delta ,Gamma , ho , Vega using formulas for these parameters. Calculate the same parameters approximately using the options calculator. (c) Check that following relationship holds Theta +rxDelta +(1)/(2)sigma ^(2)x^(2)Gamma =rP 5. (a) The stock price is 80 the volatility of the stock is 20%. Assuming that the time to expiration is 3 months and the interest rate is 1% per annum calculate the price P of the European call option with strike 81 (b) Calculate , T, , Vega using formulas for these parameters. Calculate the same parameters approximately using the options calculator. (c) Check that following relationship holds 2