8006 Exam Dumps : Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

As a bond approaches maturity, its value will be driven less by the time value of money or its coupons, and more by its redemption value, ie the par. Therefore as maturity approaches, its value converges to its par value and this phenomenon is called pull to par.

Short calls and short puts have negative gamma, ie their delta increases at a decreasing rate as the price of the underlying change. Likewise, remember that long calls and long puts have positive gamma.

The LIBOR square is a (rare) derivative contract which pays, as mentioned in the question, the square of the interest rate move between two dates. If LIBOR at inception is y, and upon settlement is x, the contract pays (x - y)^2 for x > y; and -(x - y)^2 for x < y.

For any question that involves calculating delta or gamma, and the payoff is described in terms of variables as is the case here, remember that delta is always the first derivative and gamma is the second derivative. For this question, let us calculate the second derivative and see what the gamma is:

If x > y, then the payoff is (x - y)^2

The first derivative wrt x is 2(x - y)

The second derivative wrt x is 2.

ie, the gamma is 2

If x < y, then the payoff is -(x - y)^2

The first derivative wrt x is -2(x - y)

The second derivative wrt x is -2.

ie, the gamma is -2

If x = y, then the payoff is 0. Both the first and the second derivatives are zero. ie the gamma is 0.

Based on the above, we see that the contract can have a gamma of either 0, +2 or -2. 1 is not a possible value for gamma, and therefore Choice 'b' is the correct answer.