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...

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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. (a) By 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. (b) Which of the five put options produced the highest annualized return? Provide two reasons to explain why the particular put option provided the highest return.
Answered Same DayMar 19, 2021

Answer To: Suppose you have advanced expertise in timing the market, and you were able to predict exactly the...

Shakeel answered on Mar 19 2021
129 Votes
Black-Scholes Model for Value of Call Options Calculation
Solution 1
        Template - Black-Scholes Opti
on Value
        On February 19th                                            On March 12th
        Input Data                                            Input Data
        Stock Price now (P)    3393.52                    3393.52    3393.52    3393.52    3393.52        Stock Price now (P)    2478.86    2478.86    2478.86    2478.86    2478.86
        Exercise Price of Option (EX)    3600                    3200    2800    2400    2000        Exercise Price of Option (EX)    3600    3200    2800    2400    2000
        Number of periods to Exercise in years (t)    0.0833333333                    0.0833333333    0.0833333333    0.0833333333    0.0833333333        Number of periods to Exercise in years (t)    0.0219178082    0.0219178082    0.0219178082    0.0219178082    0.0219178082
        Compounded Risk-Free Interest Rate (rf)    1.64%                    1.64%    1.64%    1.64%    1.64%        Compounded Risk-Free Interest Rate (rf)    0.35%    0.35%    0.35%    0.35%    0.35%
        Standard Deviation (annualized s)    12.58%                    12.58%    12.58%    12.58%    12.58%        Standard Deviation (annualized s)    80.58%    80.58%    80.58%    80.58%    80.58%
        Output Data                                            Output Data
        Present Value of Exercise Price...
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