New - Reading 43 - The Arbitrage-Free Valuation Framework

Question 1

What is Arbitrage-free valuation?

Answer 1

Arbitrage-free valuation refers to an approach to security valuation that determines security values that are consistent with the absence of arbitrage opportunities,

Question 2

What is the principal of no-arbitrage?

Answer 2

That in a well functioning market, prices adjust until there are no arbitrage opportunities

Question 3

What is The Law of One Price?

Answer 3

That two goods that are perfect substitutes must sell for the same current price in the absence of transaction costs

Question 4

What are the two types of arbitrage opportunities?

Answer 4

1. Value Additivity - the value of the whole equals the sum of the values of the parts
2. Dominance - A financial asset with a risk-free payoff in the future must have a positive price today

Question 5

What are 2 functions in the valuation process that the interest rate tree performs?

Answer 5

1. Generate the cash flows that are interest rate dependent
2. Supply the interest rates used to determine the present values of the cash flows

Question 6

What is the purpose of an interest rate model?

Answer 6

It seeks to identify the elements or factors that are believed to explain the dynamics of interest rates

Question 7

Why are interest rate models referred to as one factor models?

Answer 7

b/c only one interest rate is being modeled over time

Question 8

What are the two primary reasons for using a lognornal model of interest rates?

**Talking about an interest rate tree**

Answer 8

1. non-negativity of interest rates
2. higher volatility of interest rates

Question 9

What is the equation used in an interest rate tree to determine implied upper & lower forward rates?

Answer 9

Question 10

What are the 2 methods used to estimate interest rate volatility?

Answer 10

1. By estimating historical interest rate volatility
2. Based on observed market prices of interest rate derivatives (aka “implied volatility”)

Question 11

What is the name of the method to find the value of a bond at a given node?

Answer 11

backward induction valuation

Question 12

What is the equation to calculate a bond’s value at a node?

Answer 12

Question 13

What is an alternative approach to backwise induction in a binomial tree?

Answer 13

Pathwise Valuation

it calculates the present value of a bond for each possible interest rate path and take the averahe of these values across paths

Question 14

What are the steps to calculate a Pathwise Valuation?

Answer 14

1. Specify a list of all potential paths throught the tree
2. Determine the present value of a bond along each potential path
3. Calculate the average across all possible paths

Question 15

What is a Monte Carlo Method used for?

Answer 15

It is an alternative method for simulating a large number of potential interest rate paths in an effort to discover how a value of a security is affected

Question 16

What are the steps in using the Monte Carlo method?

Answer 16

1. Simulate numerous paths of one-month interest rates under some volatility assumption and probability distribution
2. Generate spot rates from the simulated future one-month interest rates
3. Determine the cash flow along each interest rate path
4. Calculate the present value for each path
5. Calculate the average present value across all interest rate paths

Question 17

Who do you determine the arbitrage free value of a bond?

Answer 17

Steps:

1. Project all cash flows on a timeline
2. Discount each cash flow back with appropriate spot rate
3. Calculate the sum of all Present Values

Question 18

How do you determine what are the correct spot rates to use?

Answer 18

Bootstrapping

Question 19

How do you calculate the aribtrage free price of a bond?

**ciritical concept**

Answer 19

discount all of the bond’s cash flows back at the implied interest rate