108156.pdf

10 Mathematics for Finance Suppose that you have $10,000 to invest in a portfolio. You decide to buy x= 50 shares, which fixes t ...

Introduction: A Simple Market Model 11 1.5 Forward Contracts........................................ Aforward contractis an ag ...

12 Mathematics for Finance Assumptions 1.1 to 1.5 as well as the No-Arbitrage Principle extend readily to this case. The forward ...

Introduction: A Simple Market Model 13 Cash $55 from the risk-free investment. Buy the asset forFdollars, closing the long forw ...

14 Mathematics for Finance difference of $20 between the market price of stock and the strike price. In practice, the latter is ...

Introduction: A Simple Market Model 15 no matter whether the stock priceS(1) goes up to $120 or down to $80. This is known asr ...

16 Mathematics for Finance Proof Suppose thatC(0) + 114 A(0)>^12 S(0).If this is the case, then at time 0: Issue and sell 1 ...

Introduction: A Simple Market Model 17 arbitrage profit resulting from the risk-free investment of−C(0)− 114 A(0) + 1 2 S(0) p ...

18 Mathematics for Finance a call option with strike price $100 and exercise time 1 if a)A(1) = 105 dollars, b)A(1) = 115 dollar ...

Introduction: A Simple Market Model 19 1.7 Managing Risk with Options The availability of options and other derivative securit ...

20 Mathematics for Finance at time 0 borrow money to buy a call option with strike price $100; then, at time 1 repay the loan w ...

2. Risk-Free Assets............................................ 2.1 Time Value of Money It is a fact of life that $100 to be rec ...

22 Mathematics for Finance 2.1.1 Simple Interest..................................... Suppose that an amount is paid into a bank ...

Risk-Free Assets 23 Throughout this book the unit of time will be one year. We shall transform any period expressed in other u ...

24 Mathematics for Finance Exercise 2.4 Find the principal to be deposited initially in an account attracting sim- ple interest ...

Risk-Free Assets 25 just by the original deposit, but also by all the interest earned so far. In these circumstances we shall ...

26 Mathematics for Finance Figure 2.2 Annual compounding at 10% (m=1,r=0.1,P=1) Exercise 2.6 What is the interest rate if a depo ...

Risk-Free Assets 27 which can be verified directly using the binomial formula: ( 1+ r m )m =1+r+ 1 −m^1 2! r^2 +···+ ( 1 −m^1 ...

28 Mathematics for Finance Exercise 2.10 Find the present value of $100,000 to be received after 100 years if the interest rate ...

Risk-Free Assets 29 2.1.3 Streams of Payments Anannuity is a sequence of finitely many payments of a fixed amount due at equal ...