Question

Suppose you have advanced expertise in timing the market, and you were able to predict exactly the beginning of the market collapse on Wednesday, February 19, 2020, when the S&P 500 index hit a high of 3,393.52. You were also able to perfectly forecast the turning point on Thursday, March 12, 2020, when the S&P 500 index hit a low of 2,478.86. Suppose that put options on the S&P 500 index were available on February 19, with strike prices of 3,600, 3,200, 2,800, 2,400, and 2,000, all maturing on Friday, March 20, 2020. Assume that the appropriate risk-free rate of interest on February 19 was 1.64% and that it was 0.35% on March 12. Similarly, assume that the volatility of the S&P 500 index as measured on February 19 was 12.58% and that it was 80.58% on March 12. Using a Black-Scholes-Merton option pricing model, calculate the prices of the five put options on February 19 (at purchase) and again on March 12 (at sale). Calculate the dollar profit made on each put option. Finally, calculate the annualized percentage return obtained on each put option. Show these results (purchase price, sale price, dollar profit, and annualized return) in a table.   Using a Black-Scholes-Merton option pricing model, calculate the prices of the five put options on February 19 (at purchase) and again on March 12 (at sale). Calculate the dollar profit made on each put option. Finally, calculate the annualized percentage return obtained on each put option. Show these results (purchase price, sale price, dollar profit, and annualized return) in a table.                                                                                                                                                [20]

Answer 1

Strike Price	FEB.19	MAR.12
Risk Free rate	Volatility	At purchase	$ Profit	Annualized return	Risk Free rate	Volatility	At Sale	$ Profit	Annualized return
3600	0.0164	0.1258	3595.15	4.85	2.26	0.0035	0.8058	3599.72	0.28	4.96
3200	0.0164	0.1258	3195.69	4.31	2.01	0.0035	0.8058	3199.76	0.24	4.25
2800	0.0164	0.1258	2796.23	3.77	1.76	0.0035	0.8058	2799.78	0.22	3.90
2400	0.0164	0.1258	2396.77	3.23	1.50	0.0035	0.8058	2399.82	0.18	3.19
2000	0.0164	0.1258	1997.31	2.69	1.25	0.0035	0.8058	1999.85	0.15	2.66
				18.85					1.07