Mathematical Modeling in Finance with Stochastic Processes
1.7. STOCHASTIC PROCESSES 61 and the collisions of molecules in a gas are a “random walk” responsible for diffusion. In this pro ...
62 CHAPTER 1. BACKGROUND IDEAS Figure 1.7: The family tree of some stochastic processes ...
1.7. STOCHASTIC PROCESSES 63 of elementary probability theory. In elementary probability theory, random variables are a mapping ...
64 CHAPTER 1. BACKGROUND IDEAS Weisstein, Eric W. “Stochastic Process.” From MathWorld–A Wolfram Web Resource. Stochastic Proce ...
tions (CDOs) 1.8 A Binomial Model of Mortgage Collateralized Debt Obliga- Vocabulary Atrancheis a portion or slice of a set of ...
66 CHAPTER 1. BACKGROUND IDEAS For simplicity, each loan will have precisely one of 2 outcomes. Either the home-buyer will pay ...
1.8. A BINOMIAL MODEL OF MORTGAGE COLLATERALIZED DEBT OBLIGATIONS (CDOS) 67 Now from the point of view of the contract buyer, th ...
68 CHAPTER 1. BACKGROUND IDEAS as owning a mortgage loan. Reduction of risk with the same payout is very desirable for many inve ...
1.8. A BINOMIAL MODEL OF MORTGAGE COLLATERALIZED DEBT OBLIGATIONS (CDOS) 69 Assume that the underlying mortgages actually have a ...
70 CHAPTER 1. BACKGROUND IDEAS 0 to 100 and the base mortgage default probability 0.01 to 0.15 1.8 Default probabilities as a fu ...
1.8. A BINOMIAL MODEL OF MORTGAGE COLLATERALIZED DEBT OBLIGATIONS (CDOS) 71 simple. Lenders will restructure shaky loans or they ...
72 CHAPTER 1. BACKGROUND IDEAS Problems to Work for Understanding Suppose that there is a 20% decrease in the default rate from ...
Chapter 2 Binomial Option Pricing Models 2.1 Single Period Binomial Models Rating Student: contains scenes of mild algebra or ca ...
2 Binomial Option Pricing Models Replication of the option payouts with the single security and the single bond leads to pricin ...
2.1 The single period binomial model. A single stock of initial valueS, in the time interval [0,T] it can either increase by a ...
76 CHAPTER 2. BINOMIAL OPTION PRICING MODELS Figure 2.1: The single period binomial model. ...
2.1. SINGLE PERIOD BINOMIAL MODELS 77 portfolio will have the same value as the derivative if φSD+ψBexp(rT) = f(SD) φSU+ψBexp(rT ...
78 CHAPTER 2. BINOMIAL OPTION PRICING MODELS same quantity. At the end of the period, the value of the derivative would be exact ...
2.1. SINGLE PERIOD BINOMIAL MODELS 79 combination of the risky stock and risk-free bond replicates the derivative. As such the m ...
80 CHAPTER 2. BINOMIAL OPTION PRICING MODELS Problems to Work for Understanding Consider a stock whose price today is $50. Supp ...
«
1
2
3
4
5
6
7
8
9
10
»
Free download pdf