Printed April 16, 2009
Exercise on Probability Essentials
By Author. Jean Jacod, Philip Protter
Byoung jin Choi e-mail: choibj@chungbuk.ac.kr
Abstract In this book we solve a exercise of the Probability Essentials wrote by Jean Jacod, Philip Protter.
Auth
Solutions of Selected Problems from Probability Essentials, Second Edition
Solutions to selected problems of Chapter 2 2.1 Let's first prove by induction that #(2n ) = 2n if = cfw_x1 , . . . , xn . For n = 1 it is clear that #(21 ) = #(cfw_, cfw_x1 ) = 2.
Printed April 10, 2009
Exercise on Probability Essentials
By Author. Jean Jacod, Philip Protter
Byoung jin Choi e-mail: choibj@chungbuk.ac.kr
Abstract In this book we solve a exercise of the Probability Essentials wrote by Jean Jacod, Philip Protter.
Auth
Chapter 8
Swaps
Question 8.1. We rst solve for the present value of the cost per two barrels: $22 $23 = 41.033. + 1.06 (1.065)2 We then obtain the swap price per barrel by solving: x x = 41.033 + 1.06 (1.065)2 x = 22.483, which was to be shown. Question 8
Chapter 5
Financial Forwards and Futures
Question 5.1. Four different ways to sell a share of stock that has a price S(0) at time 0. Description Outright Sale Security Sale and Loan Sale Short Prepaid Forward Contract Short Forward Contract Question 5.2.
Chapter 4
Introduction to Risk Management
Question 4.1. The following table summarizes the unhedged and hedged prot calculations: Copper price in Total cost one year $0.70 $0.90 $0.80 $0.90 $0.90 $0.90 $1.00 $0.90 $1.10 $0.90 $1.20 $0.90 Unhedged prot $0.
Chapter 3
Insurance, Collars, and Other Strategies
Question 3.1. This question is a direct application of the Put-Call-Parity (equation (3.1) of the textbook. Mimicking Table 3.1., we have: S&R Index 900.00 950.00 1000.00 1050.00 1100.00 1150.00 1200.00 S
Chapter 2
An Introduction to Forwards and Options
Question 2.1. The payoff diagram of the stock is just a graph of the stock price as a function of the stock price:
In order to obtain the prot diagram at expiration, we have to nance the initial investment
Chapter 1
Introduction to Derivatives
Question 1.1. This problem offers different scenarios in which some companies may have an interest to hedge their exposure to temperatures that are detrimental to their business. In answering the problem, it is useful