Assignment Task
Task
Illustrate and explain the iterative process to find out the Black-Scholes implied volatility for a European call option. For this, take as a reference a traded stock option. You have to be aware that most of the traded stock options are American, which is why the data is supposed to be taken as a reference (or a guide) to conduct your analysis. You may also find that the above website shows a value for the implied volatility; however, this question is not only about reporting that value. The main objective is to explain and illustrate the iterative procedure based on trial and error, which you can do `by hand’ by substituting several times the Black-Scholes formula, using Excel or some other numerical software as long as you can show the required steps to find out the implied volatility. Explain your procedure and results.
2 Consider the equation 24.2 in the textbook by Hull and the following inconsistency fora hypothetical bond. Initially, the value of the bond’s spread is 0.2 and the value of the recovery rate is 0.2. Now, consider a decrease in the bond’s risk (higher recovery rate and a lower spread) such that the new value of the spread is 0.15 and the new value of the recovery rate is 0.5. Although the change in the parameters suggest a decrease in the bond’s risk, the numerical value of the hazard rate according to equation 24.2 increased. Does this make financial sense? Are we misinterpreting the equation 24.2? Are we using the equation wrong?
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