Question #6

Reading: Reading 31 Valuation of Contingent Claims

PDF File: Reading 31 Valuation of Contingent Claims.pdf

Page: 3

Status: Unattempted

Part of Context Group: Q6-9 First in Group
Shared Context
of 111 The value of a put option is positively related to all of the following EXCEPT: A) risk-free rate. B) exercise price. C) time to maturity. Max Perrot, CFA, works for WWF, a mortgage banking company which originates residential mortgage loans. On a monthly basis, WWF issues agency mortgage-backed securities (MBS) backed by their loans. WWF sells the MBS in the open market soon after securitization, but retains the servicing rights to the loans. WWF currently owns the third largest mortgage servicing portfolio in the U.S. Perrot has recently been promoted to Senior Vice President of Asset and Liability Management for WWF. Perrot's new responsibilities encompass hedging WWF's newly created MBS prior to their sale, as well as managing the interest rate exposure on the servicing portfolio. Both types of assets are extremely sensitive to changes in interest rates, though not necessarily in the same manner. Although WWF has retained all of the servicing rights of its loans in the past, they are not opposed to the selling of portions of the portfolio if market conditions are right. WWF's management wants Perrot in his new position to focus primarily on preserving the value of the servicing portfolio through hedging strategies that are cost effective to execute. Also, any hedge strategy used by Perrot must be extremely liquid in the event that a portion of the servicing portfolio is sold and the hedge needs to be unwound. The upper management of WWF anticipates a period of volatility in interest rates, and they have asked Perrot to project expected returns of a hedged position under a variety of interest rates scenarios. Perrot's predecessor lacked experience in hedging with swaps and futures contracts, but he had used them periodically with lackluster results. Through his inaction, he had exposed the firm to significant asset and liability mismatch, which had increased dramatically over the past two years as both production and the servicing portfolio had grown. Perrot, on the other hand, had extensive experience with hedging with derivatives in his prior job. He is familiar with executing hedging strategies utilizing not only swap and futures, but also with options such as caps and floors. He decides that before he presents any potential hedging strategy to WWF's management, he would first like to bring them up to speed on the basic hedging concepts. He prepares a brief presentation on the relationships between interest rates and options, and outlines some basic hedging strategies. He anticipates many questions that may arise from his presentation, and prepares a handout in a question and answer format.
Question
Assume that a three-year semi-annually settled floor with a strike rate of 8% and a notional amount of $100 million is being analyzed. The reference rate is six-month London Interbank Offered Rate (LIBOR). Suppose that LIBOR for the next four semi-annual periods is as follows: Period LIBOR 1 7.5% 2 8.2% 3 8.1% 4 8.7% What is the payoff for the floor for period 1?
Answer Choices:
A. $0
B. $250,000
C. $500,000
Explanation
The payoff for each semi-annual period is computed as follows: Payoff = notional amount × (floor rate − six-month LIBOR) / 2 so for period 1: = $100 million × (8.0% − 7.5%) / 2 = $250,000
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