Question #54 - Reading 31 Valuation of Contingent Claims

Reading: Reading 31 Valuation of Contingent Claims

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Shared Context

- Bower has studied swaps extensively. However, he is not sure which of the following is the swap fixed rate for a one-year interest rate swap based on 90-day LIBOR with quarterly payments. Using the information in Table 1 and the formula below, what is the most appropriate swap fixed rate for this swap? where A) 5.75%. B) 5.65%. C) 6.01%. C= 1 −Z4 Z1 + Z2 + Z3 + Z4 Zn = price of n − zero − coupon bond per $ of principal 1 1 + RN

Question

Bower computes the implied volatility of a one year caplet on the 90-day LIBOR forward rates to be 18.5%. Using the given information what does this mean for the caplet's market price relative to its theoretical price? The caplet's market price is:

Answer Choices:

A. overvalued

B. undervalued

C. undervalued or overvalued

Explanation

Z90−day = = 0.98644 Z180−day = = 0.97264 Z270−day = = 0.95866 Z360−day = = 0.94451 The quarterly fixed rate on the swap = = 0.05549/3.86225 = 0.01437 = 1.437% 1 1+(0.055×90/360) 1 1+(0.05625×180/360) 1 1+(0.57499×270/360) 1 1+(0.058749×360/360) 1−0.94451 0.98644+0.97264+0.95866+0.94451 Volatility and option prices are always positively related. Therefore, since the option implied volatility is lower than the estimated volatility, this implies that the caplet is undervalued relative to its theoretical value.

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