The Following Information Relates to Questions
Meredith Alvarez Is

question 7

Multiple Choice

The following information relates to Questions
Meredith alvarez is a junior fixed-income analyst with Canzim asset Management. her su-pervisor, Stephanie hartson, asks alvarez to review the asset price and payoff data shown in exhibit 1 to determine whether an arbitrage opportunity exists.exhibit 1 Price and Payoffs for two risk-Free assets
$\begin{array} { l c c } \text { Asset } & \text { Price Today } & \text { Payoff in One Year } \\\hline \text { Asset A } & \$ 500 & \$ 525 \\\text { Asset B } & \$ 1,000 & \$ 1,100\end{array}$
hartson also shows alvarez data for a bond that trades in three different markets in the same currency. These data appear in exhibit 2.
exhibit 2 2% Coupon, Five-Year Maturity, annual-Pay bond
$\begin{array} { l c c c } & \text { New York } & \text { Hong Kong } & \text { Mumbai } \\\hline \text { Yield to Maturity } & 1.9 \% & 2.3 \% & 2.0 \% \\\hline\end{array}$
hartson asks alvarez to value two bonds (bond C and bond D) using the binomial tree in exhibit 3. exhibit 4 presents selected data for both bonds.
exhibit 3 binomial interest rate tree with Volatility = 25%
$\begin{array}{llcc} \hline\text {Time 0 } & \text { Time 1} &\text {Time 2 } &\\ \text { } &&2.7183 \%\\ \text { } &2.8853 \%&\\ 1.500 \% &&1.6487 \% \\&1.7500 \% &\\&&1.0000 \%\\\hline\end{array}$

exhibit 4 Selected Data on annual-Pay bonds
$\begin{array} { l c c } \text { Bond } & \text { Maturity } & \text { Coupon Rate } \\\hline \text { Bond C } & 2 \text { years } & 2.5 \% \\\text { Bond D } & 3 \text { years } & 3.0 \% \\\hline\end{array}$
hartson tells alvarez that she and her peers have been debating various viewpoints regard-ing the conditions underlying binomial interest rate trees. The following statements were made in the course of the debate.
Statement 1: The only requirements needed to create a binomial interest rate tree are current benchmark interest rates and an assumption about interest rate volatility.
Statement 2: Potential interest rate volatility in a binomial interest rate tree can be es-timated using historical interest rate volatility or observed arket prices from interest rate derivatives.
Statement 3: a bond value derived from a binomial interest rate tree with a relatively
high volatility assumption will be different from the value calculated by discounting the bond's cash flows using current spot rates. based on data in exhibit 5, hartson asks alvarez to calibrate a binomial interest rate tree starting with the calculation of implied forward rates shown in exhibit 6.
exhibit 5 Selected Data for a binomial interest rate tree
$\begin{array} { l c l } \text { Maturity } & \text { Par Rate } & \text { Spot Rate } \\\hline 1 & 2.5000 \% & 2.5000 \% \\2 & 3.5000 \% & 3.5177 \% \\\hline\end{array}$
exhibit 6 Calibration of binomial interest rate
$\begin{array}{l}\text { Tree with Volatility } = 25 \%\\\begin{array} { l c } \hline \text { Time } 0 & \text { Time } 1 \\\hline & 5.8365 \% \\2.500 \% &\\&\text { Lower one-period forward rate }\\\hline\end{array}\end{array}$
hartson mentions pathwise valuations as another method to value bonds using a binomial
interest rate tree. using the binomial interest rate tree in exhibit 3, alvarez calculates the pos-sible interest rate paths for bond D shown in exhibit 7.
exhibit 7 interest rate Paths for bond D
$$\begin{array} { l l l l } \text { Path } & { \text { Time 0 } } & { \text { Time 1 } } & \text { Time 2 } \\\hline 1 & 1.500 \% & 2.8853 \% & 2.7183 \% \\2 & 1.500 & 2.8853 & 1.6487 \\3 & 1.500 & 1.7500 & 1.6487 \\4 & 1.500 & 1.7500 & 1.0000 \\\hline\end{array}$$
before leaving for the day, hartson asks alvarez about the value of using the Monte Carlo method to simulate a large number of potential interest rate paths to value a bond. alvarez makes the following statements.
Statement 4: increasing the number of paths increases the estimate's statistical accuracy.
Statement 5: The bond value derived from aMonte Carlo simulation will be closer to the bond's true fundamental value.
-based on exhibits 3 and 4, the value of bond C at the upper node at time 1 is closest to:

• A) 97.1957.
• B) 99.6255.
• C) 102.1255.

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Definitions:

Natural Selection

The process by which biological traits become either more or less common in a population as a function of the effect of inherited traits on the survival and reproduction of individuals.

Advantageous Genes

Genetic traits that provide a benefit to the individual, increasing the likelihood of survival and reproduction.

Subsequent Generations

Subsequent generations refer to the offspring or descendants that follow the current generation, highlighting the lineage or succession in families or species.

Natural Selection

The process by which organisms better adapted to their environment tend to survive and produce more offspring, a key mechanism in evolution.