An Introduction to Contemporary Mathematics

... An Introduction to the Mathematics of Money David Lovelock Marilou Mendel An Introduction to the Mathematics of Money Saving and Investing A Larry Wright David Lovelock Department of Mathematics ... refers to the third table in Chapter 1, and Problem 1.5 refers to the fifth problem in Chapter The symbol indicates the end of an example, and the...

Ngày tải lên: 28/06/2014, 21:20

... = 50 and Nt = 500, so k = × 10−3 and h = 0.2, we found that err0 = 1.5 × 10−3 for FTCS and err0 = 1.7 × 10−3 for BTCS With Crank– Nicolson we were able to reduce Nt to 50, so k = × 10−2 , and ... written in the matrix–vector forms (23.9) and (23.11), and the Crank–Nicolson method is given by (24.8) The τ = condition (19.2) specifies V j0 = max(B + j h − E, 0) and the left-han...

Ngày tải lên: 20/06/2014, 18:20

... American options Mathematical Finance, 12:271–286 Rogers, L C G and E J Stapleton (1998) Fast accurate binomial pricing of options Finance and Stochastics, 2:3–17 Rogers, L C G and O Zane (1999) ... Hodder & Stoughton Lo, Andrew W and Craig MacKinlay (1999) A Non-Random Walk Down Wall Street Princeton, NJ: Princeton University Press Longstaff, F A and E S Schwartz (2001) Valuing Am...

Ngày tải lên: 20/06/2014, 18:20

... intentionally left blank AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation This is a lively textbook providing a solid introduction to financial option valuation ... contributions to a broad range of problems in numerical analysis AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation D...

Ngày tải lên: 20/06/2014, 18:20

... rand and randn to generate U(0, 1) and N(0, 1) samples, respectively To make the experiments reproducible, we set the random number generator seed to 100; that is, we used rand(‘state’,100) and ... pseudo-random numbers Our justification for this omission is that random number generation is a highly advanced, active, research topic and it is unreasonable to expect non-experts...

Ngày tải lên: 20/06/2014, 18:20

... known to investors, and hence any change in the price is due to new information We may build this into our model by adding a random ‘fluctuation’ increment to the interest rate equation and making ... way to compute a quantile–quantile plot, as seen in Figures 4.4, 4.6 and 5.3 It is listed in Figure 5.4 We use MATLAB’s N(0, 1) pseudo-random number generator, randn The line sample...

Ngày tải lên: 20/06/2014, 18:20

... see (Rogers and Zane, 1999), for example A completely different approach is to abandon any attempt to understand the processes that drive asset prices (in particular to pay no heed to the efficient ... the company and has many insights into the practical issues involved in collecting and analysing vast amounts of financial data EXERCISES 7.1 7.2 Confirm the results (7.4) and (7.5...

Ngày tải lên: 20/06/2014, 18:20

... , S for a call option, p := P , S for a put option and In these new variables, d1 and d2 in (8.20) and (8.21) simplify to d1 = m τ + τ and d2 = m τ − , τ (11.1) and, from (8.19) and (8.24), the ... this portfolio to replicate the option (i.e to have payoff up when S(T ) = Sup and down when S(T ) = Sdown ) leads to a pair of linear equations for A and C Find and s...

Ngày tải lên: 20/06/2014, 18:20

... number, not a random variable, so p is either in I or outside it, and it is meaningless to speak of the probability of p lying in I (the Bayesians, on the other hand, consider p a random variable ... Notes and references There are many texts that discuss general Monte Carlo simulation A ‘golden oldie’ that is still highly relevant is (Hammersley and Handscombe, 1964), whilst a short...

Ngày tải lên: 20/06/2014, 18:20

... reach, and puts a strain on computational methods 18.2 American call and put An American option is like a European option except that the holder may exercise at any time between the start date and ... Chapter that led to the Black–Scholes PDE can be adapted to cover an American put option We write P Am (S, t) to denote the American put option value at asset price S an...

Ngày tải lên: 20/06/2014, 18:20