PROBLEM 1
Duration has been calculated for the different coupon rates from 0% to 11% as mentioned in the question. The Macaulay Duration formula has been used to calculate the duration. Duration tells us about the bond price volatility with respect to the rates of interests. Duration is basically the weighted average period to obtain all the cash flows arising from the bonds. To calculate duration, the bond price has been calculated and then the Macaulay Duration formula has been applied. It shows that as the coupon rate increases, while YTM remains the same, the duration of the bond also increases. Hence, there is a direct relationship of coupon rates and bond duration.
PROBLEM 2
In the second problem, the option prices have been calculated, and the simultaneous equation approach is used to calculate the price of call option of $ 2.31. The formula has been applied to calculate all the values. In the part B of this question, the state prices qu and qd have been calculated because the market thinks that there would be a $1 in the upstate part of the world and also there would be $1 in the down state of the world. Therefore, these two state prices are determined. Using these two state prices, the value of the put option of $ 2.1 has been calculated.
PROBLEM 3
The third problem is the basic option pricing model. Under this problem, all the five variables of option pricing have been given and the formula has been applied to calculate the price which is the premium for the call option. Call option is basically the right option but not the obligation to buy the underlying commodity at some specified future date or before that at a specified price which is called the strike price or exercise price.................................
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