Financial calculus Introduction to Financial Option Valuation 10 ppt

... display real stock market data. 46 Asset price movement Jan Feb Mar Apr May Jun Jul Aug Sep 80 85 90 95 100 105 110 115 120 Price IBM daily Fig. 5.1. Daily IBM share price from January to September ... familiar to anybody who has seen stock market data displayed in graphical form. To examine this data, it is reasonable to treat it on the same level as the output from a pseudo-ran...

Ngày tải lên: 21/06/2014, 09:20

... given that no active market for options existed. But coincidentally, a month before the formula appeared, the Chicago Board Options Exchange had begun to list stock options for trading. Soon, Texas ... be able to transform this knowledge into money. Finance is consistent in its ability to build good models and consistent in its inability to make easy money. The purpose of the model is...

Ngày tải lên: 21/06/2014, 09:20

... value for the option – a value that can be recovered 105 10. 4 Black–Scholes PDE solution 101 As before, (10. 1) allows us to cancel terms, and we find that ρ = (T − t)Ee −r(T−t) N(d 2 ). (10. 4) Similar ... (10. 5) and vega = S √ T − tN  (d 1 ), (10. 6) see Exercises 10. 3 and 10. 4. 10. 3 Interpreting the Greeks It is possible to interpret some of the Greek formulas from a finan...

Ngày tải lên: 21/06/2014, 09:20

... := N(x) − 2 3 . 0 5 10 15 20 10 − 7 10 − 6 10 − 5 10 − 4 10 − 3 10 − 2 10 −1 10 0 10 1 Bisection Error Iteration 1 2 3 4 10 −12 10 10 10 − 8 10 − 6 10 − 4 10 −2 10 0 Newton Error Iteration Fig. ... possible, for exam- ple, to design a hybrid algorithm that uses a safe method, like bisection, until the iterates are close to an x  and then switches to New...

Ngày tải lên: 21/06/2014, 09:20

... from 10 1 10 2 10 3 10 4 10 5 10 6 10 −0.08 10 −0.06 10 −0.04 10 −0.02 10 0 10 0.02 Num samples Delta approximation Fig. 15.3. Monte Carlo approximations to time-zero delta of a European call option. ... Monte Carlo for Greeks 145 10 1 10 2 10 3 10 4 10 5 10 6 10 0.1 10 0.2 10 0.3 Num samples Option value approximation Fig. 15.2. Monte Carlo appr...

Ngày tải lên: 21/06/2014, 09:20

... confidence intervals for timesteps t of 10 −2 ,10 −3 and 10 −4 (so N = 10 2 ,10 3 and 10 4 ), and number of discrete sample paths M equal to 10 2 ,10 3 ,10 4 and 10 5 .Asthe theory predicts, increasing ... is 0.0983 t = 10 −2 t = 10 −3 t = 10 −4 M = 10 2 [0.0469, 0.1671] [0.0397, 0.1387] [0.0569, 0.1813] M = 10 3 [0.0961, 0.1347] [0.0756, 0. 1104 ] [0.0726,...

Ngày tải lên: 21/06/2014, 09:20

... σ  is computed in order to value an option, then a widely quoted rule of thumb is to make the historical data time-frame Mt equal to that of the option: to value an option that expires in six ... proportional to √ M. This makes it an expensive business to improve the approximation by taking more samples. To get an extra digit of accuracy, that is, to shrink a confidence i...

Ngày tải lên: 21/06/2014, 09:20

... a barrier option, plus ratios of their widths M Standard Control Variate Ratio of widths 10 2 [0.0283, 0.1161] [0.0885, 0 .101 0] 7.1 10 3 [0.0823, 0.1207] [0.0947, 0.0990] 8.9 10 4 [0.0911, 0 .103 5] ... price Asian option as a control variate in the basic formulation (22.1). We used M = 10 2 , 10 3 , 10 4 , 10 5 samples. We see that the control vari- ate improves accuracy b...

Ngày tải lên: 21/06/2014, 09:20

... finite differences to option valuation. We saw in Chapter 18 that the problem of valuing an American option can be couched in terms of a linear complementarity problem. It is possible to develop 24.2 ... U i j−1 h 2 = 0. It is convenient to write this as a process that goes from time level i to i + 1, that is, to increase the time index by 1, which allows the method to be wri...

Ngày tải lên: 20/06/2014, 18:20

... options. Working paper, University of Columbia, New York. Bass, Thomas A. (1999) The Predictors. London: Penguin. Baxter, Martin and Andrew Rennie (1996) Financial Calculus: An Introduction to Derivative ... (2002) Monte Carlo valuation of American options. Mathematical Finance, 12:271–286. Rogers, L. C. G. and E. J. Stapleton (1998) Fast accurate binomial pricing of options. Finance...

Ngày tải lên: 20/06/2014, 18:20