Financial Math Problem: Black-Scholes formula

= Problem 3 (Required, 25 marks) An option writer has sold (short-sell) an option on an asset currently. This option gives the holder the right to either (1) sell 2 units of the asset at price $40 or (2) sell 1 unit of asset at price $22 (but not both) after 1 year. (*Note: On the other hand, the investor can choose not to exercise the options) Recently, the option writer decides to delta-hedge and gamma-hedge the short position using the asset and 1-year at-the-money European option. You are given that The current price of the asset is S. $20. The market information of various 1-year European put options on this asset is summarized in the following table: Strike Price Market Price Delta Gamma Option A 16 0.337674 -0.117771 0.037838 Option B 18 0.803031 -0.23112 0.058294 Option C 20 1.55191 -0.36989 0.072112 Option D 22 2.586022 -0.5125 0.075882 Option E 24 3.8696 -0.64119 0.070694 (a) Determine the current price of the options sold by the option writer. (b) Hence, determine the hedging strategy adopted by the option writer. = Problem 3 (Required, 25 marks) An option writer has sold (short-sell) an option on an asset currently. This option gives the holder the right to either (1) sell 2 units of the asset at price $40 or (2) sell 1 unit of asset at price $22 (but not both) after 1 year. (*Note: On the other hand, the investor can choose not to exercise the options) Recently, the option writer decides to delta-hedge and gamma-hedge the short position using the asset and 1-year at-the-money European option. You are given that The current price of the asset is S. $20. The market information of various 1-year European put options on this asset is summarized in the following table: Strike Price Market Price Delta Gamma Option A 16 0.337674 -0.117771 0.037838 Option B 18 0.803031 -0.23112 0.058294 Option C 20 1.55191 -0.36989 0.072112 Option D 22 2.586022 -0.5125 0.075882 Option E 24 3.8696 -0.64119 0.070694 (a) Determine the current price of the options sold by the option writer. (b) Hence, determine the hedging strategy adopted by the option writer