An Introduction to Financial Option Valuation: Mathematics, Stochastics and Computation 3 pptx

... 6.6 t Fig. 23. 7. BTCS solution on the heat equation ( 23. 2), ( 23. 3) and ( 23. 4) with initial and boundary conditions ( 23. 5). Here N x = 14 and N t = 9, so ν ≈ 6.6. The expansion ( 23. 14) shows that ... methods 0 5 10 15 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1 x FTCS: ν = 0 .3 t Fig. 23. 4. FTCS solution on the heat equation ( 23. 2), ( 23. 3) and ( 23. 4) with initial and boun...

Ngày tải lên: 20/06/2014, 18:20

... distribution, 22, 24, 28 up -and- in call, 190, 2 23 up -and- in put, 190 up -and- out call, 190, 194, 195, 197 up -and- out put, 190 variance, 24, 142 variance reduction, 1 43, 232 and hedging, 233 antithetic variates, ... 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) Saddle-point appr...

Ngày tải lên: 20/06/2014, 18:20

... 21 3. 1 Motivation 21 3. 2 Random variables, probability and mean 21 3. 3 Independence 23 3.4 Variance 24 3. 5 Normal distribution 25 3. 6 Central Limit Theorem 27 3. 7 Notes and references 28 3. 8 ... 234 23 Finite difference methods 237 23. 1 Motivation 237 23. 2 Finite difference operators 237 23. 3 Heat equation 238 23. 4 Discretization 239 23. 5 FTCS and BTCS 2...

Ngày tải lên: 20/06/2014, 18:20

... function of α X, for α ∈ R? Show that (3. 7) holds. 3. 3.  Using (3. 6) and (3. 7) show that (3. 10) and (3. 11) are equivalent and establish (3. 12). 3. 4.  A continuous random variable X with density function f ... 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...

Ngày tải lên: 20/06/2014, 18:20

... 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), ... yesterday and is expected to cost the young city trader involved his job. The deal amounted to 30 0m rather than £3m and flashed across stock market screens just as the stock mar...

Ngày tải lên: 20/06/2014, 18:20

... ability to build good models and consistent in its inability to make easy money. The purpose of the model is to understand the factors that influence and move option prices butinthe absence of an ability ... 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...

Ngày tải lên: 20/06/2014, 18:20

... 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 ... is to scale the option values by the asset price, by letting c := C S , for a call option, and p := P S , for a put option. In these new variables, d 1 and d 2 in (8.20) and (...

Ngày tải lên: 20/06/2014, 18:20

... 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 ... errors for M = 2 16 and M = 2 17 are 5 .31 × 10 3 and 3. 64 × 10 3 , respectively. The ratio of these errors is ≈ 1.5, which is close to the asymptotic (M →∞)value of √ 2....

Ngày tải lên: 20/06/2014, 18:20

... 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 ... Chapter 8 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 and...

Ngày tải lên: 20/06/2014, 18:20

... 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