An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation 8 pptx
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_13 pot
... in the matrix–vector forms (23.9) and (23.11), and the Crank–Nicolson method is given by (24 .8) . The τ = 0 condition (19.2) specifies V 0 j = max(B + jh − E, 0) and the left-hand boundary condition ... boundary conditions C(0,τ) = 0andC(L,τ) = L. (24.4) Similarly, from (8. 26) and (8. 27) we obtain P(0,τ) = Ee −rτ and P(L,τ) = 0 (24.5) for a European put. We are now able to use a...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_14 pot
... G. and E. J. Stapleton (19 98) Fast accurate binomial pricing of options. Finance and Stochastics, 2:3–17. Rogers, L. C. G. and O. Zane (1999) Saddle-point approximations to option prices. Annals ... Index dividends, 49, 182 double barrier option, 191 down -and- in call, 188 , 189 down -and- in put, 190 down -and- out call, 187 – 189 , 260–261, 265 down -and- out put, 190 drift,...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_1 pot
... The MathWorks, Inc. AN INTRODUCTION TO FINANCIAL OPTION VALUATION Mathematics, Stochastics and Computation This is a lively textbook providing a solid introduction to financial option valuation for ... Upper and lower bounds on option values 14 2.7 Notes and references 16 2 .8 Program of Chapter 2 and walkthrough 17 3 Random variables 21 3.1 Motivation 21 3.2 R...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_3 pptx
... 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 ... samples from N(0, 1) and U(0, 1) random number generators. 3 Random variables OUTLINE • discrete and continuous random variables • expected value and variance • uniform and nor...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_4 ppt
... 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 samples = randn(M,1), ... 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 ran- dom ‘fluctuation’ increment to the interest rate...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_5 ppt
... formulas (8. 19) and (8. 24). 8. 7. Show that lim E→0 C(S, t) = S in (8. 19) and lim E→0 P(S, t) = 0in (8. 24), and give a financial interpretation of the results. 8. 8. Write down a PDE and final ... relation (8. 3). [Hint: use Exer- cise 3.7.] 8. 2. Show that (8. 21) can be replaced by (8. 22). 8. 3. Confirm that C(S, t) in (8. 19) satisfies (8. 16), (8. 17) and (8. 18...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_7 pdf
... problem and it is marvelously intuitive. MARK P. KRITZMAN (Kritzman, 2000) To put it simply, if there is an arbitrage price, any other price is too dangerous to quote. MARTIN BAXTER AND ANDREW ... S(T) = 0, and hence in (12.3) W(0, t) = e −r(T−t) (0). This matches (8. 17) and (8. 26) for the call and put, respectively. Finally, we note that the arguments given to justify (8...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_8 pptx
... a and variance var(X) = b 2 are not known. Suppose • we are interested in computing an approximation to a (and possibly b), and • we are able to take independent samples of X using a pseudo-random ... introduce another computational approach. The binomial method is straightforward to describe and implement, and, as we will see in Chapters 18 and 19, has the advantage that i...
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation_9 pot
... the Black–Scholes analysis, places analytic formulas out of reach, and puts a strain on computational methods. 18. 2 American call and put An American option is like a European option except that ... 18 American options OUTLINE • American call and put • equivalence of European and American call • Black–Scholes for American put • binomial method for American options • optimal ....
Ngày tải lên: 20/06/2014, 18:20
An Introduction to Financial Option Valuation Mathematics Stochastics and Computation_1 doc
... arguments to those above can be used to obtain simple upper and lower bounds on the values C and P of European call and put options. To study the call option, consider two portfolios: π A : one call option ... than π B at time 0 then it would be possible to sell π A (that is, sell the call option and borrow the cash) and buy π B (that is, buy one put option and one...
Ngày tải lên: 21/06/2014, 07:20